geom.c File Reference

Implementation of the basic geometric functions. More...

#include "geom.h"
#include "error.h"
#include "defines.h"
#include <math.h>
#include <gsl/gsl_linalg.h>

Functions
boolean	pointLeftOfLine (double px, double py, double x1, double y1, double x2, double y2)
	Determines if a point is at the left of a vector.
boolean	pointRightOfLine (double px, double py, double x1, double y1, double x2, double y2)
	Determines if a point is at the right of a vector.
void	ComputeBoundingBox (unsigned int n, double x, double y, Tinterval ix, Tinterval iy)
	Determines the axis aligned bounding box of a set of points in R^2.
void	ComputeBoundingBox3d (unsigned int n, double x, double y, double z, Tinterval ix, Tinterval iy, Tinterval iz)
	Determines the axis aligned bounding box of a set of points in R^3.
boolean	RectangleCircleClipping (double r2, Tinterval x, Tinterval y, Tinterval x_new, Tinterval y_new)
	Clips a rectangle and a circle.
boolean	BoxSphereClipping (double r2, Tinterval x, Tinterval y, Tinterval z, Tinterval x_new, Tinterval y_new, Tinterval z_new)
	Clips a 3D box and a sphere.
boolean	RectangleParabolaClipping (Tinterval x, double alpha, Tinterval y, Tinterval x_new, Tinterval y_new)
	Clips a 2D box and a scaled parabola.
boolean	BoxSaddleClipping (Tinterval x, Tinterval y, double alpha, Tinterval z, Tinterval x_new, Tinterval y_new, Tinterval z_new)
	Clips a 3D box and a scaled saddle.
void	DefineNormalVector (double v, double n)
	Defines a unitary vector normal to a given vector.
void	CrossProduct (double v1, double v2, double *v3)
	Computes the cross product of two 3d vectors.
double	DotProduct (double v1, double v2)
	Computes the dot product of two 3d vectors.
int	tolerant_SV_decomp (int M, int N, gsl_matrix U, gsl_matrix V, gsl_vector *S)
	Computes the Singular Value Decomposition of a matrix.

Detailed Description

Implementation of the basic geometric functions.

See also:: geom.h.

Definition in file geom.c.

Function Documentation

boolean pointLeftOfLine	(	double	px,
		double	py,
		double	x1,
		double	y1,
		double	x2,
		double	y2
	)

Determines if a 2D point is at the left of a vector in R^2.

Parameters:

	px	X coordinate of the point.
	py	Y coordinate of the point.
	x1	X coordinate of the first point defining the vector.
	y1	Y coordinate of the first point defining the vector.
	x2	X coordinate of the second point defining the vector.
	y2	Y coordinate of the second point defining the vector.

Returns:: TRUE if point at the left of the vector.

See also:: pointRightOfLine

Definition at line 19 of file geom.c.

References ROUNDDOWN, and ROUNDNEAR.

boolean pointRightOfLine	(	double	px,
		double	py,
		double	x1,
		double	y1,
		double	x2,
		double	y2
	)

Determines if a 2D point is at the right of a vector in R^2.

Parameters:

	px	X coordinate of the point.
	py	Y coordinate of the point.
	x1	X coordinate of the first point defining the vector.
	y1	Y coordinate of the first point defining the vector.
	x2	X coordinate of the second point defining the vector.
	y2	Y coordinate of the second point defining the vector.

Returns:: TRUE if point at the right of the vector.

See also:: pointLeftOfLine

Definition at line 35 of file geom.c.

References ROUNDNEAR, and ROUNDUP.

void ComputeBoundingBox	(	unsigned int	n,
		double *	x,
		double *	y,
		Tinterval *	ix,
		Tinterval *	iy
	)

Determines the axis aligned bounding box of a set of points in R^2.

Parameters:

	n	The number of points to be bounded.
	x	Array with the X coordinates of the points.
	y	Array with the Y coordinates of the points.
	ix	Output interval in the X axis.
	iy	Output interval in the Y axis.

Definition at line 54 of file geom.c.

References NewInterval().

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void ComputeBoundingBox3d	(	unsigned int	n,
		double *	x,
		double *	y,
		double *	z,
		Tinterval *	ix,
		Tinterval *	iy,
		Tinterval *	iz
	)

Determines the axis aligned bounding box of a set of points in R^3.

Parameters:

	n	The number of points to be bounded.
	x	Array with the X coordinates of the points.
	y	Array with the Y coordinates of the points.
	z	Array with the Z coordinates of the points.
	ix	Output interval in the X axis.
	iy	Output interval in the Y axis.
	iz	Output interval in the Z axis.

Definition at line 74 of file geom.c.

References NewInterval().

Referenced by NewInPatchJoint().

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boolean RectangleCircleClipping	(	double	r2,
		Tinterval *	x,
		Tinterval *	y,
		Tinterval *	x_new,
		Tinterval *	y_new
	)

Reduces the ranges defining a 2D box so that it is adjusted to a zero centered circle with a given radius.

