Index Page FRMDIFF User's Guide

## Table of Contents

       FRMDIFF User's Guide
          Abstract
          Summary
          If You Are in a Hurry
             To Check if Two CK Files Provide Identical Data
             To Assess Difference Between Two CK Files
             To Sample Quaternions from a CK File
             To Compute Transformation Between Two Frames
          Usage
          Options

       Inputs
          Kernel Files
             Primary Kernel Files
             Additional Kernel Files
          Comparison Runs vs. Sampling Runs
          Runs with Two, One, and No Primary Kernel File(s)
             Runs with Two Primary Kernel Files
             Runs with One Primary Kernel File
             Runs Without Primary Kernel Files
          ``From'', ``To'', and ``Coverage'' Frames
             ``From'' Frames
             ``To'' Frames
             ``Coverage'' Frames
          Times for Comparison/Sampling
             Coverage Window
             Times within Coverage Window
          Angular Velocities

       Output
          Overview of Report Types
             Time Tag Format for ``dump*'' Reports
             Numeric Format for ``dump*'' Reports
             Angle Units for ``dumpaa'' and ``dumpea'' Reports
          Report Header
             Report Header for Comparing Two Orientations
             Report Header for Coverage/Gaps for Two Orientations
             Report Header for Sampling an Orientation
             Report Header for Coverage/Gaps for An Orientation
          Report Formats
             Basic Report (no ``-t'' or ``-t basic'')
             Statistics Report (``-t stats'')
             Angle and Axis Dump Report (``-t dumpaa'')
             Matrix Dump Report (``-t dumpm'')
             SPICE-Style Quaternion Dump Report (``-t dumpqs'')
             ``Other''-Style Quaternion Dump Report (``-t dumpqo'')
             Euler Angles Dump Report (``-t dumpea'')
             Coverage Intervals Dump Report (``-t dumpc''):
             Coverage Gaps Dump Report (``-t dumpg'')

       Examples
          Checking if Two CKs Provide the Same Orientation
          Comparing Predicted and Reconstructed CKs
          Comparing Orientations from a CK Read Using Different SCLKs
          Comparing Binary and Text PCKs
          Comparing Two Text PCKs
          Sampling Orientation from a CK
          Sampling Orientation of a Built-in Frame
          Sampling Orientation of a Dynamic Frame
          Sampling Orientation With Two Different ``Coverage'' Frames
          Displaying Overlap in Coverage between Two CKs
          Displaying Gaps in a CK File

       Miscellaneous Things to Consider
          ``Apples vs. Oranges''
          Using Euler Angles for Small Rotation Differences
          Single Epoch

       References

       Acronyms

       Appendix 1: Comparison, Sampling and Report Quantity Algorithms
          Computing Rotation and Angular Velocity Difference
          Sampling Rotation and Angular Velocity
          Converting Rotation to Angle/Axis
          Converting Rotation to SPICE-Style Quaternion
          Converting Rotation to ``Other''-Style quaternion
          Converting Rotation to Euler Angles

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# FRMDIFF User's Guide

Last revised on 2014 JAN 21 by B. V. Semenov.

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## Abstract

FRMDIFF is a program that samples orientation of a reference frame known to SPICE or computes differences between orientations of two reference frames known to SPICE, and either displays this orientation or these differences, or shows statistics about it or them.

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## Summary

FRMDIFF provides means for sampling orientation of a single reference frame, or for comparing orientations of two reference frames known to SPICE and supported by data from SPICE kernels.

To sample orientation of a single frame the program computes a set of transformations from one frame (the ``from'' frame) to another frame (the ``to'' frame) over an interval of time with fixed or variable time step, using a given set of kernel files. Then, depending on the requested type of output report, it prints to the screen a table containing these transformations expressed as total rotation angles and axes, quaternions, matrices or Euler angles and angular velocities, or only magnitude of the maximum rotation and angular velocity, or results of a simple statistical analysis of rotations.

To compare orientations of two frames the program computes a set of transformations from one frame (the ``from'' frame) to another frame (the ``to'' frame) over an interval of time with a fixed or variable time step using one set of kernels, computes a set of transformations for the same or a different ``from''-``to'' frame combination at the same times using the same or a different set of kernels, and then computes the difference in rotation and angular velocity between the corresponding transformations. Depending on the requested type of output report the program prints to the screen only maximum differences in rotation and angular velocity, or a complete table of rotation and angular velocity differences expressed as total rotation angles and axes, matrices, quaternions, or Euler angles, or results of a simple statistical analysis of the rotation differences.

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## If You Are in a Hurry

This section shows four very common FRMDIFF usage scenarios with just enough explanations to get you going. An extensive set of detailed examples is provided at the end of this User's Guide.

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### To Check if Two CK Files Provide Identical Data

To check if two CK files containing orientation for the same structure with respect to the same reference frame provide identical data, run FRMDIFF as follows:

       % frmdiff -k <lsk> <sclk> <fk> -s <step> <ck1> <ck2>

where ``<lsk>'', ``<sclk>'', ``<fk>'', ``<ck1>'' and ``<ck2>'' are the names of LSK, SCLK, FK, and two CK files (all five are required), and ``step'' is the time step, in seconds. If the maximum rotation angle in the output is zero (or close to zero, accounting for round off), then the CKs contain the same data. To include angular velocities in comparison, add ``-a yes'' before ``-s'', like this:

       % frmdiff -k <lsk> <sclk> <fk> -a yes -s <step> <ck1> <ck2>

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### To Assess Difference Between Two CK Files

To assess the difference between two CK files containing orientation for the same structure with respect to the same reference frame as a function of time, run FRMDIFF as follows:

       % frmdiff -k <lsk> <sclk> <fk> -t dumpaa -s <step> <ck1> <ck2>

where ``<lsk>'', ``<sclk>'', ``<fk>'', ``<ck1>'' and ``<ck2>'' are the names of LSK, SCLK, FK, and two CK files (all five are required); ``-t dumpaa'' sets the output format to the rotation angle and axis dump; and ``step'' is the time step, in seconds. The program's output, which can be rather lengthy, can be re-directed to a file using the ``>'' pipe. Using the data captured in the file the total rotation angle (column 2) can be plotted against TDB seconds (column 1) to analyze the difference. To print output time tags as UTC in ISO date format instead of TDB seconds, add

       -f 'YYYY-MM-DDTHR:MN:SC.### ::RND'

before ``-k''. To use the Euler angle dump output instead of the rotation angle and axis dump output, replace ``dumpaa'' with ``dumpea''. To include angular velocities in the comparison, add ``-a yes'' before ``-s'', like this (the command line below is wrapped to fit the page width):

       % frmdiff -k <lsk> <sclk> <fk> -t dumpaa -a yes -s <step>
                 <ck1> <ck2>

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### To Sample Quaternions from a CK File

To sample orientation provided in a CK file and print it as SPICE-style quaternions, run FRMDIFF as follows:

       % frmdiff -k <lsk> <sclk> <fk> -t dumpqs -s <step> <ck>

where ``<lsk>'', ``<sclk>'', ``<fk>'', and ``<ck>'' are the names of LSK, SCLK, FK, and CK files (all four are required); ``-t dumpqs'' sets the output format to the SPICE-style quaternion dump; and ``step'' is the time step, in seconds. The program's output can be re-directed to a file using the ``>'' pipe. To print output time tags as UTC in ISO date format, add

       -f 'YYYY-MM-DDTHR:MN:SC.### ::RND'

before ``-k''. To use the ``other''-style quaternion dump instead of the SPICE-style quaternion dump, replace ``dumpqs'' with ``dumpqo''. To include angular velocities, add ``-a yes'' before ``-s''; to print angular velocities in the structure frame rather than the base frame, also add ``-m to'', like this (the command line below is wrapped to fit the page width):

       % frmdiff -k <lsk> <sclk> <fk> -t dumpqo -a yes -m to
                 -s <step> <ck>

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### To Compute Transformation Between Two Frames

To compute transformation from one frame known to SPICE to another frame known to SPICE and display this transformation as Euler angles, run FRMDIFF as follows (the command line below is wrapped to fit the page width):

       % frmdiff -k <kernels> -t dumpea
                 -b <begintime> -e <endtime> -s <step>
                 -f1 <from_frame> -t1 <to_frame>

where ``<kernels>'' are the names of kernel files needed to compute the transformation (an LSK must be included); ``-t dumpea'' sets the output format to the Euler angles dump; ``<begintime>'' and ``<endtime>'' set the begin and end time, as UTC, for the period of interest; ``step'' is the time step, in seconds; and ``<from_frame>'' and ``<to_frame>'' are the names of the frames from which and to which the transformation can be computed. For lengthy reports the program's output should be re-directed to a file using the ``>'' pipe.

Note that if the ``<to_frame>'' is a CK-based (Class 3) or PCK-based (Class 2) frame, the list of kernels (``<kernels>'') includes CKs or binary PCKs providing data for that frame, and ``-b <begintime> -e <endtime>'' are omitted, the program will automatically determine the ``<to_frame>''s data availability time window and will compute transformations with specified step over that whole window.

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## Usage

FRMDIFF is a command line program with the following usage:

       % frmdiff [options] <first kernel> <second kernel>
       % frmdiff [options] <kernel>
       % frmdiff [options]

where either of the kernels can be a CK, a PCK, an FK, or any other SPICE kernel. The options are:

       -k  <supporting kernel(s) name(s)>
       -f1 <first ``from'' frame, name or ID>
       -t1 <first ``to'' frame, name or ID>
       -c1 <first frame for coverage look up, name or ID>
       -k1 <additional supporting kernel(s) for first file>
       -f2 <second ``from'' frame, name or ID>
       -t2 <second ``to'' frame, name or ID>
       -c2 <second frame for coverage look up, name or ID>
       -k2 <additional supporting kernel(s) for second file>
       -a  <compare angular velocities, yes|no (default: no)>
       -m  <frame for angular velocities, from|to (default: from)
       -b  <interval start time>
       -e  <interval stop time>
       -n  <number of points: 1 to 1000000 (default: 1000)>
       -s  <time step in seconds>
       -f  <time format, et|sclk|sclkd|ticks|picture_for_TIMOUT>
           (default: et)>
       -t  <report: basic|stats|dumpaa|dumpm|dumpqs|dumpqo|dumpea
           |dumpc|dumpg>
       -o  <rotation axes order (default: z y x)>
       -x  <units for output angles>
       -d  <number of significant digits: 6 to 17 (default: 14)>

The order of options and case of the option keys are not significant. The values provided after the option keys must be separated from keys by one or more spaces. Un-recognized options are not specifically checked for; instead they are treated as continuation of the value provided using the preceding recognized option.

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## Options

Kernel file names and control parameters are provided to the program using the following command line options (only a brief description of each option is given in the list below; details, defaults, and dependencies are discussed later in this document):

<first kernel>
  is the name of the first primary kernel. When two primary kernels are provided to the program this name must be the second to last item on the command line.

<second kernel>
  is the name of the second primary kernel. When two primary kernels are provided to the program this name must be the last item on the command line.

<kernel>
  is the name of the only primary kernel. When only one primary kernel is provided to the program this name must be the last item on the command line.

-k <kernels>
  is used to specify the list of additional kernels that should be used for both frame transformations to be computed. Kernel names following ``-k'' must be separated by spaces.

-f1 <frame>
  is used to specify the ``from'' frame for the first (or only) frame transformation to be computed. This frame must be known to SPICE and can be specified using the frame name, ID, or class ID.

-t1 <frame>
  is used to specify the ``to'' frame for the first (or only) frame transformation to be computed. This frame must be known to SPICE and can be specified using the frame name, ID, or class ID.

-c1 <frame>
  is used to specify the ``coverage'' frame to be used to look up the first coverage window. This frame must be known to SPICE and must be either a PCK-based (Class 2) or CK-based (Class 3) frame. It can be specified using the frame name, frame ID, or, if the first (or only) primary kernel is a CK or a binary PCK, class ID. If the first (or only) primary kernel file is a CK or a binary PCK, it must contain data for this frame.

-k1 <kernels>
  is used to specify the list of additional kernels that should be used only for the first frame transformation to be computed. Kernel names following ``-k1'' must be separated by spaces.

-f2 <frame>
  is used to specify the ``from'' frame for the second (or only) frame transformation to be computed. This frame must be known to SPICE and can be specified using the frame name, ID, or class ID.

-t2 <frame>
  is used to specify the ``to'' frame for the second (or only) frame transformation to be computed. This frame must be known to SPICE and can be specified using the name, ID, or class ID.

-c2 <frame>
  is used to specify the ``coverage'' frame to be used to look up the second coverage window. This frame must be known to SPICE and must be either a PCK-based (Class 2) or CK-based (Class 3) frame. It can be specified using the frame name, frame ID, or, if the second (or only) primary kernel is a CK or a binary PCK, class ID. If the second (or only) primary kernel file is a CK or a binary PCK, it must contain data for this frame.

-k2 <kernels>
  is used to specify the list of additional kernels that should be used only for the second frame transformation to be computed. Kernel names following ``-k2'' must be separated by spaces.

-b <time>
  is used to specify the coverage window begin time. This option must be provided when no primary kernels and ``coverage'' frames are specified. The time string provided using this option can be in any form accepted by SPICE's str2et_c function.

-e <time>
  is used to specify the coverage window end time. This option must be provided when no primary kernels and ``coverage'' frames are specified. The time string provided using this option can be in any form accepted by SPICE's str2et_c function.

-n <number>
  is used to specify the number of points within the coverage window, for which the frame transformation(s) must be computed. The number must be an integer between 1 and 1,000,000. The default value is 1000.

-s <step>
  is used to specify the step, in seconds, for determining points within the coverage window, for which the frame transformation(s) must be computed. The step must be greater than 1E-8. This option supersedes ``-n''.

