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:

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:

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:

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:

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:

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