Math/Geometry

Math related to geometric calculations. More...

Functions
arma::mat	arl::math::getLineSegment (const arma::vec &p1, const arma::vec &p2, double dlambda)
	Calculates a discrete line segments between two points in the N-dimensional space. The function assumes that the two given points are of the same dimension. More...
bool	arl::math::areCoplanar (const std::vector< KDL::Vector > &point, double epsilon=1e-6)
	Checks if a set of 3D points are cooplannar. More...
bool	arl::math::areCoplanar (const std::vector< Eigen::Vector3d > &point, double epsilon=1e-6)
	Checks if a set of 3D points are cooplannar. More...
void	arl::math::sortCircularOrder (const std::vector< KDL::Vector > &input, std::vector< KDL::Vector > *output)
	Sorts a set of unsorted points in circular ordering. More...
std::vector< Eigen::Vector3d >	arl::math::sortCircularOrder (const std::vector< Eigen::Vector3d > &input)
	Sorts a set of unsorted points in circular ordering. More...
bool	arl::math::isWithinPolygon (const arma::vec &point, const arma::mat &polygon)
	Checks if a point lies within a polygon. More...
double	arl::math::getMinimumDistanceOfPointFromLine (const Eigen::Vector3d &line_point_1, const Eigen::Vector3d &line_point_2, const Eigen::Vector3d &point)
	Calculates the minimum distance of a 3D point from a line which is defined by two 3D points, see [4]. More...

Detailed Description

Math related to geometric calculations.

Function Documentation

bool arl::math::areCoplanar	(	const std::vector< KDL::Vector > &	point,
		double	epsilon = 1e-6
	)

Checks if a set of 3D points are cooplannar.

Epsilon = 0 means zero tolerance to errors. Epsilon = 1 means that an arbitrary number of points will be considered as coplanar.

Parameters

point	The set of points to be tested
epsilon	A param which determines the error tolerance

Returns

True if they are coplaner. False otherwise

Deprecated:

Use arl::math::areCoplanar(const std::vector<Eigen::Vector3d>& point, double epsilon = 1e-6) instead

bool arl::math::areCoplanar	(	const std::vector< Eigen::Vector3d > &	point,
		double	epsilon = 1e-6
	)

Checks if a set of 3D points are cooplannar.

Epsilon = 0 means zero tolerance to errors. Epsilon = 1 means that an arbitrary number of points will be considered as coplanar.

Parameters

point	The set of points to be tested
epsilon	A param which determines the error tolerance

Returns

True if they are coplaner. False otherwise

arma::mat arl::math::getLineSegment	(	const arma::vec &	p1,
		const arma::vec &	p2,
		double	dlambda
	)

Calculates a discrete line segments between two points in the N-dimensional space. The function assumes that the two given points are of the same dimension.

Parameters

p1	The first N-dimensional point (start of line segment)
p2	The second N-dimensional point (end of line segment)
dlambda	The step for the discritization of the line segment

Returns

A MxN matrix with M points of the line segment of N dimension.

double arl::math::getMinimumDistanceOfPointFromLine	(	const Eigen::Vector3d &	line_point_1,
		const Eigen::Vector3d &	line_point_2,
		const Eigen::Vector3d &	point
	)

Calculates the minimum distance of a 3D point from a line which is defined by two 3D points, see [4].

Parameters

line_point_1	The first point defining the line
line_point_2	The second point defining the line
point	The point for finding the distance

Returns

The minumum distance

bool arl::math::isWithinPolygon	(	const arma::vec &	point,
		const arma::mat &	polygon
	)

Checks if a point lies within a polygon.

Parameters

point	The point to check
The	vertices of the polygon. Should be co-planar.

Returns

True if the point lies within the polygon, false otherwise.

Find the normal vector of the plane of the given points

Find the orthonormal basis of the normal vector

Project the point

Project the polygon points

Find the normal vector of the plane of the given points

Find the orthonormal basis of the normal vector

Project the point

Project the polygon points

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void arl::math::sortCircularOrder	(	const std::vector< KDL::Vector > &	input,
		std::vector< KDL::Vector > *	output
	)

Sorts a set of unsorted points in circular ordering.

This method takes the centroid of the points, calculates the vector of each point to the centroid and sort them by using the minimum angle. This method can not guarantee to work with large point clouds with equal minimum angles occur.

Parameters

input	The set of points to be sorted
output	The resulted sorted set of points

Deprecated:

Use arl::math::sortCircularOrder(const std::vector<Eigen::Vector3d>& input) instead

std::vector< Eigen::Vector3d > arl::math::sortCircularOrder

(

const std::vector< Eigen::Vector3d > &

input

)

Sorts a set of unsorted points in circular ordering.

This method takes the centroid of the points, calculates the vector of each point to the centroid and sort them by using the minimum angle. This method can not guarantee to work with large point clouds with equal minimum angles occur.

Parameters

input

The set of points to be sorted

Returns

The resulted sorted set of points