-t <report_type>
  is used specify the type of report that the program should display:

                                 basic   to display only the maximum
                                         rotation angle and angular
                                         velocity (AV) magnitude (default)

                                 stats   to display statistics on rotation
                                         angles and AVs

                                 dumpaa  to display a table of rotation
                                         angles and axes

                                 dumpm   to display a table of matrices

                                 dumpqs  to display a table of SPICE-style
                                         quaternions

                                 dumpqo  to display a table of ``other''-
                                         style quaternions

                                 dumpea  to display a table of Euler angles

                                 dumpc   to display a table of coverage
                                         intervals

                                 dumpg   to display a table of coverage
                                         gaps

-a <av_flag>
  is used to tell the program whether angular velocities should be computed along with rotations:

                                 no      to compute only rotations
                                         (default)

                                 yes     to compute rotations and
                                         angular velocities

-m <av_frame>
  is used to tell the program in which frame angular velocities should be reported:

                                 from    to output angular velocities in
                                         ``from'' frame (default)

                                 to      to output angular velocities in
                                         ``to'' frame

-f <time_type>
  is used to specify the type of time tag to be used in tabular reports (``-t'' with ``dumpm'', ``dumpqs'', ``dumpqo'', ``dumpea'', ``dumpc'', or ``dumpg''):

                                 et      to display times as TDB seconds
                                         past J2000 (default)

                                 sclk    to display times as string SCLKs

                                 sclkd   to display times as decimal SCLKs

                                 ticks   to display times as encoded SCLK
                                         ticks

                                 <PICT>  any time format picture accepted
                                         by the @TIMOUT @routine (for
                                         example ``YYYY-MM-DDTHR:MN:SC.###
                                         ::RND'' for time tags for be
                                         displayed as UTCs in ISO date
                                         format)

-o <axes>
  is used to specify the list of axes determining the order of rotations used for converting rotation matrices to Euler angles. The value must be a space-delimited list of three axes from the set of ``X'', ``Y'', ``Z'' (case-insensitive). The second axis must differ from the first and third axes. The default order is ``Z Y X''.

-x <units>
  is used to specify the units for the angles in the rotation angle and axis dump (``-t dumpaa'') and Euler angle dump (``-t dumpea'') reports; ignored for all other report types. Supported units are:

                                 radians (default)
                                 degrees
                                 arcminutes
                                 arcseconds
                                 hourangle
                                 minuteangle
                                 secondangle

-d <number>
  is used to specify the number of significant digits in the output numeric times (TDB seconds past J2000, decimal SCLKs and encoded SCLK ticks) and rotation component values or rotation difference component values included in the dump, coverage and coverage gap reports. The number must be an integer between 6 and 17. The default value is 14.

-v
  causes the program to display only the version line. This option overrides all other options.

-u
  causes the program to display the usage message. This option overrides all other options except ``-v''.

-h
  causes the program to display a brief help message. This option overrides all other options except ``-v'' and ``-u''.

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# Inputs

For a successful run the program must be supplied with kernel files providing sufficient data to compute the frame transformation(s) of interest, and with control parameters clearly specifying, together with default values determined from the kernels, what transformations should be computed and at what times. Both the kernels and the control parameters are provided to the program using command line options.

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## Kernel Files

In most cases one or more kernel files must be provided to the program to perform comparison or sampling of frame orientations. Depending on how the kernel files are provided, they fall into one of two categories -- primary kernel files and additional kernel files.

Primary kernel files -- two, one, or none -- are provided at the end of the command line without any command line keys. Normally these kernel files contain orientations that differ (for example, predicted and reconstructed CKs for the same frame and time period, two versions of an FK with different alignment data for the same frame, etc.), or contain orientation to be sampled. These kernel files are also examined by the program to determine the default values for the ``from'', ``to'', and ``cov'' frames, and to determine the coverage window boundaries. Note that becasue the program slightly contracts coverage windows determined from CK files to compensate for roundoff occuring in SCLK to ET time conversions, in general FRMDIFF cannot be used to sample or compare CKs with discrete data, e.g. Type 1 CKs or Type 3 CKs with singleton intervals. For additional discussion of this limitation see the ``Coverage Window'' section below.

Additional kernel files -- none, or as many as needed -- are provided anywhere on the command line (except at the very end) using the ``-k'', ``-k1'', and ``-k2'' keys. Normally these kernel files contain additional SPICE data needed to compute requested orientations (for example, LSK and SCLK files providing supporting time conversion data, FK files providing frame definitions needed by SPICE to recognize specified frames, etc).

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### Primary Kernel Files

The primary kernels can be of any type -- CK, PCK, FK, SCLK, LSK or even SPK -- and are provided as the last or the last two items on the command line. Since the primary kernel files do not require specific command line keys, the program determines if they were given by examining the last two words on the command line as follows:

`--` If the last word on the command line is not the name of an existing file, the program assumes that no primary kernel files were given.

`--` If the last word on the command line is the name of an existing file but the second to last word is not, the program assumes that only one primary kernel was given.

`--` If both last two words are names of existing files, the program assumes that it was given two primary kernel files

Due to the parsing approach described above, misspelling a primary kernel name leads to the program deciding that it either runs with no primary kernel files (if the last file name is misspelled) or that it runs with one primary kernel instead of two (if the second to last file name is misspelled). In either case, the misspelled file name(s) is(are) treated as a part of the value of the command line option immediately preceding it(them) causing the program to signal an error indicating an incorrect option value.

On the other hand, if any of the options for specifying additional kernel files (``-k'', ``-k1'', ``-k2'') followed by actual files names is provided at the end of the command line (for the case of no primary kernels) or immediately preceding the only primary file (for one primary kernel case), the last one or the last two additional kernels are mistakenly picked as the primary kernel(s). In this situation the program usually signals an error indicating that orientation could not be computed because insufficient data was loaded.

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### Additional Kernel Files

As for primary kernels, additional kernels can also be of any type -- CK, PCK, FK, SCLK, LSK or even SPK. Unlike primary kernels, additional kernels are specified using the dedicated ``-k'', ``-k1'', and ``-k2'' keys. Any number of additional kernels can be provided using any of the three keys, with kernel file names listed in any order, separated by blanks. While in some rare cases no additional kernel files are required, in most cases at least an LSK file and an SCLK file containing time correlation data and an FK file containing frame definitions should be specified using these keys. The additional kernels are used by the program as follows:

`--` All additional kernel files provided using the ``-k'' are loaded and used for both ``from''-``to'' frame combinations.

`--` All additional kernel files provided using ``-k1'' are loaded and used only for the first ``from''-``to'' frame combination.

`--` All additional kernel files provided using ``-k2'' are loaded and used only for the second ``from''-``to'' frame combination.

Neither the combined set of additional kernel files given using ``-k''/``-k1'' nor the combined set of additional kernel files given using ``-k''/``-k2'' can contain enough data to compute corresponding orientations at any time in the time buffer without loading the corresponding primary file(s). If they do, the program signals an error. The two exceptions from this requirement are:

`--` when no primary kernel files are specified the additional kernel files given using ``-k''/``-k1'' and ``-k''/``-k2'' should contain enough data to compute the corresponding orientations

`--` when both ``from'' and ``to'' frames in one or both``from''-``to'' frame pairs are built-in frames, the check for inability to compute orientations without loading primary kernel files is skipped

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## Comparison Runs vs. Sampling Runs

The program automatically decides whether it should compare two orientations or sample one orientation, based on the primary kernels provided at the end of the command line, additional kernel files provided using the ``-k1'' and ``-k2'' keys, and on the ``from'' and ``to'' frames specified on the command line using the ``-f1'', ``-t1'', ``-f2'', and ``-t2'' keys and/or determined from the primary kernel data.

To run the program in comparison mode, it is enough to satisfy any of the following guidelines for specifying inputs that tell the program to compute two different orientations:

`--` provide two different primary kernels

`--` provide two different sets of orientation-specific additional kernels using ``-k1'' and ``-k2''

`--` specify two different ``from'' frames using ``-f1'' and ``-f2''

`--` specify two different ``to'' frames using ``-t1'' and ``-t2''

To run the program in sampling mode, it is required to satisfy all of the following guidelines telling the program to compute a single orientation:

`--` provide only one primary kernel or no primary kernels

`--` provide no orientation-specific additional kernels using ``-k1'' and ``-k2''

`--` specify only one ``from'' frame using either ``-f1'' or ``-f2'' or no ``from'' frames

`--` specify only one ``to'' frame using either ``-t1'' or ``-t2'' or no ``to'' frames

There are only two cases when the program runs in sampling mode after being given two primary kernels and/or two orientation-specific additional kernel sets. These cases are:

`--` When run with two primary kernel files, the program samples orientation only if these kernel files are the same file and additional kernel files provided using the ``-k1''/``-k2'' keys are the same files listed the same order and ``from'' frames provided using the ``-f1''/``-f2'' keys or determined automatically are the same and ``to'' frames provided using the ``-t1''/``-t2'' keys or determined automatically are the same.

`--` When run with one primary kernel file or no primary kernel files but with some orientation-specific additional kernels, the program will sample orientation only if additional kernel files provided using the ``-k1''/``-k2'' keys are the same files listed in the same order and the ``from'' frames provided using the ``-f1''/``-f2'' keys or determined automatically are the same frames and the ``to'' frames provided using the ``-t1''/``-t2'' keys or determined automatically are the same frames.

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## Runs with Two, One, and No Primary Kernel File(s)

The number and types of primary kernel files and the mode in which the program is run (``comparing'' vs. ``sampling'') directly affect the requirements in regards to which command line options must be provided, approaches for determining default values for omitted options, and ways in which kernels are loaded and orientations are computed. The three subsections below discuss specifics of runs with two, one, and no primary kernel files.

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### Runs with Two Primary Kernel Files

When two primary kernel files are provided on the command line:

`--` All ``-*1'' and ``-*2'' options, and ``-b'' and ``-e'' options can be omitted if one of the primary files (or both primary files) are a CK or a binary PCK, for which defaults for these options can be picked from the file(s).

`--` ``-f1'' or ``-f2'' or both, ``-t1'' or ``-t2'' or both, and sufficient coverage information (e.g. a sufficient combination of ``-b'', ``-e'', ``-c1'', and ``-c2'') must be specified if neither of the primary files is a CK or binary PCK because the program has no way of picking defaults for the ``from'' frame(s), ``to'' frame(s), and time boundaries for any other types of primary kernels.

`--` If the program is run in comparison mode, the first primary file and the additional kernel files given using ``-k'' and ``-k1'' are loaded and orientations for the first default/specified ``from''-``to'' frame combination are computed at times within the default/specified time window, then the second primary file and the additional kernel files given using ``-k'' and ``-k2'' are loaded and orientations for the second default/specified ``from''-``to'' frame combination are computed at the same times within the default/specified time window, then the differences between the corresponding orientations are computed and printed in the specified format.

`--` If the program is run in sampling mode, the first primary file and the additional kernel files given using ``-k'' and ``-k1'' are loaded and orientations for the first default/specified ``from''-``to'' frame combination are computed at times within the default/specified time window and printed in the specified format.

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### Runs with One Primary Kernel File

When one primary kernel file is provided on the command line:

`--` All ``-*1'' and ``-*2'' options, and ``-b'' and ``-e'' options can be omitted if the primary file is a CK or a binary PCK, for which defaults for these options can be picked from the file.

`--` ``-f1'' or ``-f2'' or both, ``-t1'' or ``-t2'' or both, and sufficient coverage information (e.g. a sufficient combination of ``-b'', ``-e'', ``-c1'', and ``-c2'') must be specified if the primary file is not a CK or a binary PCK because the program has no way of picking defaults for the ``from'' frame(s), ``to'' frame(s) and time boundaries for any other types of primary kernels.

`--` If the program is run in comparison mode, the primary file and the additional kernel files given using ``-k'' and ``-k1'' are loaded and orientations for the first ``from''-``to'' frame combination are computed at times within the default/specified time window, then the primary file and the additional kernel files given using ``-k'' and ``-k2'' are loaded and orientations for the second ``from''-``to'' frame combination are computed at the same times within the default/specified time window, then the differences between corresponding orientations are computed and printed in the specified format.

`--` If the program is run in sampling mode, the primary file and the additional kernel files given using ``-k'' and ``-k1'' are loaded and orientations for the first ``from''-``to'' frame combination are computed at times within the default/specified time window and then printed in the specified format.

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### Runs Without Primary Kernel Files

When no primary kernel files are specified on the command line:

`--` ``-f1'' or ``-f2'' or both, ``-t1'' or ``-t2'' or both, and sufficient coverage information (e.g. a sufficient combination of ``-b'', ``-e'', ``-c1'', and ``-c2'') must be specified because the program has no way of picking defaults for the ``from'' frame(s), ``to'' frame(s), and time boundaries when it is not given any primary kernel(s) to examine.

`--` If the program is run in comparison mode, the additional kernel files given using ``-k'' and ``-k1'' are loaded and orientations for the first ``from''-``to'' frame combination are computed at times within the default/specified time window, then the additional kernel files given using ``-k'' and ``-k2'' are loaded and orientations for the second ``from''-``to'' frame combination are computed at the same times within the default/specified time window, then the differences between corresponding orientations are computed and printed in the specified format.

`--` If the program is run in sampling mode, the additional kernel files given using ``-k'' and ``-k1'' are loaded and orientations for the first ``from''-``to'' frame combination are computed at times within the default/specified time window and then printed in the specified format.

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## ``From'', ``To'', and ``Coverage'' Frames

The program has six command line keys -- ``-f1'', ``-t1'', ``-c1'', ``-f2'', ``-t2'', and ``-c2'' -- to specify frames to be used to compute rotations (``-f*'' and ``-t*'' keys) and to determine coverage from primary or additional CK or binary PCK files (``-c*'' keys). A single frame can be specified using each of these keys using the frame name, frame ID, or frame class ID (only for runs with primary kernel files that are CKs or binary PCKs).