Parameters:

	r2	Squared radius of the circle.
	x	Interval defining the X axis for the 2D box.
	y	Interval defining the Y axis for the 2D box.
	x_new	Interval defining the X axis of the box after the clipping.
	y_new	Interval defining the Y axis of the box after the clipping.

Returns:: TRUE if the intersection is not empty.

Definition at line 102 of file geom.c.

References Intersection(), IntervalAdd(), IntervalInvert(), IntervalPow(), IntervalSqrt(), NewInterval(), Union(), and ZERO.

Referenced by CropEquation().

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boolean BoxSphereClipping	(	double	r2,
		Tinterval *	x,
		Tinterval *	y,
		Tinterval *	z,
		Tinterval *	x_new,
		Tinterval *	y_new,
		Tinterval *	z_new
	)

Reduces the ranges defining a 3D box so that it is adjusted to a zero centered sphere with a given radius.

Parameters:

	r2	Squared radius of the sphere.
	x	Interval defining the X axis for the 3D box.
	y	Interval defining the Y axis for the 3D box.
	z	Interval defining the Z axis for the 3D box.
	x_new	Interval defining the X axis of the box after the clipping.
	y_new	Interval defining the Y axis of the box after the clipping.
	z_new	Interval defining the Z axis of the box after the clipping.

Returns:: TRUE if the intersection is not empty.

Definition at line 154 of file geom.c.

References Intersection(), IntervalAdd(), IntervalInvert(), IntervalPow(), IntervalSqrt(), NewInterval(), Union(), and ZERO.

Referenced by CropEquation().

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boolean RectangleParabolaClipping	(	Tinterval *	x,
		double	alpha,
		Tinterval *	y,
		Tinterval *	x_new,
		Tinterval *	y_new
	)

Reduces the ranges defining a 2D box so that it is adjusted to a scaled parabola, $\alpha y=x^2$ .

Parameters:

	x	Interval defining the X axis for the 2D box.
	alpha	The scale factor.
	y	Interval defining the Y axis for the 2D box.
	x_new	Interval defining the X axis of the box after the clipping.
	y_new	Interval defining the Y axis of the box after the clipping.

Returns:: TRUE if the intersection is not empty.

Definition at line 224 of file geom.c.

References Intersection(), IntervalInvert(), IntervalPow(), IntervalProduct(), IntervalScale(), IntervalSqrt(), NewInterval(), ROUNDDOWN, ROUNDNEAR, ROUNDUP, and Union().

Referenced by CropEquation().

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boolean BoxSaddleClipping	(	Tinterval *	x,
		Tinterval *	y,
		double	alpha,
		Tinterval *	z,
		Tinterval *	x_new,
		Tinterval *	y_new,
		Tinterval *	z_new
	)

Reduces the ranges defining a 3D box so that it is adjusted to scaled saddle equation, $\alpha z=x y$ .

Parameters:

	x	Interval defining the X axis for the 3D box.
	y	Interval defining the Y axis for the 3D box.
	alpha	The scale factor.
	z	Interval defining the Z axis for the 3D box.
	x_new	Interval defining the X axis of the box after the clipping.
	y_new	Interval defining the Y axis of the box after the clipping.
	z_new	Interval defining the Z axis of the box after the clipping.

Returns:: TRUE if the intersection is not empty.

Definition at line 264 of file geom.c.

References CopyInterval(), Intersection(), IntervalDivision(), IntervalProduct(), IntervalScale(), IsInside(), NewInterval(), ROUNDDOWN, ROUNDNEAR, and ROUNDUP.

Referenced by CropEquation().

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void DefineNormalVector	(	double *	v,
		double *	n
	)

Defines a unitary vector normal to a given vector in R^3. Observe that there is a continous set of normal vectors to a given vector. We just pick one of them.

Parameters:

	v	The output vector.
	n	The reference vector.

Definition at line 313 of file geom.c.

References Error().

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void CrossProduct	(	double *	v1,
		double *	v2,
		double *	v3
	)

Computes the cross product of two 3d vectors.

Parameters:

	v1	First 3d vector.
	v2	Second 3d vector.
	v3	The output 3d vector.

Definition at line 349 of file geom.c.

Referenced by NewInPatchJoint().

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double DotProduct	(	double *	v1,
		double *	v2
	)

Computes the dot product of two 3d vectors.

Parameters:

	v1	First 3d vector.
	v2	Second 3d vector.

Returns:: The dot produt.

Definition at line 362 of file geom.c.

Referenced by NewInPatchJoint().

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int tolerant_SV_decomp	(	int	M,
		int	N,
		gsl_matrix *	U,
		gsl_matrix *	V,
		gsl_vector *	S
	)

Computes the Singular Value Decomposition A = USV^T of a matrix based on the GSL library.

Parameters:

	M	Numer of rows of the U matrix.
	N	Numer of colums of the U matrix.
	U	Matrix that is decomposed. It is also the U-matrix of the decomposition.
	V	V-matrix of the decomposition.
	S	Vector representing the values. of the S Diagonal matrix of the decomposition.

Returns:: 0 if no error is encountered in the SVD.

Definition at line 368 of file geom.c.

geom.c File Reference

Functions

Detailed Description

Function Documentation