Point.h

Note

The documentation on this page was automatically extracted from the DOLFIN C++ code and may need to be edited or expanded.

class Point

A Point represents a point in \(\mathbb{R}^3\) with coordinates \(x, y, z,\) or alternatively, a vector in \(\mathbb{R}^3\), supporting standard operations like the norm, distances, scalar and vector products etc.

Point(const double x=0.0, const double y=0.0, const double z=0.0)

Create a point at (x, y, z). Default value (0, 0, 0).

Arguments

x (double)

The x-coordinate.

y (double)

The y-coordinate.

z (double)

The z-coordinate.

Point(std::size_t dim, const double* x)

Create point from array

Arguments

dim (std::size_t)

Dimension of the array.

x (double)

The array to create a Point from.

Point(const Array<double>& x)

Create point from Array

Arguments

x (Array<double>)

Array of coordinates.

Point(const Point& p)

Copy constructor

Arguments

p (Point)

The object to be copied.

double& operator[](std::size_t i)

Return address of coordinate in direction i

Arguments

i (std::size_t)

Direction.

Returns

double

Address of coordinate in the given direction.

double operator[](std::size_t i) const

Return coordinate in direction i

Arguments

i (std::size_t)

Direction.

Returns

double

The coordinate in the given direction.

double x() const

Return x-coordinate

Returns

double

The x-coordinate.

double y() const

Return y-coordinate

Returns

double

The y-coordinate.

double z() const

Return z-coordinate

Returns

double

The z-coordinate.

double* coordinates()

Return coordinate array

Returns

list of doubles

The coordinates.

const double* coordinates() const

Return coordinate array (const. version)

Returns

list of doubles

The coordinates.

Point operator+(const Point& p) const

Compute sum of two points

Point operator-(const Point& p) const

Compute difference of two points

const Point& operator+=(const Point& p)

Add given point

const Point& operator-=(const Point& p)

Subtract given point

Point operator-()

Unary minus

Point operator*(double a) const

Multiplication with scalar

const Point& operator*=(double a)

Incremental multiplication with scalar

Point operator/(double a) const

Division by scalar

const Point& operator/=(double a)

Incremental division by scalar

const Point& operator=(const Point& p)

Assignment operator

double squared_distance(const Point& p) const

Compute squared distance to given point

Arguments

p (Point)

The point to compute distance to.

Returns

double

The squared distance.

Example

Point p1(0, 4, 0);
Point p2(2, 0, 4);
info("%g", p1.squared_distance(p2));

output:

6

double distance(const Point& p) const

Compute distance to given point

Arguments

p (Point)

The point to compute distance to.

Returns

double

The distance.

Example

Point p1(0, 4, 0);
Point p2(2, 0, 4);
info("%g", p1.distance(p2));

output:

6

double norm() const

Compute norm of point representing a vector from the origin

Returns

double

The (Euclidean) norm of the vector from the origin to the point.

Example

Point p(1.0, 2.0, 2.0);
info("%g", p.norm());

output:

3

double squared_norm() const

Compute norm of point representing a vector from the origin

Returns

double

The squared (Euclidean) norm of the vector from the origin of the point.

Example

Point p(1.0, 2.0, 2.0);
info("%g", p.squared_norm());

output:

9

const Point cross(const Point& p) const

Compute cross product with given vector

Arguments

p (Point)

Another point.

Returns

Point

The cross product.

double dot(const Point& p) const

Compute dot product with given vector

Arguments

p (Point)

Another point.

Returns

double

The dot product.

Example

Point p1(1.0, 4.0, 8.0);
Point p2(2.0, 0.0, 0.0);
info("%g", p1.dot(p2));

output:

2

Point rotate(const Point& a, double theta) const

Rotate around a given axis

Arguments

a (Point)

The axis to rotate around. Must be unit length.

theta (_double_)

The rotation angle.

Returns

Point

The rotated point.

std::string str(bool verbose=false) const

Return informal string representation (pretty-print)

Arguments

verbose (bool)

Flag to turn on additional output.

Returns

std::string

An informal representation of the function space.

Point operator*(double a, const Point& p)

Multiplication with scalar