Whether the frame is specified by the name, ID, or class ID, it must be known to SPICE, i.e. it must either be a built-in frame or one of the frames defined in the FK file(s) provided as primary or additional kernels. If the frame name, ID, or class ID specified on the command line or picked from the primary file is not recognized after loading the kernel files provided using ``-k''/``-k1'' and the first primary file for the ``-*1'' frames, or provided using ``-k''/``-k2'' and the second primary file for the ``-*2'' frames, the program signals an error.

Not all six frames have to be specified for every program run. In fact in many cases only one, two, or even no frames can be given and the program will set the rest to default values based on the other frames that are provided and/or by examining the primary kernel files. The three subsections below discuss specifying and picking defaults for the ``from'', ``to'', and ``coverage'' frames.

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### ``From'' Frames

The following rules apply to specifying and picking defaults for the ``from'' frames:

`--` If both ``-f1'' and ``-f2'' are specified, orientations are computed with respect to these ``from'' frames.

`--` If only ``-f1'' or only ``-f2'' is specified, the specified ``from'' frame is used for both ``from'' frames.

`--` If neither ``-f1'' nor ``-f2'' is specified and only one of the primary kernel files is a CK or a binary PCK, the ``from'' frame from the last segment of this CK or PCK file is used for both ``from'' frames.

`--` If neither ``-f1'' nor ``-f2'' is specified and both primary kernel files are CKs or binary PCKs, the ``from'' frame from the last segment of the first primary CK or PCK file is used for both ``from'' frames.

`--` If neither ``-f1'' nor ``-f2'' is specified and no primary files are given or neither of the primary files is a CK or binary PCK, the program signals an error.

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### ``To'' Frames

The following rules apply to specifying and picking defaults for the ``to'' frames:

`--` If ``-t1'' and ``-t2'' are specified, orientations are computed for these ``to'' frames.

`--` If only ``-t1'' or only ``-t2'' is specified, the specified ``to'' frame is used for both ``to'' frames.

`--` If neither ``-t1'' nor ``-t2'' is specified and only one of the primary kernel files is a CK or a binary PCK, the frame from the last segment of this CK or PCK is used for both ``to'' frames.

`--` If neither ``-t1'' nor ``-t2'' is specified and both primary kernel files are CKs or binary PCKs, the frame from the last segment of the first CK or PCK is used for both ``to'' frames.

`--` If neither ``-t1'' nor ``-t2'' is specified and no primary files are given or neither of the primary files is a CK or binary PCK, the program signals an error.

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### ``Coverage'' Frames

The following rules apply to specifying and picking defaults for the ``coverage'' frames:

`--` Only PCK-based (Class 2) or CK-based (Class 3) frames can be specified using ``-c1'' and ``-c2''. Specifying frames of any other class using these keys is an error.

`--` If ``-c1'' is not specified and the first ``to'' frame is a PCK-based (Class 2) or CK-based (Class 3) specified using ``-t1'' or picked by default, the first ``coverage'' frame is set to the first ``to'' frame. Similarly, if ``-c2'' is not specified and the second ``to'' frame is a PCK-based (Class 2) or CK-based (Class 3) specified using ``-t2'' or picked by default, the second ``coverage'' frame is set to the second ``to'' frame.

`--` If ``-c1'' is specified or set by default to the first ``to'' frame, and the first (or only) primary kernel is a CK or binary PCK file containing data for this frame, then this frame is used to look up the first coverage window from this primary file. Similarly, if ``-c2'' is specified or set by default to the second ``to'' frame, and the second (or only) primary kernel is a CK or binary PCK file containing data for this frame, then this frame is used to look up the second coverage window from this primary file.

`--` If ``-c1'' is specified and the first (or only) primary kernel is a CK or binary PCK file that does not contains data for this frame, then the program signals an error. Similarly, if ``-c2'' is specified and the second (or only) primary kernel is a CK or binary PCK file that does not contains data for this frame, then the program signals an error.

`--` If ``-c1'' is set by default to the first ``to'' frame and the first (or only) primary kernel is a CK or binary PCK file that does not contains data for this frame, then the program does not attempt to determine the first coverage window for this frame based on the primary or additional kernels. Similarly, if ``-c2'' is set by default to the second ``to'' frame and the second (or only) primary kernel is a CK or binary PCK file that does not contains data for this frame, then the program does not attempt to determine the second coverage window for this frame based on the primary or additional kernels.

`--` If ``-c1'' is specified or set by default to the first ``to'' frame, and the first (or only) primary kernel is not a CK or binary PCK file, then this frame is used to look up the first coverage window from the kernels specified using ``-k'' and ``-k1''. Similarly, if ``-c2'' is specified or set by default to the second ``to'' frame, and the second (or only) primary kernel is not a CK or binary PCK file, then this frame is used to look up the second coverage window from the kernels specified using ``-k'' and ``-k2''.

`--` If ``-c1'' is specified or set by default to the first ``to'' frame and no primary kernels are given, then this frame is used to look up the first coverage window from the kernels specified using ``-k'' and ``-k1''. Similarly, if ``-c2'' is specified or set by default to the second ``to'' frame, and no primary kernels are given, then this frame is used to look up the second coverage window from the kernels specified using ``-k'' and ``-k2''.

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## Times for Comparison/Sampling

The program picks times at which orientation(s) are computed based on the coverage window determined by examining the primary or additional files(s) and/or specified using the ``-b'' and ``-e'' keys, and on either the number of points within that window specified using the ``-n'' key or the time step specified using the ``-s'' key''.

The coverage window begin and end times specified using the ``-b'' and ``-e'' options can be in any format accepted by SPICE's str2et_c function (see str2et_c header for details). If one or both of these times are provided, an LSK file must be provided as one of the additional or primary kernels.

The number of points specified using the ``-n'' key must be an integer between 1 to 1,000,000 while the step specified using the ``-s'' key must be in seconds and be greater than 1.0E-8. If both ``-n'' and ``-s'' are specified, ``-s'' takes precedence.

The coverage window determined by examining the primary or additional kernels -- especially if these kernels are CK files, which frequently have gaps in coverage -- may consist of many intervals, some of which may be singletons (with the interval begin time equal to the interval end time). Whether the coverage window consists of only one interval or of many intervals, the program computes times within the window in such a way that the interval ends are always included in the set of points. The rest of times are distributed within the intervals, stepping from the beginning of each interval with the specified step. If the number of points is given instead of the step, the step is computed using the measure of the coverage window (the sum of the lengths of the individual intervals) and the specified number of points.

Not all of the keys controlling selection of points have to be specified for every program run. In some cases none of these options are required; in the other cases ``-b'', ``-e'', ``-c1'', and/or ``-c2'' must be specified. The two subsections below discuss specifics of providing and picking defaults for the coverage window and step or number of points.

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### Coverage Window

The program determines the coverage window either by examining the primary or additional kernels (resulting in the ``default coverage window''), or by using the begin and end times specified using the ``-b'' and ``-e'' keys, or as a combination of both.

The default coverage window can be determined only from the primary or additional kernel files that are binary PCK files (using SPICE's pckcov_c function) or CK files (using SPICE's ckcov_c function) and only if these kernels contain data for the ``coverage'' frames either specified using the ``-c1''/``-c2'' keys or set to default values as described earlier in this document. When both ``coverage'' frames are specified or set to default values, the program determines the frame-specific coverage window for each of them using the corresponding primary or additional kernels and sets the default coverage window to the intersection of these two frame-specific coverage windows. When only one ``coverage'' frame is specified or set to the default value, the program determines the frame-specific coverage window for that frame using corresponding primary or additional kernels and sets the default coverage window to that frame-specific coverage window.

In cases when a frame-specific coverage window is obtained from the corresponding primary kernel, the program examines only that primary kernel to construct the desired frame-specific coverage window. In cases when a frame-specific coverage window is obtained from additional kernels, the program examines all kernels of a particular type -- all CKs if the ``coverage'' frame is a CK-based frame or all binary PCKs if the ``coverage'' frame is a PCK-based frame -- listed explicitly with the ``-k''/``-k1'' or ``-k''/``-k2'' keys or included in meta-kernels provided with these keys and constructs the frame-specific coverage window as the union of coverages obtained from individual additional kernels.

When the program determines the coverage window for a CK file it slightly contracts the actual coverage window given by the CK data to compensate for roundoff occuring in SCLK-ET time conversions. The contraction is done by adjusting inward the window interval boundary times by three times the amout of maximum roundoff that was determined by converting all boundary times from SCLK to ET then back to SCLK. This adjustment is done to ensure that the program is able to compute orientation at any time within the comparison or sampling time domain using the high level SPICE frames routines (pxform_c and sxform_c). While this contraction does not have any noticable effect when the program is run with CKs containing continuous data, it makes the program unuseable with CKs containing disrete data -- Type 1 CKs and Type 3 CKs with singleton intervals -- because such contraction eliminates all singleton intervals corresponding to the discrete time point from the comparison window. The error messages that the program would display in such cases say that CK files do not provide any roundoff-adjusted coverage for a particular CK-based frame. An exception to this limitation is the rare ciscumstance when SCLK-ET time conversions have no round off; in such cases the program will work on CKs containing discrete data.

If the default coverage window was determined from primary or additional kernel file(s) and either ``-b'' or ``-e'', or both ``-b'' and ``-e'' were specified, it is truncated according to these begin and end times. If the time specified using ``-b'' is before the start of the default window, this time is ignored. If the time specified using ``-b'' is after the end of the default coverage window, the program signals an error. If the time specified using ``-e'' is after the end of the default window, this time is ignored. If the time specified using ``-e'' is before the start of the default coverage window, the program signals an error.

If no ``coverage'' frames are specified or set by default, or if one or both ``coverage'' frames are given but corresponding primary or additional kernels don't contain any data for them, both the coverage window begin time and the coverage window end time must be specified using the ``-b'' and ``-e'' keys because the program has no way to determining the default coverage window. If either ``-b'' or ``-e'' is not provided in such cases, the program signals an error.

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### Times within Coverage Window

The program picks times within the coverage window based on the number of points specified using the ``-n'' key or the time step specified using the ``-s'' key''.

When neither the number of points is specified using ``-n'' nor the step is specified using ``-s'', the number of points is set to a default value determined by examining the coverage window. If the total number of endpoints -- 2 for each non-singleton interval, 1 for each singleton interval -- for all intervals in the coverage window is greater than 1000, the number of points is set to the number of endpoints and the step is not computed. Otherwise it is set to 1000 or a number less than but close to 1000 (the actual number is determined at run-time based on the lengths of the intervals) and the step is computed by dividing the measure of the coverage window by the number of points minus the number of endpoints.

When the number of points is specified using ``-n'' but this number is less than the number of the coverage window interval endpoints, the value given using ``-n'' is ignored and the number of points is set to the number of interval endpoints and the step is not computed. Otherwise the number of points is set to the value provided using ``-n'' or a number less than but close to this value (the actual number is determined at run time based on the lengths of the intervals) and the step is computed by dividing the measure of the coverage window by the number of points minus the number of endpoints.

When step is specified using ``-s'', the number of points is computed by adding the number of interval endpoints to the total of the numbers of points that can fit within each non-singleton interval when it's stepped through with this step. If the resultant number of points is greater than 1,000,000, the program signals an error.

Whether the step was provided or computed using the provided or default number of points, the set of times at which orientation is computed includes all interval ends -- 2 for each non-singleton interval, 1 for each singleton interval -- plus additional points computed by stepping with this step within each non-singleton interval starting from the interval start time. The last point within each non-singleton interval is computed such that it always lies inside the 1.5*step to 0.5*step range off the interval end.

Care should be taken when picking the step using ``-s'' or specifying the number of points using ``-n''. Picking a very small step for a large time window, or very many points for any window, leads to very long run times. In some cases the number of points computed using the step may even be greater that 1,000,000, preventing the program from running because its buffers are not large enough to deal with so many points. On the other hand, picking a large step or too few points prevents the program from doing a thorough comparison.

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## Angular Velocities

The ``-a'' key is used to tell the program to compute angular velocities in addition to orientations. When the value provided using ``-a'' is ``yes'', the program computes angular velocities and reports them or their differences along with the orientation or orientation differences. If the key is omitted or set to ``no'', the program does not compute angular velocities. For any value other than ``yes'' or ``no'' the program reports an error.

If the program samples or compares angular velocities (``-a yes''), the ``-m'' key is used to specify whether they or their differences should be reported in the ``from'' frame(s) or the ``to'' frame(s). When the value provided using the ``-m'' key is ``to'', the program reports angular velocities or their differences in the ``to'' frames. If the key is omitted or set to ``from'', the program reports angular velocities or their differences in the ``from'' frames. For any value other than ``to'' or ``from'' the program reports an error.

In order for the program to compute angular velocities the data provided to it must support this computation. This is not an issue for any frames except for CK-based frames. Therefore, when using CK files, whether as primary or as additional kernels, it's important to make sure that these CKs include angular velocities before requesting the program to compute angular velocities.

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# Output

In a successful run the program prints to the screen a report consisting of the report header and report data. The report header provides the complete information about kernels and control parameters used by the program. The report data provides information about the orientation and angular velocity differences (for comparison runs) or orientations and angular velocities (for sampling reports) in a variety of ways, called report types. The algorithms used to compute orientations and angular velocities and their differences and to convert them to various representations used in the reports are shown in ``Appendix 1''.

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## Overview of Report Types

The report data can be of one of the following types depending on the value provided using the ``-t'' key:

basic
  the basic report including only the maximum and the average rotation angle difference (for comparison runs) or rotation angle (for sampling runs) and, if requested, the maximum and the average angular velocity magnitude difference (for comparison runs) or angular velocity magnitude (for sampling runs). This is the default report displayed when ``-t'' is omitted.

stats
  the statistics report including a small set of statistical information on the difference between two frame orientations (for comparison runs) or statistics on a single orientation (for sampling runs). In addition to the items from the basic report (maximums and averages), this report includes RMS of the rotation angle difference/angle and angular velocity difference/angular velocity and the times when the maximum value of the rotation angle difference/angle and the angular velocity difference/angular velocity were found.

dumpaa
  the angle and axis dump report containing a table listing the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as the rotation angle and axis and, if requested, the components and the magnitude of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the orientations were computed.

dumpm
  the matrix dump report containing a table listing the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as a 3x3 rotation matrix and, if requested, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the orientations were computed.

dumpqs
  the SPICE-style quaternion dump report containing a table listing the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as a SPICE-style quaternion and, if requested, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the orientations were computed.

dumpqo
  produces the ``other''-style quaternion dump report containing a table listing the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as SPICE-style quaternion and, if requested, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the orientations were computed.

dumpea
  the Euler angle dump report containing a table listing the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as three Euler angles and, if requested, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the orientations were computed.

dumpc
  the coverage intervals dump report containing a table listing the start and stop times and durations for the intervals inside the coverage window, during which orientation(s) can be computed.

dumpg
  the coverage gaps dump report containing a table listing the start and stop times and duration for the gaps inside the coverage window, during which orientation(s) cannot be computed.

The ``basic'' and ``stats'' report are useful for quick assessment of whether and by how much two frame transformations differ (for comparison runs) or of the maximum/average magnitude of one frame transformation (for sampling runs). The ``dumpaa'', ``dumpm'', ``dumpqs'', ``dumpqo'', and ``dumpea'' are useful to capture detailed information about differences of two transformations (in comparison runs) or information about a single transformation (for sampling runs) in various formats as a function of time, for analysis or use in other applications. The ``dumpc'' and ``dumpg'' reports are useful for CK or binary PCK coverage overlap analysis.

All reports have rigid formats. The only items in the reports that can be altered by command line options are:

`--` the format of time tags in all ``dump*'' reports; the time format is changed using the ``-f'' key

`--` the number of significant digits in the output numeric times (TDB seconds past J2000, decimal SCLKs and encoded SCLK ticks) and rotation component values or rotation difference component values included in all ``dump*'' reports; the number of significant digits is changed using the ``-d'' key

`--` units for the angles in the dump reports that include angles (``dumpaa'' and ``dumpea''); the units are changed using the ``-x'' key

`--` the order of rotations in the Euler angles dump report (``dumpea''); the order is changed using the ``-o'' key

`--` absence or presence of angular velocities in all non-coverage related dump reports (``dumpaa'', ``dumpm'', ``dumpqs'', ``dumpqo'', and ``dumpea''); whether angular velocities are included or not is controlled by the ``-a'' key as discussed earlier in this document.

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### Time Tag Format for ``dump*'' Reports

The format of the time tags in the ``dump*'' reports is controlled using the ``-f'' key. The following values can be provided using ``-f'':

et
  to display times as TDB seconds past J2000 (default format when ``-f'' is omitted)

sclk
  to display times as string SCLKs

sclkd
  to display times as decimal SCLKs

ticks
  to display times as encoded SCLK ticks

<PICTUR>
  a time format picture acceptable for timout_c function. For example:

                        YYYY-MM-DDTHR:MN:SC.### ::RND    for UTC ISO date
                        YYYY-DOYTHR:MN:SC.### ::RND      for UTC ISO DOY
                        JULIAND.######### ::TDB          for Julian day TDB

When one of the SCLK formats (``sclk'', ``sclkd'', ``ticks'') is specified, TDB times used internally by the program are converted to SCLK times using the SCLK ID associated with one of the ``to'' or ``coverage'' CK-based frames in the following priority order (from highest to lowest): first ``to'' frame, first ``coverage'' frame, second ``to'' frame, second ``coverage'' frame. If neither of the ``to'' or ``coverage'' frames is a CK frame, the program signals an error.

When decimal SCLK tags are requested, the SCLK string returned by SPICE's sce2s_c function is converted to ``decimal'' SCLK by stripping off the partition, using the left field as the integer part and converting the rest of the fields to the decimal fraction of the left field using the SCLK field values from the string SCLK and SCLK moduli and offsets from the SCLK kernel file. For example, the SCLK string ``1/883612839.255'' that has seconds in the left field and a count of ticks having duration of 1/256 of a second in the right field is converted to this DP SCLK 883612839.996094. This conversion is supported only for type 1 clocks.

When one of the numeric formats (``et'', ``sclkd'', ``ticks'') is specified, times are displayed in the scientific format with 14 significant digits (e.g. +1.2345678901234E+01), unless ``-d'' is used to specify a different number of significant digits.

``-f'' does not apply to times in the report header and the statistics report, in which the times are always displayed as TDBs in calendar and seconds past J2000 numeric (in scientific format with 14 significant digits) formats.

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### Numeric Format for ``dump*'' Reports

The default format of numeric time tags (TDB seconds past J2000, decimal SCLKs and encoded SCLK ticks), rotation and angular velocity component values, and rotation and angular velocity difference component values in all ``dump*'' reports is the scientific format with 14 significant digits (e.g. +1.2345678901234E+01). A different number of significant digits can be specified using the ``-d'' option as an integer in the range from 6 to 17. If specified, the number of significant digits is used for all numeric items in the ``dump*'' report data part (table) but is not used for any numbers in the table header or in the data part of the non-``dump*'' (``basic'' and ``stats'') reports.

The default format, with 14 significant digits, is usually adequate for output from all comparison runs and from all sampling runs that are intended to produce tables of rotations or rotation differences for plotting but, due to round off, it may not be adequate for sampling runs that are intended to generate tables of quaternions, angles, or matrices for subsequent interpolation or packaging into CK files. For such outputs the number of significant digits should be increased to 16 -- if output rotations are planned to be packaged into an CK file using the MSOPCK program that employs a custom parser to ingest input numeric data -- or 17 -- if output rotations will read by an application that uses language-native means to parse input numeric data.

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### Angle Units for ``dumpaa'' and ``dumpea'' Reports

The angles in the ``dumpaa'' and ``dumpea'' reports can be displayed using one of the following units depending on the value provided using the ``-x'' key:

                        radians (default)
                        degrees
                        arcminutes
                        arcseconds
                        hourangle
                        minuteangle
                        secondangle

``-f'' applies neither to the angles in the basic and statistics reports (in which the angles are always displayed in radians) nor to angular velocities in any reports (which are always displayed in radians per second).

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## Report Header

The top portion of each report generated by the program is occupied by the report header providing complete information about the kernels and control parameters used by the program. The format and the set of information provided in the report header depends on

`--` the type of run (comparison vs. sampling)

`--` the type of report (data dump, coverage dump, etc.)

`--` the set of kernels that were provided

`--` whether angular velocities were computed

`--` and various miscellaneous control parameters.

All lines in the report header have

       #

as the first character. This allows common plotting programs, such as GNUPLOT, to skip these header lines when plotting the ``dump''-type reports generated by the program.

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### Report Header for Comparing Two Orientations

For runs comparing two orientations the report header has the following format (the line numbers given on the left are not present in the actual report; they are provided for referencing purposes only):

        1  #
        2  # Comparison of N rotations
        3  #
        4  #    from 'FROM1NAME' (FROM1ID) to 'TO1NAME' (TO1ID)
        5  #    computed using
        6  #
        7  #       -K/KERNEL1  -K/KERNEL2  ... -K/KERNELn
        8  #       -K1/KERNEL1 -K1/KERNEL2 ... -K1/KERNELm
        9  #       FIRSTKERNEL
       10  #
       11  # with N rotations
       12  #
       13  #    from 'FROM2NAME' (FROM2ID) to 'TO2NAME' (TO2ID)
       14  #    computed using
       15  #
       16  #       -K/KERNEL1  -K/KERNEL2  ... -K/KERNELn
       17  #       -K2/KERNEL1 -K2/KERNEL2 ... -K2/KERNELm
       18  #       SECONDKERNEL
       19  #
       20  # with a S second (DDDAYS:HR:MN:SC.MSECND) step size
       21  # within the continuous time period
       22  #
       23  #    from 'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       24  #    to   'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       25  #
       26  # including differences in AVs relative to the FRAME frames.
       27  #
       28  # TIMESPEC.
       29  #

where:

`--` on lines 2 and 11 ``N'' is replaced with the actual number of comparison points

`--` on lines 4 and 13 ``FROM1NAME'', ``FROM1ID'', ``TO1NAME'', ``TO1ID'', ``FROM2NAME'', ``FROM2ID'', ``TO2NAME'', and ``TO2ID'' are replaced with the actual names/IDs used to compute transformations for comparison

`--` lines 7, 8, 9, 16, 17, and 18 contain lists of additional kernels provided using the ``-k'', ``-k1'', and ``-k2'' keys and primary kernels provided at the end of the command line, listed in the order in which they were loaded by the program. These lines are present only when corresponding kernel files are given on the command line.

`--` on line 20 the actual step replaces ``S'' and ``DDDAYS:HR:MN:SC.MSECND'' (step expressed as days, hours, minutes, seconds). If transformations are computed only at the interval endpoints, the whole line is replaced with the following string: ``at continuous coverage intervals' endpoints''

`--` line 21 has the form shown above when there are no gaps in coverage window. Otherwise the whole line is replaced with the following string: ``within the non-continuous (with M gaps) time period'' where ``M'' is replaced with the actual number of gaps.

`--` on lines 23 and 24 times are replaced with the first and last times from the set of times for which the comparison was made.

`--` lines 26 and 27 are displayed only when angular velocities are compared. The FRAME is set to ``from'' or ``to'' depending on the frame in which the angular velocity difference is reported.

`--` line 28 and 29 are displayed for all report types except ``basic'' and ``stats''. Depending on the output time type specified using the ``-f'' key TIMESPEC is replaced with one of the following strings:

                -f et       ``Times are TDB seconds past J2000.''

                -f sclk     ``Times are SCLKs computed using SCLK
                            ID <nnn>.''

                -f sclkd    ``Times are decimal SCLKs computed using
                            SCLK ID <nnn>.''

                -f ticks    ``Times are SCLK ticks computed using
                            SCLK ID <nnn>.''

                -f PICTURE  ``Times were generated by TIMOUT using
                            '<format>' format.''

`` where ``nnn'' is replaced with the SCLK ID used to convert TDB to SCLK.

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### Report Header for Coverage/Gaps for Two Orientations

For runs displaying coverage or gaps in coverage for two orientations the report header has the following format (the line numbers given on the left are not present in the actual report; they are provided only for referencing purposes):

        1  #
        2  # Coverage overlap for rotation
        3  #
        4  #    from 'FROM1NAME' (FROM1ID) to 'TO1NAME' (TO1ID)
        5  #    computed using
        6  #
        7  #       -K/KERNEL1  -K/KERNEL2  ... -K/KERNELn
        8  #       -K1/KERNEL1 -K1/KERNEL2 ... -K1/KERNELm
        9  #       FIRSTKERNEL
       10  #
       11  # and rotation
       12  #
       13  #    from 'FROM2NAME' (FROM2ID) to 'TO2NAME' (TO2ID)
       14  #    computed using
       15  #
       16  #       -K/KERNEL1  -K/KERNEL2  ... -K/KERNELn
       17  #       -K2/KERNEL1 -K2/KERNEL2 ... -K2/KERNELm
       18  #       SECONDKERNEL
       19  #
       20  # with a S second (DDDAYS:HR:MN:SC.MSECND) step size
       21  # within the continuous time period
       22  #
       23  #    from 'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       24  #    to   'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       25  #
       26  # TIMESPEC.
       27  #

where:

`--` on lines 4 and 13 ``FROM1NAME'', ``FROM1ID'', ``TO1NAME'', ``TO1ID'', ``FROM2NAME'', ``FROM2ID'', ``TO2NAME'', and ``TO2ID'' are replaced with the actual names/IDs used to compute transformations for comparison

`--` lines 7, 8, 9, 16, 17, and 18 contain lists of additional kernels provided using the ``-k'', ``-k1'', and ``-k2'' keys and primary kernels provided at the end of the command line, listed in the order in which they were loaded by the program. These lines are present only when corresponding kernel files are given on the command line.

`--` on line 20 the actual step replaces ``S'' and ``DDDAYS:HR:MN:SC.MSECND'' (step expressed as days, hours, minutes, seconds). If transformation is computed only at the interval endpoints, the whole line is replaced with the following string: ``at continuous coverage intervals' endpoints''.

`--` line 21 has the form shown above when there are no gaps in the coverage window. Otherwise the whole line is replaced with the following string: ``within the non-continuous (with M gaps) time period'' where ``M'' is replaced with the actual number of gaps.

`--` on lines 23 and 24 times are replaced with the first and last times from the set of times for which the comparison was made.

`--` on line 26, depending on the output time type specified using the ``-f'' key, ``TIMESPEC'' is replaced with one of the following strings:

                -f et       ``Times are TDB seconds past J2000.''

                -f sclk     ``Times are SCLKs computed using SCLK
                            ID <nnn>.''

                -f sclkd    ``Times are decimal SCLKs computed using
                            SCLK ID <nnn>.''

                -f ticks    ``Times are SCLK ticks computed using
                            SCLK ID <nnn>.''

                -f PICTURE  ``Times were generated by TIMOUT using
                            '<format>' format.''

`` where ``nnn'' is replaced with the SCLK ID used to convert TDB to SCLK.

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### Report Header for Sampling an Orientation

For runs sampling an orientation the report header has the following format (the line numbers given on the left are not present in the actual report; they are provided for referencing purposes only):

        1  #
        2  # Sampling of N rotations
        3  #
        4  #    from 'FROMNAME' (FROMID) to 'TONAME' (TOID)
        5  #    computed using
        6  #
        7  #       -K/KERNEL1  -K/KERNEL2  ... -K/KERNELn
        8  #       -K1/KERNEL1 -K1/KERNEL2 ... -K1/KERNELm
        9  #       FIRSTKERNEL
       10  #
       11  # with a S second (DDDAYS:HR:MN:SC.MSECND) step size
       12  # within the continuous time period
       13  #
       14  #    from 'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       15  #    to   'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       16  #
       17  # including angular velocities relative to the FRAME frame.
       18  #
       19  # TIMESPEC
       20  #

where:

`--` on line 2 ``N'' is replaced with the actual number of comparison points

`--` on line 4 ``FROMNAME'', ``FROMID'', ``TONAME'', and ``TOID'' are replaced with the actual names/IDs used to compute transformations

`--` lines 7, 8, and 9 contain lists of additional kernels provided using ``-k'' and ``-k1'' (or ``-k2'') keys and the primary kernel provided at the end of the command line, listed in the order in which they were loaded by the program. These lines are present only when the corresponding kernel files are given on the command line.

`--` on line 11 the actual step replaces ``S'' and ``DDDAYS:HR:MN:SC.MSECND'' (step expressed as days, hours, minutes, seconds). If transformation is computed only at the interval endpoints, the whole line is replaced with the following string: ``at continuous coverage intervals' endpoints''

`--` line 12 has the form shown above when there are no gaps in the coverage window. Otherwise the whole line is replaced with the following string: ``within the non-continuous (with M gaps) time period'' where ``M'' is replaced with the actual number of gaps.

`--` on lines 14 and 15 times are replaced with the first and last times from the set of times for which transformation was computed.

`--` lines 17 and 18 are displayed only when angular velocities are computed. The FRAME is set to ``from'' or ``to'' depending on the frame in which the angular velocity is reported.

`--` line 19 and 20 are displayed for all report types except ``basic'' and ``stats''. Depending on the output time type specified using the ``-f'' key TIMESPEC is replaced with one of the following strings:

                -f et       ``Times are TDB seconds past J2000.''

                -f sclk     ``Times are SCLKs computed using SCLK
                            ID <nnn>.''

                -f sclkd    ``Times are decimal SCLKs computed using
                            SCLK ID <nnn>.''

                -f ticks    ``Times are SCLK ticks computed using
                            SCLK ID <nnn>.''

                -f PICTURE  ``Times were generated by TIMOUT using
                            '<format>' format.''

`` where ``nnn'' is replaced with the SCLK ID used to convert TDB to SCLK.

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### Report Header for Coverage/Gaps for An Orientation

For runs displaying coverage or gaps in coverage for an orientation the report header has the following format (the line numbers given on the left are not present in the actual report; they are provided for referencing purposes only):

        1  #
        2  # Coverage for rotation
        3  #
        4  #    from 'FROMNAME' (FROMID) to 'TONAME' (TOID)
        5  #    computed using
        6  #
        7  #       -K/KERNEL1  -K/KERNEL2  ... -K/KERNELn
        8  #       -K1/KERNEL1 -K1/KERNEL2 ... -K1/KERNELm
        9  #       FIRSTKERNEL
       10  #
       11  # with a S second (DDDAYS:HR:MN:SC.MSECND) step size
       12  # within the continuous time period
       13  #
       14  #    from 'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       15  #    to   'YYYY MON DD HR:MN:SC.### TDB' (SSS.###### TDB seconds)
       16  #
       17  # TIMESPEC
       18  #

where:

`--` on line 4 ``FROMNAME'', ``FROMID'', ``TONAME'', and ``TOID'' are replaced with the actual names/IDs used to compute transformations.

`--` lines 7, 8, and 9 contain lists of additional kernels provided using the ``-k'' and ``-k1'' (or ``-k2'') keys and the primary kernel provided at the end of the command line, listed in the order in which they were loaded by the program. These lines are present only when the corresponding the kernel files are given on the command line.

`--` on line 11 the actual step replaces ``S'' and ``DDDAYS:HR:MN:SC.MSECND'' (step expressed as days, hours, minutes, seconds). If transformation is computed only at the interval endpoints, the whole line is replaced with the following string: ``at continuous coverage intervals' endpoints''

`--` line 12 has the form shown above when there are no gaps in the coverage window. Otherwise the whole line is replaced with the following string: ``within the non-continuous (with M gaps) time period'' where ``M'' is replaced with the actual number of gaps.

`--` on lines 14 and 15 times are replaced with the first and last times from the set of times for which transformation was computed.

`--` on line 17, depending on the output time type specified using the ``-f'' key TIMESPEC is replaced with one of the following strings:

                -f et       ``Times are TDB seconds past J2000.''

                -f sclk     ``Times are SCLKs computed using SCLK
                            ID <nnn>.''

                -f sclkd    ``Times are decimal SCLKs computed using
                            SCLK ID <nnn>.''

                -f ticks    ``Times are SCLK ticks computed using
                            SCLK ID <nnn>.''

                -f PICTURE  ``Times were generated by TIMOUT using
                            '<format>' format.''

`` where ``nnn'' is replaced with the SCLK ID used to convert TDB to SCLK.

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## Report Formats

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### Basic Report (no ``-t'' or ``-t basic'')

The basic report indicates if the two frame transformations are different, or if a single transformation is a non-zero transformation, by displaying only the maximum and the average rotation angle difference (for comparison runs) or rotation angle (for sampling runs) and, if requested using the ``-a'' key, the maximum and the average angular velocity magnitude difference (for comparison runs) or angular velocity magnitude (for sampling runs).

The basic report has the following format:

       Absolute difference magnitudes:

                                           maximum             average

         Rotation (rad):                  MAX_ANGLE         AVERAGE_ANGLE
         Angular Velocity (rad/s):        MAX_RATE          AVERAGE_RATE

where:

`--` ``MAX_ANGLE'', ``AVERAGE_ANGLE'', ``MAX_RATE'', ``AVERAGE_RATE'' are the maximum and average rotation angle difference (for comparison runs) or angle (for sampling runs) and angular velocity difference (for comparison runs) or angular velocity magnitude (for sampling runs) determined for the set of frame transformation differences or frame transformations computed by the program within the coverage window.

`--` The word ``difference'' is omitted from the ``Absolute difference magnitudes:'' line when the program is run in sampling mode.

`--` The line ``Angular Velocity ...'' is omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

`--` All ``*ANGLE'' and ``*RATE'' values are printed in the ``x.xxxxxxxxxxxxxE+xx'' format.

`--` All ``*ANGLE'' values are always printed in radians (i.e. units specified using the ``-x'' key have no effect on the values in this report).

`--` All ``*RATE'' values are always printed in radians per second.

`--` Neither the custom time format specified using ``-f'' nor the number of significant digits specified using ``-d'' apply to this report.

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### Statistics Report (``-t stats'')

The statistics report provides a small set of statistical information on the difference of two frame transformations (for comparison runs) or a single transformation (for sampling runs). It includes the same items as the basic report (maximums and averages) plus a few additional parameters such as RMS of the rotation angle difference/angle and angular velocity difference/angular velocity and the times when the maximum value of the rotation angle difference/angle and angular velocity difference/angular velocity were found.

The statistics report has the following format:

       1) Average difference

          1a) Rotation (rad):                               AVERAGE_ANGLE

          1b) Angular velocity (rad/s):                     AVERAGE_RATE

       2) RMS of difference

          2a) Rotation (rad):                               RMS_OF_ANGLE

          2b) Angular velocity (rad/s):                     RMS_OF_RATE

       3) Maximum rotation difference

          3a) Rotation (rad):                               MAX_ANGLE

          3b) Epoch (TDB, seconds past J2000):              TDB_SECONDS

          3c) Epoch (TDB, calendar format):         YYYY-MON-DD-HR:MN:SC.MMM

       4) Maximum angular velocity difference

          4a) Angular velocity (rad/s):                     MAX_RATE

          4b) Epoch (TDB, seconds past J2000):              TDB_SECONDS

          4c) Epoch (TDB, calendar format):         YYYY-MON-DD-HR:MN:SC.MMM

where:

`--` ``MAX_ANGLE'', ``AVERAGE_ANGLE'', ``RMS_OF_ANGLE'', ``MAX_RATE'', ``AVERAGE_RATE'', ``RMS_OF_RATE'' are the maximum, average, and RMS of rotation angle difference (for comparison runs) or angle (for sampling runs) and angular velocity difference (for comparison runs) or angular velocity magnitude (for sampling runs) determined for the set of frame transformation differences or frame transformations computed by the program within the coverage window. ``TDB_SECONDS'' and ``YYYY-MON-DD-HR:MN:SC.MMM'' are the times, as TDB seconds past J2000 and TDB in calendar date format, when the maximums were found.

`--` The word ``difference'' is omitted from the lines starting with ``1)'', ``2)'', ``3)'', and ``4)'' when the program is run in sampling mode.

`--` All lines pertaining to angular velocity are omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

`--` All ``*ANGLE'' and ``*RATE'' values are printed in ``x.xxxxxxxxxxxxxE+xx'' format.

`--` All ``*ANGLE'' values are always printed in radians (i.e. units specified using the ``-x'' key have no effect on the values in this report).

`--` All ``*RATE'' values are always printed in radians per second.

`--` ``TDB_SECONDS'' are printed in the ``xxxxxxxxxx.xxxxxx'' format.

`--` Neither the custom time format specified using ``-f'' nor the number of significant digits specified using ``-d'' apply to this report.

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### Angle and Axis Dump Report (``-t dumpaa'')

The angle and axis dump report displays the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as the rotation angle and axis and, if requested using the ``-a'' key, the components and the magnitude of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the frame transformations were computed. The angle is displayed in units specified using the ``-x'' key -- ``radians'' (default), ``degrees'', ``arcminutes'', ``arcseconds'', ``hourangle'', ``minuteangle'', or ``secondangle''. The time tags are displayed in the format specified using the ``-f'' key, discussed earlier in this document.

The angle and axis dump report has the following format:

       # angle is shown in UNITS.
       #
       # time, angle, axis_x, axis_y, axis_z, av_x, av_y, av_z, av_magnitude
       TIME ANGLE AXIS(1) AXIS(2) AXIS(3) AV(1) AV(2) AV(3) |AV|
       ...
       TIME ANGLE AXIS(1) AXIS(2) AXIS(3) AV(1) AV(2) AV(3) |AV|

where:

`--` Items on each data line are separated by spaces.

`--` All items except TIME are printed in the ``+x.xxxxxxxxxxxxxE+xx'' format, either with the default 14 significant digits or with the number of significant digits specified using the ``-d'' option. TIME is displayed in the format specified using the ``-f'' key.

`--` The ANGLE is displayed in units specified using the ``-x'' key. The AV components and magnitude are always displayed in radians per second.

`--` The AV difference/AV components and the corresponding labels in the table header line are omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

`--` UNITS is replaced with the units used to display the angles.

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### Matrix Dump Report (``-t dumpm'')

The matrix dump report displays the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as a 3x3 rotation matrix and, if requested using the ``-a'' key, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the frame transformations were computed. The time tags are displayed in the format specified using the ``-f'' key, discussed earlier in this document.

The matrix dump report has the following format:

       # time, m11, m12, m13, m21, m22, m23, m31, m32, m33, av_x, av_y, av_z
       TIME M11 M12 M13 M21 M22 M23 M31 M32 M33 AV(1) AV(2) AV(3)
       ...
       TIME M11 M12 M13 M21 M22 M23 M31 M32 M33 AV(1) AV(2) AV(3)

where:

`--` Items on each data line are separated by spaces.

`--` All items except TIME are printed in the ``+x.xxxxxxxxxxxxxE+xx'' format, either with the default 14 significant digits or with the number of significant digits specified using the ``-d'' option. TIME is displayed in the format specified using the ``-f'' key.

`--` The AV components are always displayed in radians per second.

`--` The AV difference/AV components and the corresponding labels in the table header line are omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

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### SPICE-Style Quaternion Dump Report (``-t dumpqs'')

The SPICE-style quaternion dump report displays the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as a SPICE-style quaternion and, if requested using the ``-a'' key, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which the frame transformations were computed. The time tag is displayed in the format specified using the ``-f'' key, discussed earlier in this document.

The SPICE-style quaternion dump report has the following format:

       # time, q_cos, q_sin1, q_sin2, q_sin3, av_x, av_y, av_z
       TIME QS(1) QS(2) QS(3) QS(4) AV(1) AV(2) AV(3)
       ...
       TIME QS(1) QS(2) QS(3) QS(4) AV(1) AV(2) AV(3)

where:

`--` Items on each data line are separated by spaces.

`--` All items except TIME are printed in the ``+x.xxxxxxxxxxxxxE+xx'' format, either with the default 14 significant digits or with the number of significant digits specified using the ``-d'' option. TIME is displayed in the format specified using the ``-f'' key.

`--` The AV components are always displayed in radians per second.

`--` The AV difference/AV components and the corresponding labels in the table header line are omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

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### ``Other''-Style Quaternion Dump Report (``-t dumpqo'')

The ``other''-style quaternion dump report displays the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as the ``other''-style (or engineering-style) quaternion and, if requested using the ``-a'' key, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling reports), along with the time, for each of the times at which frame transformations were computed. The time tags are displayed in the format specified using the ``-f'' key, discussed earlier in the document.

The ``other''-style quaternion dump report has the following format:

       # time, q_sin1, q_sin2, q_sin3, q_cos, av_x, av_y, av_z
       TIME QO(1) QO(2) QO(3) QO(4) AV(1) AV(2) AV(3)
       ...
       TIME QO(1) QO(2) QO(3) QO(4) AV(1) AV(2) AV(3)

where:

`--` Items on each data line are separated by spaces.

`--` All items except TIME are printed in the ``+x.xxxxxxxxxxxxxE+xx'' format, either with the default 14 significant digits or with the number of significant digits specified using the ``-d'' option. TIME is displayed in the format specified using the ``-f'' key.

`--` The AV components are always displayed in radians per second.

`--` The AV difference/AV components and the corresponding labels in the table header line are omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

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### Euler Angles Dump Report (``-t dumpea'')

The Euler angles dump report displays the orientation difference (for comparison runs) or orientation (for sampling runs) expressed as three Euler angles and, if requested using the ``-a'' key, the components of the angular velocity difference (for comparison runs) or angular velocity (for sampling runs), along with the time, for each of the times at which frame transformations were computed. The order of rotations is specified using the ``-o'' key as sequence of three axes from the set of ``X'', ``Y'', ``Z'' (case-insensitive), separated by spaces. The second axis in the sequence must differ from the first and third axes. When ``-o'' is not provided, the default order is set to ``Z Y X''. The angles are displayed in the units specified using the ``-x'' key -- ``radians'' (default), ``degrees'', ``arcminutes'', ``arcseconds'', ``hourangle'', ``minuteangle'', or ``secondangle''. The time tags are displayed in the format specified using the ``-f'' key, discussed earlier in this document.

The Euler angles dump report has the following format:

       # angles are shown in UNITS
       #
       # time, angle_AXIS3, angle_AXIS2, angle_AXIS1, av_x, av_y, av_z
       TIME ANGLE3 ANGLE2 ANGLE1 AV(1) AV(2) AV(3)
       ...
       TIME ANGLE3 ANGLE2 ANGLE1 AV(1) AV(2) AV(3)

where:

`--` Items on each data line are separated by spaces.

`--` All items except TIME are printed in the ``+x.xxxxxxxxxxxxxE+xx'' format, either with the default 14 significant digits or with the number of significant digits specified using the ``-d'' option. TIME is displayed in the format specified using the ``-f'' key.

`--` The ANGLEs are displayed in the units specified using the ``-x'' key. The AV components are always displayed in radians per second.

`--` The AV difference/AV components and the corresponding labels in the table header line are omitted when AVs are not compared/sampled (no ``-a'' or ``-a no'').

`--` UNITS is replaced with the units used to display angles.

`--` ``AXIS1'', ``AXIS2'', ``AXIS3'' are replaced with the corresponding axis labels (X,Y, or Z).

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### Coverage Intervals Dump Report (``-t dumpc''):

The coverage intervals dump report displays the start and stop times for the intervals inside the coverage window, during which frame transformations can be computed. The time tags are displayed in the format specified using the ``-f'' key, discussed earlier in the document.

The coverage intervals dump report has the following format:

       # int_start_time, int_end_time, int_duration_sec, int_duration_string
       STARTTIME STOPTIME SECONDS DAYS:HR:MN:SC.MMMMMM
       ...
       STARTTIME STOPTIME SECONDS DAYS:HR:MN:SC.MMMMMM

where:

`--` Items on each data line are separated by spaces.

`--` The interval durations are printed as seconds in the ``xxxxxxxxxxxx.xxxxxx'' format (replaces SECONDS) and in days, hours, minutes, seconds format (replaces DAYS:HR:MN:SC.MMMMMM). The STARTTIMEs and STOPTIMEs are displayed in the format specified using the ``-f'' key.

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### Coverage Gaps Dump Report (``-t dumpg'')

The coverage gaps dump report displays the start and stop times for the gaps inside the coverage window, during which frame transformations cannot be computed. The time tags are displayed in the format specified using the ``-f'' key, discussed earlier in this document.

The coverage gaps dump report has the following format:

       # gap_start_time, gap_end_time, gap_duration_sec, gap_duration_string
       STARTTIME STOPTIME SECONDS DAYS:HR:MN:SC.MMMMMM
       ...
       STARTTIME STOPTIME SECONDS DAYS:HR:MN:SC.MMMMMM

`--` Items on each data line are separated by spaces.

`--` The gap durations are printed as seconds in the ``xxxxxxxxxxxx.xxxxxx'' format (replaces SECONDS) and in days, hours, minutes, seconds format (replaces DAYS:HR:MN:SC.MMMMMM). The STARTTIMEs and STOPTIMEs are displayed in the format specified using the ``-f'' key.

`--` If the coverage window has no gaps, the string ``There are no gaps in coverage.'' is printed instead of the data records.

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# Examples

The examples below illustrate some of the common FRMDIFF usage scenarios. In all examples the files are assumed to be in the current directory, the FRMDIFF command lines, which usually occupy a single line, span multiple lines and use the UNIX shell style continuation character (backslash), and the report lines are truncated to fit the width of the page (``...'' at the end of a line indicates that it was truncated).

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## Checking if Two CKs Provide the Same Orientation

In this example the program is run to check if the daily reconstructed MRO CK ``mro_sc_2009-01-26.bc'' and the weekly reconstructed MRO CK ``mro_sc_psp_090120_090126.bc'' provide the same data. The CK files are provided as primary kernels to make the program run in comparison mode. The LSK ``naif0009.tls'' and SCLK ``MRO_SCLKSCET.00027.tsc'', required to support time conversions, and the FK ``mro_v13.tf'', required because it defines the MRO spacecraft frame and the frame used as the base frame in the CKs, apply to both CKs and, therefore, are provided using the ``-k'' key. To make sure the comparison is thorough the step is set to 1 second using the ``-s'' key. No other options need to be specified because the primary kernels are CKs, which the program can examine to automatically pick the ``from'' and ``to'' frames and the coverage window. The basic report displaying the maximum difference will suffice for this case; therefore, there is no need to specify the ``-t'' option.

       % frmdiff -k naif0009.tls MRO_SCLKSCET.00027.tsc mro_v13.tf \
                 -s 1 \
                 mro_sc_2009-01-26.bc mro_sc_psp_090120_090126.bc
       # int_start_time, int_end_time, int_duration_sec, int_duration_string
       #
       # Comparison of 86401 rotations
       #
       #    from 'MRO_MME_OF_DATE' (-74900) to 'MRO_SPACECRAFT' (-74000)
       #    computed using
       #
       #       naif0009.tls MRO_SCLKSCET.00027.tsc mro_v13.tf
       #       mro_sc_2009-01-26.bc
       #
       # with 86401 rotations
       #
       #    from 'MRO_MME_OF_DATE' (-74900) to 'MRO_SPACECRAFT' (-74000)
       #    computed using
       #
       #       naif0009.tls MRO_SCLKSCET.00027.tsc mro_v13.tf
       #       mro_sc_psp_090120_090126.bc
       #
       # with a 1.0000000000000 second (0:00:00:01.000000) step size
       # within the continuous time period
       #
       #    from '2009 JAN 26 00:01:06.261' TDB (286200066.26113 TDB seco...
       #    to   '2009 JAN 27 00:01:06.024' TDB (286286466.02413 TDB seco...
       #

       Absolute difference magnitudes:

                                            maximum                 avera...

         Rotation (rad):             +0.0000000000000E+00      +0.0000000...

The zero maximum rotation difference indicates that these two CKs provide the same data.

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## Comparing Predicted and Reconstructed CKs

In this example the program is run to assess, for a specified period of time, the difference of the spacecraft orientation provided by the predicted CASSINI spacecraft CK ``09009_09025pa_fsiv_lud2.bc'' and the reconstructed CASSINI spacecraft CK ``09006_09011ra.bc''. The CK files are provided as primary kernels to make the program run in comparison mode. The LSK ``naif0009.tls'' and the SCLK ``cas00130.tsc'', required to support time conversions, and the FK ``cas_v40.tf'', required because it defines the CASSINI spacecraft frame, apply to both CKs and, therefore, are provided using the ``-k'' key. The angle and axis dump report is requested using ``-t dumpaa'' and the step is set to 10 seconds using ``-s 10''. The time boundaries for the period of interest are specified using ``-b'' and ``-e''. No other options need to be specified because the primary kernels are CKs, which the program can examine to automatically pick the ``from'' and ``to'' frames and the default coverage window (which is intersected with the window of interest specified using ``-b'' and ``-e''). The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -k naif0009.tls cas00130.tsc cas_v40.tf \
                 -s 10 -b 2009-JAN-09 00:00 -e 2009-JAN-10 00:00 -t dumpaa \
                 09009_09025pa_fsiv_lud2.bc 09006_09011ra.bc \
                 > output.txt
       % cat output.txt
       #
       # Comparison of 3143 rotations
       #
       #    from 'J2000' (1) to 'CASSINI_SC_COORD' (-82000)
       #    computed using
       #
       #       naif0009.tls cas00130.tsc cas_v40.tf
       #       09009_09025pa_fsiv_lud2.bc
       #
       # with 3143 rotations
       #
       #    from 'J2000' (1) to 'CASSINI_SC_COORD' (-82000)
       #    computed using
       #
       #       naif0009.tls cas00130.tsc cas_v40.tf
       #       09006_09011ra.bc
       #
       # with a 10.000000000000 second (0:00:00:10.000000) step size
       # within the non-continuous (with 1 gaps) time period
       #
       #    from '2009 JAN 09 15:17:06.359' TDB (284786226.35996 TDB seco...
       #    to   '2009 JAN 10 00:01:06.184' TDB (284817666.18419 TDB seco...
       #
       # Times are TDB seconds past J2000.
       #
       # angle is shown in radians.
       #
       # time, angle, axis_x, axis_y, axis_z
       +2.8478622635996E+08 +5.4958832051797E-05 +8.2101753099566E-01 +4....
       +2.8478623635996E+08 +5.4931030131424E-05 +8.2046010733260E-01 +4....
       +2.8478624635996E+08 +5.4903290577181E-05 +8.1990116349661E-01 +4....
       ...
       +2.8481765833081E+08 +2.3714852496640E-05 +4.7607884330795E-01 -8....
       +2.8481766618419E+08 +1.7506382825421E-05 -3.3218433215999E-01 -6....

The orientation difference expressed as the rotation angle (column 2) can be plotted against TDB seconds (column 1) for analysis.

Note that the time window shown in the report header is different from the requested window specified using the ``-b'' and ``-e'' options. The reason for that is the lack of coverage for the requested windows in one of the CKs (``09009_09025pa_fsiv_lud2.bc'').

To find out when the difference between two orientations is the greatest without plotting the difference as suggested above, the program can be re-run with the same options to generate a statistics report (``-t stats''). For such a run it makes sense to also decrease the time step in order to determine the time of interest more accurately, for example by setting the step to 1 second (``-s 1'').

       % frmdiff -k naif0009.tls cas00130.tsc cas_v40.tf \
                 -s 1 -b 2009-JAN-09 00:00 -e 2009-JAN-10 00:00 -t stats \
                 09009_09025pa_fsiv_lud2.bc 09006_09011ra.bc
       #
       # Comparison of 31414 rotations
       #
       #    from 'J2000' (1) to 'CASSINI_SC_COORD' (-82000)
       #    computed using
       #
       #       naif0009.tls cas00130.tsc cas_v40.tf
       #       09009_09025pa_fsiv_lud2.bc
       #
       # with 31414 rotations
       #
       #    from 'J2000' (1) to 'CASSINI_SC_COORD' (-82000)
       #    computed using
       #
       #       naif0009.tls cas00130.tsc cas_v40.tf
       #       09006_09011ra.bc
       #
       # with a 1.0000000000000 second (0:00:00:01.000000) step size
       # within the non-continuous (with 1 gaps) time period
       #
       #    from '2009 JAN 09 15:17:06.359' TDB (284786226.35996 TDB seco...
       #    to   '2009 JAN 10 00:01:06.184' TDB (284817666.18419 TDB seco...
       #

       1) Average difference

          1a) Rotation (rad):                               0.00007738559...

       2) RMS of difference

          2a) Rotation (rad):                               0.00016380723...

       3) Maximum rotation difference

          3a) Rotation (rad):                               0.00098956656...

          3b) Epoch (TDB, seconds past J2000):              284788762.33081

          3c) Epoch (TDB, calendar format):         2009-JAN-09-15:59:22.330

As seen in the report the maximum difference between orientations provided by these CKs between 2009-JAN-09 15:17:06 TDB and 2009-JAN-10 00:01:06 TDB is about 1 milliradian near 2009-JAN-09 15:59:22 TDB.

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## Comparing Orientations from a CK Read Using Different SCLKs

In this example the program is run to assess the effect that using an out-of-date SCLK kernel has on the 2001 Mars Odyssey spacecraft orientation computed from the M01 CK file ``m01_sc_2009-01-27.bc''. To make the program run in comparison mode, the current SCLK ``ORB1_SCLKSCET.00157.tsc'' and the out-of-date SCLK ``ORB1_SCLKSCET.00147.tsc'' are provided using the ``-k1'' and ``-k2'' keys while the CK is provided as the only primary kernel. (Alternatively, the SCLK kernels could be provided as two primary kernels while the CK could be provided using the ``-k'' key, in which case the ``from'' and ``to'' frames and the coverage boundaries would have to be specified because the program would not be able to determine defaults from the SCLK kernels.) The LSK ``naif0009.tls'', required to support time conversions, and the FK ``m01_v28.tf'', required because it defines the M01 spacecraft frame, are provided using the ``-k'' key. The angle and axis dump report is requested using ``-t dumpaa'' and the step size is set to 10 seconds using ``-s 10''. No other options need to be specified because the primary kernel is a CK, which the program can examine to automatically pick the ``from'' and ``to'' frames and the default coverage window. The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -k naif0009.tls m01_v28.tf \
                 -k1 ORB1_SCLKSCET.00157.tsc \
                 -k2 ORB1_SCLKSCET.00147.tsc \
                 -s 10 -t dumpaa \
                 m01_sc_2009-01-27.bc \
                 > output.txt
       % cat output.txt
       #
       # Comparison of 8283 rotations
       #
       #    from 'MARSIAU' (16) to 'M01_SPACECRAFT' (-53000)
       #    computed using
       #
       #       naif0009.tls m01_v28.tf
       #       ORB1_SCLKSCET.00157.tsc
       #       m01_sc_2009-01-27.bc
       #
       # with 8283 rotations
       #
       #    from 'MARSIAU' (16) to 'M01_SPACECRAFT' (-53000)
       #    computed using
       #
       #       naif0009.tls m01_v28.tf
       #       ORB1_SCLKSCET.00147.tsc
       #       m01_sc_2009-01-27.bc
       #
       # with a 10.000000000000 second (0:00:00:10.000000) step size
       # within the non-continuous (with 2 gaps) time period
       #
       #    from '2009 JAN 27 00:01:07.301' TDB (286286467.30114 TDB seco...
       #    to   '2009 JAN 28 00:01:03.083' TDB (286372863.08345 TDB seco...
       #
       # Times are TDB seconds past J2000.
       #
       # angle is shown in radians.
       #
       # time, angle, axis_x, axis_y, axis_z
       +2.8628646730114E+08 +1.6811778261922E-04 -1.6518133891799E-03 -1....
       +2.8628647730114E+08 +1.6807590586987E-04 -2.5417591048513E-03 -9....
       ...
       +2.8637285336657E+08 +1.5490156847677E-04 -1.0767849826583E-03 -1....
       +2.8637286308345E+08 +1.5459290844816E-04 +5.3342008940173E-05 +1....

The orientation difference expressed as rotation angle (column 2) can be plotted against TDB seconds (column 1) for analysis.

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## Comparing Binary and Text PCKs

In this example the program is run to compare Earth orientations provided by the high precision Earth orientation binary PCK file ``earth_000101_090421_090128.bpc'' and the low precision Earth orientation text PCK file ``pck00008.tpc''. The PCK files are specified as two primary kernels to make the program run in comparison mode. For this run both ``to'' frames must be specified because the frame associated with the high precision orientation -- ``ITRF93'' -- is different from the frame associated with the low precision orientation -- ``IAU_EARTH''. These two frames are provided using the ``-t1'' and ``-t2'' keys. Note that neither the coverage boundaries nor the ``from'' frames need to be specified because the program can set them to default values obtained by examining the binary PCK. The step is set to 1 hour (``-s 3600'') and the report type is picked to be the Euler angle dump (``-t dumpea'') with the rotation axis order Z,Y,X (``-o z y x''). Reporting differences as Euler angles might be desirable in this case because the angles will show how much of the difference is in the pole tilt (combination of angles about X and Y) and how much of it is in the rotation about the pole (angle about Z). The ``-x'' option used to report angles in degrees (``-x degrees''). The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -t1 ITRF93 -t2 IAU_EARTH \
                 -s 3600 -t dumpea -o Z Y X -x degrees \
                 earth_000101_090421_090128.bpc pck00008.tpc \
                 > output.txt
       % cat output.txt
       #
       # Comparison of 81553 rotations
       #
       #    from 'ECLIPJ2000' (17) to 'ITRF93' (13000)
       #    computed using
       #
       #       earth_000101_090421_090128.bpc
       #
       # with 81553 rotations
       #
       #    from 'ECLIPJ2000' (17) to 'IAU_EARTH' (10013)
       #    computed using
       #
       #       pck00008.tpc
       #
       # with a 3600.0000000000 second (0:01:00:00.000000) step size
       # within the continuous time period
       #
       #    from '2000 JAN 01 00:01:04.183' TDB (-43135.816087188 TDB sec...
       #    to   '2009 APR 21 00:01:06.185' TDB (293544066.18557 TDB seco...
       #
       # Times are TDB seconds past J2000.
       #
       # angles are shown in degrees.
       #
       # time, ang3_about_Z, ang2_about_Y, ang1_about_X
       -4.3135816087188E+04 +4.6935841900452E-02 -1.3237283886873E-03 -1....
       -3.9535816087188E+04 +4.6935945731300E-02 -8.1268845525487E-04 -2....
       ...
       +2.9354046418391E+08 +5.9885369786058E-02 -1.7263299596662E-03 +1....
       +2.9354406618557E+08 +5.9885381660130E-02 -1.9758128919827E-03 +5....

The Euler angles about Z, Y, and X (column 2, 3, 4) can be plotted against TDB seconds (column 1) for analysis.

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## Comparing Two Text PCKs

In this example the program is run to compare Mars orientations provided by the text PCK file ``pck00006.tpc'' containing 1994 IAU constants and the text PCK ``pck00008.tpc'' containing IAU 2000 constants. The PCK files are specified as two primary kernels to make the program run in comparison mode. Since both files are neither CKs nor binary PCKs, the ``from'' and ``to'' frames and the time boundaries for coverage window must be specified using the ``-t1'' (or ``-t2''), ``-f1'' (or ``-f2''), and ``-b'' and ``-e'' keys. Since the time boundaries are provided on the command line, the LSK ``naif0009.tls'' required for time conversions must be provided using ``-k'' (either ``-k1'' or ``-k2'' can also be used). The step is set to 1 hour (``-s 3600'') and the report type is picked to be the Euler angles dump (``-t dumpea'') with the rotation axis order Z,Y,X (``-o z y x''). Reporting differences as Euler angles might be desirable in this case because the angles will show how much of the difference is in the pole tilt (combination of angles about X and Y) and how much of it is in the rotation about the pole (angle about Z). The ``-x'' option is used to report angles in degrees (``-x degrees''). The ``-f'' option is used to print times as UTC in ISO date format (``-f YYYY-MM-DDTHR:MN:SC ::RND''). The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -k naif0009.tls -f1 J2000 -t1 IAU_MARS \
                 -b 2005-01-01 -e 2006-01-01 \
                 -t dumpea -o z y x -x degrees \
                 -f YYYY-MM-DDTHR:MN:SC ::RND -s 3600 \
                 pck00006.tpc pck00008.tpc \
                 > output.txt
       % cat output.txt
       #
       # Comparison of 8761 rotations
       #
       #    from 'J2000' (1) to 'IAU_MARS' (10014)
       #    computed using
       #
       #       naif0009.tls
       #       pck00006.tpc
       #
       # with 8761 rotations
       #
       #    from 'J2000' (1) to 'IAU_MARS' (10014)
       #    computed using
       #
       #       naif0009.tls
       #       pck00008.tpc
       #
       # with a 3600.0000000000 second (0:01:00:00.000000) step size
       # within the continuous time period
       #
       #    from '2005 JAN 01 00:01:04.183' TDB (157809664.18393 TDB seco...
       #    to   '2006 JAN 01 00:01:05.183' TDB (189345665.18393 TDB seco...
       #
       # Times were generated by TIMOUT using 'YYYY-MM-DDTHR:MN:SC ::RND'...
       #
       # angles are shown in degrees.
       #
       # time, ang3_about_Z, ang2_about_Y, ang1_about_X
       2005-01-01T00:00:00 +2.7193295981800E-01 +4.3458477098658E-04 +4.0...
       2005-01-01T01:00:00 +2.7193298908895E-01 +3.1750496671468E-04 +5.0...
       ...
       2005-12-31T23:00:00 +2.7218789688912E-01 +3.4616175147429E-04 -4.9...
       2006-01-01T00:00:00 +2.7218792598016E-01 +4.5965878416891E-04 -3.9...

The Euler angles about Z, Y, and X (column 2, 3, 4) can be plotted against UTC (column 1) for analysis.

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## Sampling Orientation from a CK

In this example the program is run to sample the orientation and angular velocity of Deep Impact Flyby (DIF) spacecraft from the daily CK ``dif_sc_2009-01-27.bc'' every five seconds over the whole period covered by the file and and print the orientation as engineering style quaternions and angular velocities expressed in the spacecraft frame, tagged with DP SCLKs. In addition to the CK file the LSK ``naif0009.tls'' and SCLK ``DIF_SCLKSCET.00036.tsc'', required to support time conversions, and the FK ``di_v17.tf'', required because it defines the DIF spacecraft frame, must be provided to the program. The CK file is provided as the only primary kernel and all other kernels are provided using ``-k'' to make the program run in sampling mode. The step is set to 5 seconds using ``-s 5''. The report type is set to the ``other''-style quaternion dump using ``-t dumpqo''. The output time format is set to DP SCLK using ``-f sclkd''. ``-a yes'' and ``-m to'' are specified to add angular velocities rotated to the spacecraft frame (the ``to'' frame) to the output. No other options need to be specified because the primary kernel is a CK, which the program can examine to automatically pick the ``from'' and ``to'' frames and the coverage window. The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -k naif0009.tls DIF_SCLKSCET.00036.tsc di_v17.tf \
                 -s 5 -t dumpqo -f sclkd -a yes -m to \
                 dif_sc_2009-01-27.bc \
                 > output.txt
       % cat output.txt
       #
       # Sampling of 16864 rotations
       #
       #    from 'J2000' (1) to 'DIF_SPACECRAFT' (-140000)
       #    computed using
       #
       #       naif0009.tls DIF_SCLKSCET.00036.tsc di_v17.tf
       #       dif_sc_2009-01-27.bc
       #
       # with a 5.0000000000000 second (0:00:00:05.000000) step size
       # within the non-continuous (with 2 gaps) time period
       #
       #    from '2009 JAN 27 00:01:06.713' TDB (286286466.71354 TDB seco...
       #    to   '2009 JAN 28 00:01:05.346' TDB (286372865.34683 TDB seco...
       #
       # including angular velocities relative to 'to' frame.
       #
       # Times are decimal SCLKs computed using SCLK ID -140.
       #
       # time, q_sin1, q_sin2, q_sin3, q_cos, av_x, av_y, av_z
       2.8628543276953E+08 +6.9350853049532E-01 +3.7594179111024E-01 -6.1...
       2.8628543776953E+08 +6.9350851552324E-01 +3.7594215798843E-01 -6.1...
       ...
       2.8637182501172E+08 +6.9259444035804E-01 +3.8202205741497E-01 -6.0...
       2.8637183010156E+08 +6.9259433874053E-01 +3.8202240378948E-01 -6.0...

Top

## Sampling Orientation of a Built-in Frame

In this example the program is run to print the rotation from the ``J2000'' frame to the ``ECLIPJ2000'' frame, both of which are built-in frames. To get this rotation, ``J2000'' is specified using ``-f1'' and ``ECLIPJ2000'' is specified using ``-t1''. While it may seem that no kernels would be needed in this case, it is not true. An LSK must be provided to the program because the time at which the orientation should be computed must be provided on the command line twice using the ``-b'' and ``-e'' keys and this time has to be converted to TDB inside the program. Therefore the program is given the LSK ``naif0009.tls'' using the ``-k'' option and an arbitrary time (``2000-01-01'') twice using the ``-b'' and ``-e'' options. The Euler angle dump report is picked using ``-t dump'' with the axis order X,Y,Z picked using ``-o x y z''. The angles are requested to be printed in degrees using ``-x degrees''.

       % frmdiff -k naif0009.tls \
                 -f1 J2000 -t1 ECLIPJ2000 \
                 -b 2000-01-01 -e 2000-01-01 \
                 -t dumpea -o x y z -x degrees
       #
       # Sampling of 1 rotations
       #
       #    from 'J2000' (1) to 'ECLIPJ2000' (17)
       #    computed using
       #
       #       naif0009.tls
       #
       # at continuous coverage intervals' endpoints
       # within the continuous time period
       #
       #    from '2000 JAN 01 00:01:04.183' TDB (-43135.816087188 TDB sec...
       #    to   '2000 JAN 01 00:01:04.183' TDB (-43135.816087188 TDB sec...
       #
       # Times are TDB seconds past J2000.
       #
       # angles are shown in degrees.
       #
       # time, ang3_about_X, ang2_about_Y, ang1_about_Z
       -4.3135816087188E+04 +2.3439291111111E+01 +0.0000000000000E+00 +0....

Top

## Sampling Orientation of a Dynamic Frame

In this example the program is run to sample orientation of the Geocentric Solar Ecliptic frame (``GSE''), a dynamic frame defined in the FK ``RSSD0002.TF'', relative to the ``J2000'' inertial frame and print this orientation as Euler angles tagged with Julian day TDB. The frames are specified using ``-f1'' and ``-t1''. All kernels needed to compute this transformation and convert times -- the FK, LSK ``NAIF0009.TLS'' and SPK ``DE405.BSP'' -- are listed using the ``-k'' key. Since there are no primary kernels, the default coverage window cannot be picked automatically. Therefore the coverage window boundaries are specified using ``-b'' and ``-e''. The step is set to 1 day using ``-s 86400''. The Euler angles dump report is requested using ``-t dumpea''. The time format for output is set to be the Julian day TDB using

       -f 'JULIAND.######### ::TDB''

The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -k RSSD0002.TF NAIF0009.TLS DE405.BSP \
                 -f1 J2000 -t1 GSE \
                 -b 2008-01-01 -e 2009-01-01 -s 86400 \
                 -t dumpea -f 'YYYY-MM-DD HR:MN:SC.### ::RND ::TDB' \
                 > output.txt
       % cat output.txt
       #
       # Sampling of 367 rotations
       #
       #    from 'J2000' (1) to 'GSE' (1500399)
       #    computed using
       #
       #       RSSD0002.TF ../lsk/NAIF0009.TLS ../spk/DE405.BSP
       #
       # with a 86400.000000000 second (1:00:00:00.000000) step size
       # within the continuous time period
       #
       #    from '2008 JAN 01 00:01:05.183' TDB (252417665.18391 TDB seco...
       #    to   '2009 JAN 01 00:01:06.183' TDB (284040066.18393 TDB seco...
       #
       # Times were generated by TIMOUT using 'JULIAND.######### ::TDB' f...
       #
       # angles are shown in radians.
       #
       # time, ang3_about_Z, ang2_about_Y, ang1_about_X
       2454466.500754400 -1.3994266054604E+00 +1.6337747151270E-06 +4.090...
       2454467.500754400 -1.3816355414305E+00 +1.6343360047251E-06 +4.090...
       ...
       2454831.500754400 -1.4039978657128E+00 +1.8387392674578E-06 +4.090...
       2454832.500766000 -1.3862038203964E+00 +1.8393010792771E-06 +4.090...

Top

## Sampling Orientation With Two Different ``Coverage'' Frames

In this example the program is run to sample orientation of the MGS MAG +Y sensor frame, ``MGS_MAG_+Y_SENSOR'', relative to the ``J2000'' inertial frame over two hour period from 2006-04-01 11:00 to 2006-04-01 13:00 (given using ``-b'' and ``-e'') and print this orientation as Euler angles tagged with UTC in ISO-date format. The ``from'' and ``to'' frames are specified using ``-f1'' and ``-t1''. All kernels needed to compute this transformation and convert times are listed in the meta-kernel ``mgs_2006_v01.tm'' from the MGS SPICE PDS data set, specified using the ``-k'' key. Because computing this orientation requires data from MGS solar array CKs and spacecraft CKs, both of which have gaps in coverage, ``-c1'' and ``-c2'' are used to tell the program to look up available coverages for the frames ``MGS_LEFT_SOLAR_ARRAY'' and ``MGS_SPACECRAFT'' associated with data in these CKs and intersect this available coverage with the requested two hour interval to guarantee that the program won't stop from not being able to compute orientation in one of the gaps. The step is set to 1 minute using ``-s 60''. The Euler angles dump report is requested using ``-t dumpea''. The time format for output is set to be the UTC in ISO-date format using

       -f  'YYYY-MM-DDTHR:MN:SC.### ::RND'

The program's output is re-directed to the file ``output.txt'' using the ``>'' shell pipe, with the contents of the file shown using the UNIX ``cat'' command.

       % frmdiff -k  mgs_2006_v01.tm \
                 -f1 J2000 \
                 -t1 MGS_MAG_+Y_SENSOR \
                 -c1 MGS_LEFT_SOLAR_ARRAY \
                 -c2 MGS_SPACECRAFT \
                 -t  dumpea \
                 -f  'YYYY-MM-DDTHR:MN:SC.### ::RND' \
                 -b  2006-04-01 11:00 \
                 -e  2006-04-01 13:00 \
                 -s  60 \
                 > output.txt
       % cat output.txt
       #
       # Sampling of 121 rotations
       #
       #    from 'J2000' (1) to 'MGS_MAG_+Y_SENSOR' (-94051)
       #    computed using
       #
       #       mgs_2006_v01.tm
       #
       # with a 60.000000000000 second (0:00:01:00.000000) step size
       # within the non-continuous (with 1 gaps) time period
       #
       #    from '2006 APR 01 11:01:05.185' TDB (197161265.18566 TDB seco...
       #    to   '2006 APR 01 13:01:05.185' TDB (197168465.18566 TDB seco...
       #
       # Times were generated by TIMOUT using 'YYYY-MM-DDTHR:MN:SC.### ::...
       #
       # angles are shown in radians.
       #
       # time, ang3_about_Z, ang2_about_Y, ang1_about_X
       2006-04-01T11:00:00.000 +1.1187945929621E+00 -1.7969108686644E-01 ...
       2006-04-01T11:01:00.000 +1.1187852723628E+00 -1.7931962082645E-01 ...
       2006-04-01T11:02:00.000 +1.1186582180859E+00 -1.7869508126719E-01 ...
       ...
       2006-04-01T12:57:55.804 +1.1175120633959E+00 -1.7734256227094E-01 ...
       2006-04-01T12:58:55.804 +1.1174237423840E+00 -1.7692771707569E-01 ...
       2006-04-01T13:00:00.000 +1.1173605546240E+00 -1.7633741045076E-01 ...

Top

## Displaying Overlap in Coverage between Two CKs

In this example the program is run to determine the time intervals when both the MRO spacecraft CK ``mro_sc_psp_080408_080414.bc'' and MRO CRISM instrument CK ``mro_crm_psp_080413_080430.bc'' provide coverage and to display the boundaries of these intervals as UTC in ISO DOY format. The CKs are provided as the two primary kernels with other kernels -- the LSK ``naif0009.tls'' and the SCLK ``MRO_SCLKSCET.00027.65536.tsc'', required for time conversions, and the MRO FK ``mro_v13.tf'', defining frames used in the CKs, -- provided using ``-k''. The report is set to the coverage intervals dump using ``-t dumpc'' and the output time format is set to UTC in ISO DOY format using

       -f 'YYYY-DOYTHR:MN:SC.### ::RND'

For runs like this usually both ``from'' frames and both ``to'' frames should be specified using ``-f1'', ``-f2'', ``-t1'', and ``-t2'' and these frames should match the base and structure frames from the CK files (the names of the base and structure frames can be seen in the CK summary produced by the ``BRIEF'' utility program run using the ``-rel -n'' options).

       % frmdiff -k naif0009.tls MRO_SCLKSCET.00027.65536.tsc mro_v13.tf \
                 -f1 MRO_MME_OF_DATE -t1 MRO_SPACECRAFT \
                 -f2 MRO_CRISM_BASE  -t2 MRO_CRISM_ART \
                 -t dumpc -f 'YYYY-DOYTHR:MN:SC.### ::RND' \
                 mro_sc_psp_080408_080414.bc mro_crm_psp_080413_080430.bc
       #
       # Coverage overlap for rotation
       #
       #    from 'MRO_MME_OF_DATE' (-74900) to 'MRO_SPACECRAFT' (-74000)
       #    computed using
       #
       #       naif0009.tls MRO_SCLKSCET.00027.65536.tsc mro_v13.tf
       #       mro_sc_psp_080408_080414.bc
       #
       # and rotation
       #
       #    from 'MRO_CRISM_BASE' (-74011) to 'MRO_CRISM_ART' (-74012)
       #    computed using
       #
       #       naif0009.tls MRO_SCLKSCET.00027.65536.tsc mro_v13.tf
       #       mro_crm_psp_080413_080430.bc
       #
       # with a 0.56599156324219 second (0:00:00:00.565992) step size
       # within the non-continuous (with 22 gaps) time period
       #
       #    from '2008 APR 13 00:29:16.745' TDB (261318556.74553 TDB seco...
       #    to   '2008 APR 13 01:12:03.742' TDB (261321123.74222 TDB seco...
       #
       # Times were generated by TIMOUT using 'YYYY-DOYTHR:MN:SC.### ::RN...
       #
       # interval_start, interval_stop, interval_duration_sec, interval_d...
       2008-104T00:28:11.560 2008-104T00:31:11.564         180.003858    ...
       2008-104T00:43:10.558 2008-104T00:43:14.559           4.001042    ...
       ...
       2008-104T01:10:08.423 2008-104T01:10:12.424           4.000950    ...
       2008-104T01:10:54.556 2008-104T01:10:58.557           4.001042    ...

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## Displaying Gaps in a CK File

In this example the program is run to display the gaps in the CASSINI CK ``09006_09011ra.bc''. The CK is given as the only primary kernel, with all other kernels -- the LSK ``naif0009.tls'' and the SCLK ``cas00130.tsc'', required for time conversions, and the CASSINI FK ``cas_v40.tf'', defining frames used in the CK, -- provided using ``-k''. The report type is set to the coverage gaps dump using ``-t dumpg'' and the output time format is set to UTC in ISO date format using

       -f 'YYYY-MM-DDTHR:MN:SC.### ::RND'

There is no need to specify the ``to'' and ``from'' frames because the program will pick them automatically by examining the CK file.

       % frmdiff -k naif0009.tls cas00130.tsc cas_v40.tf \
                 -t dumpg -f 'YYYY-MM-DDTHR:MN:SC.### ::RND' \
                 09006_09011ra.bc
       #
       # Coverage for rotation
       #
       #    from 'J2000' (1) to 'CASSINI_SC_COORD' (-82000)
       #    computed using
       #
       #       naif0009.tls cas00130.tsc cas_v40.tf
       #       09006_09011ra.bc
       #
       # with a 439.60863577834 second (0:00:07:19.608636) step size
       # within the non-continuous (with 8 gaps) time period
       #
       #    from '2009 JAN 06 00:01:08.565' TDB (284472068.56521 TDB seco...
       #    to   '2009 JAN 11 00:01:05.243' TDB (284904065.24341 TDB seco...
       #
       # Times were generated by TIMOUT using 'YYYY-MM-DDTHR:MN:SC.### ::...
       #
       # gap_start, gap_stop, gap_duration_sec, gap_duration_string
       2009-01-06T13:45:49.779 2009-01-06T13:46:10.029          20.249856...
       2009-01-06T15:15:49.740 2009-01-06T15:16:49.990          60.249572...
       ...
       2009-01-09T15:16:43.897 2009-01-09T15:17:12.147          28.249799...
       2009-01-10T17:18:27.481 2009-01-10T17:18:55.480          27.999801...

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# Miscellaneous Things to Consider

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## ``Apples vs. Oranges''

Even though the program has the flexibility to compare any two transformations -- for example the transformation from the ``J2000'' frame to the ``IAU_MARS'' frame with the transformation from the ``MRO_SPACECRAFT'' frame to the ``MRO_CTX'' frame -- it doesn't mean that such comparisons make sense. In general, it makes sense to compare only transformations that are close to each other and have the same ``from'' frame.

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## Using Euler Angles for Small Rotation Differences

While Euler angles included in the Euler angles dump report (``-t dumpea'') may be one of the more intuitive representations of rotations, in many cases, depending on the rotation order, the angle magnitudes can be large and not representative of the small rotation differences. The total rotation angle provided in the rotation angle and axis report (``-t dumpaa'') is a much more reliable indicator of the difference of two rotations.

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## Single Epoch

Due to the algorithm which the program uses to determine the coverage window, when orientations must be compared at, or an orientation must be sampled at, a certain epoch this epoch must be provided on the command line twice, once using the ``-b'' key and once using the ``-e'' key.

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# References

`1.` Frames Required Reading (frames.req)

`2.` CK Required Reading (ck.req)

`3.` PCK Required Reading (pck.req)

`4.` ROTATIONS Required Reading (rotation.req)

`5.` TIME Required Reading (time.req)

`6.` SCLK Required Reading (sclk.req)

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# Acronyms

AV
  angular velocity

ET
  Ephemeris Time (synonymous to TDB)

SCLK
  Spacecraft CLocK time

TDB
  Barycentric Dynamical Time (synonymous to ET)

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# Appendix 1: Comparison, Sampling and Report Quantity Algorithms

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## Computing Rotation and Angular Velocity Difference

When run in comparison mode the program uses the following SPICE routines to compute the rotation and angular velocity differences at each of the times:

`--` if only rotations (without angular velocities) are to be compared:

                pxform_c ( FROM1, TO1, ET, M1 );
                pxform_c ( FROM2, TO2, ET, M2 );

                mxmt_c   ( M1, M2, MDIFF );

`--` if rotations and angular velocities in the ``from'' frames are to be compared:

                sxform_c ( FROM1, TO1, ET, X1 );
                xf2rav_c ( X1, M1, AV1 );

                sxform_c ( FROM2, TO2, ET, X2 );
                xf2rav_c ( X2, M2, AV2 );

                mxmt_c   ( M1, M2, MDIFF );
                vsub_c   ( AV1, AV2, AVDIFF );

`--` if rotations and angular velocities in the ``to'' frames are to be compared:

                sxform_c ( FROM1, TO1, ET, X1 );
                xf2rav_c ( X1, M1, AV1 );

                sxform_c ( FROM2, TO2, ET, X2 );
                xf2rav_c ( X2, M2, AV2 );

                mxmt_c   ( M1, M2, MDIFF );
                vsub_c   ( AV1, AV2, AVDIFFFR );

                mxv_c    ( M1, AVDIFFFR, AVDIFF );

where FROM1, FROM2, TO1, TO2, and ET are the ``from'' and ``to'' frames of interest and time, MDIFF and AVDIFF are the rotation and angular velocity differences to be reported.

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## Sampling Rotation and Angular Velocity

When run in sampling mode the program uses the following SPICE routines to compute the rotation and angular velocity at each of the times:

`--` if only rotation (without angular) velocity is to be sampled:

                pxform_c ( FROM, TO, ET, MDIFF );

`--` if rotation and angular velocity in the ``from'' frame is to be sampled:

                sxform_c ( FROM, TO, ET, X );
                xf2rav_c ( X, MDIFF, AVDIFF );

`--` if rotation and angular velocity in the ``to'' frame is to be sampled:

                sxform_c ( FROM, TO, ET, X );
                xf2rav_c ( X, MDIFF, AV );

                mxv_c    ( MDIFF, AV, AVDIFF );

where FROM, TO, and ET are the ``from'' and ``to'' frames of interest and time, MDIFF and AVDIFF are the rotation and angular velocity to be reported.

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## Converting Rotation to Angle/Axis

If no ``-t'' is specified, or if ``-t basic'', ``-t stats'', or ``-t dumpaa'' is specified, the program converts MDIFF to the rotation angle and axis using

                raxisa_c ( MDIFF, AXIS, ANGLE );

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## Converting Rotation to SPICE-Style Quaternion

If ``-t dumpqs'' is specified, the program converts MDIFF to the SPICE-style quaternion using

                m2q_c ( MDIFF, QS );

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## Converting Rotation to ``Other''-Style quaternion

If ``-t dumpqo'' is specified, the program converts MDIFF to the ``other''-style quaternion using

                m2q_c ( MDIFF, QS );
                QO[0] = -QS[1];
                QO[1] = -QS[2];
                QO[2] = -QS[3];
                QO[3] =  QS[0];

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## Converting Rotation to Euler Angles

If ``-t'' dumpea is specified, the program converts MDIFF to Euler angles using

                m2eul_c ( MDIFF, AXIS3, AXIS2, AXIS1, ANG3, ANG2, ANG1 );

where AXIS1-3 are either defaults (``Z Y X'') or the axes specified using the ``-o'' key. The axes are ``passed'' as input to M2EUL in the same order as they are listed using ``-o''. For example, for ``-o X Z Y'' M2EUL is called with ``( MDIFF, 1, 3, 2, ...)''.