Geometry operations

Functions
void	c_plane_normal (const c_plane *pln, double nrm[3])
	Extract a plane normal.
void	c_plane_from_3_points (const double pt1[3], const double pt2[3], const double pt3[3], c_plane *pln)
	Construct a plane through three points.
void	c_plane_from_point_and_normal (const double pt[3], const double nrm[3], c_plane *pln)
	Construct a plane from a point and normal.
void	c_plane_from_points (int n, const double *pts, int ldp, c_plane *pln)
	Fit a plane to point data.
void	c_flip_plane_normal (c_plane *pln)
	Reverse a plane normal and its equation.
void	c_line_from_2_points (const double pt1[3], const double pt2[3], c_line *ln)
	Construct a line through two points.
void	c_line_from_2_planes (const c_plane *p1, const c_plane *p2, c_line *ln)
	Construct the intersection line of two planes.
void	c_line_from_points (int n, const double *pts, int ldp, c_line *ln)
	Fit a line to point data.
void	c_evaluate_line_position (const c_line *ln, double t, double x[3])
	Evaluate a point on a line.
bool	c_is_parallel_vectors (int n, const double *x, const double *y, double tol)
	Test whether two vectors are parallel within a tolerance.
bool	c_is_parallel_lines (const c_line *x, const c_line *y, double tol)
	Test whether two lines are parallel.
bool	c_is_parallel_planes (const c_plane *x, const c_plane *y, double tol)
	Test whether two planes are parallel.
bool	c_is_point_on_plane (const double pt[3], const c_plane *pln, double tol)
	Test whether a point lies on a plane.
bool	c_is_point_on_line (const double pt[3], const c_line *ln, double tol)
	Test whether a point lies on a line.
double	c_nearest_point_on_line (const double pt[3], const c_line *ln)
	Find the parameter of the nearest point on a line.
double	c_point_to_line_distance (const double pt[3], const c_line *ln)
	Compute the distance from a point to a line.
double	c_point_to_plane_distance (const double pt[3], const c_plane *pln)
	Compute the distance from a point to a plane.
void	c_vector_plane_projection (const double x[3], const c_plane *pln, double px[3])
	Project a vector onto a plane.
void	c_point_plane_projection (const double pt[3], const c_plane *pln, double ppt[3])
	Project a point onto a plane.
void	c_plucker_line_from_2_points (const double pt1[3], const double pt2[3], c_plucker_line *ln)
	Construct a Pluecker line through two points.
void	c_plucker_line_from_line (const c_line *src, c_plucker_line *ln)
	Convert a line to Pluecker coordinates.
void	c_plucker_line_from_2_planes (const c_plane *p1, const c_plane *p2, c_plucker_line *ln)
	Construct a Pluecker line from two planes.
void	c_plucker_line_from_array (const double x[6], c_plucker_line *ln)
	Construct a Pluecker line from six coordinates.
void	c_plucker_line_mtx_mult (int n, const double *x, int ldx, const c_plucker_line *ln, double *y)
	Apply a matrix to a Pluecker line.
void	c_plucker_line_to_array (const c_plucker_line *ln, double x[6])
	Convert a Pluecker line to six coordinates.
void	c_line_common_normal (const c_line *ln1, const c_line *ln2, c_line *ln)
	Compute the common normal of two lines.
void	c_do_lines_intersect (const c_line *ln1, const c_line *ln2, bool *intersect, double *t1, double *t2, double tol)
	Determine whether two lines intersect and return their parameters.
void	c_line_from_point_and_vector (const double pt[3], const double v[3], c_line *ln)
	Construct a line from a point and direction.
void	c_poincare_map (int n, const double *x, const double *y, const double *z, const c_plane *pln, int side, int nbuffer, double *xbuffer, double *ybuffer, double *zbuffer, int *nactual)
	Compute a Poincare section map from sampled trajectories.
void	c_poincare_map_ode (c_ode_equations fcn, const double tspan[2], int n, const double *iv, int sample_count, const c_plane *pln, int side, int solver, c_poincare_coordinates coordinates, int nbuffer, double *xbuffer, double *ybuffer, double *zbuffer, int *nactual, void *user_data)
	Compute a Poincare section map by integrating an ODE and intersecting uniformly spaced solution samples with a plane.

Detailed Description

Geometry representations and operations

Function Documentation

c_plane_normal()

void c_plane_normal	(	const c_plane *	pln,
		double	nrm[3]
	)

Extract a plane normal.

Parameters

pln	Plane.
nrm	Output normal vector.

c_plane_from_3_points()

void c_plane_from_3_points	(	const double	pt1[3],
		const double	pt2[3],
		const double	pt3[3],
		c_plane *	pln
	)

Construct a plane through three points.

Parameters

pt1	First point.
pt2	Second point.
pt3	Third point.
pln	Output plane.

c_plane_from_point_and_normal()

void c_plane_from_point_and_normal	(	const double	pt[3],
		const double	nrm[3],
		c_plane *	pln
	)

Construct a plane from a point and normal.

Parameters

pt	Point on plane.
nrm	Plane normal.
pln	Output plane.

c_plane_from_points()

void c_plane_from_points	(	int	n,
		const double *	pts,
		int	ldp,
		c_plane *	pln
	)

Fit a plane to point data.

Parameters

n	Point count.
pts	Point matrix.
ldp	Leading dimension of pts.
pln	Output plane.

c_flip_plane_normal()

void c_flip_plane_normal

(

c_plane *

pln

)

Reverse a plane normal and its equation.

Parameters

pln	Plane updated in place.

c_line_from_2_points()

void c_line_from_2_points	(	const double	pt1[3],
		const double	pt2[3],
		c_line *	ln
	)

Construct a line through two points.

Parameters

pt1	First point.
pt2	Second point.
ln	Output line.

c_line_from_2_planes()

void c_line_from_2_planes	(	const c_plane *	p1,
		const c_plane *	p2,
		c_line *	ln
	)

Construct the intersection line of two planes.

Parameters

p1	First plane.
p2	Second plane.
ln	Output line.

c_line_from_points()

void c_line_from_points	(	int	n,
		const double *	pts,
		int	ldp,
		c_line *	ln
	)

Fit a line to point data.

Parameters

n	Point count.
pts	Point matrix.
ldp	Leading dimension of pts.
ln	Output line.

c_evaluate_line_position()

void c_evaluate_line_position	(	const c_line *	ln,
		double	t,
		double	x[3]
	)

Evaluate a point on a line.

Parameters

ln	Line.
t	Line parameter.
x	Output position.

c_is_parallel_vectors()

bool c_is_parallel_vectors	(	int	n,
		const double *	x,
		const double *	y,
		double	tol
	)

Test whether two vectors are parallel within a tolerance.

Parameters

n	Vector length.
x	First vector.
y	Second vector.
tol	Angular or residual tolerance.

Returns

true when parallel.

c_is_parallel_lines()

bool c_is_parallel_lines	(	const c_line *	x,
		const c_line *	y,
		double	tol
	)

Test whether two lines are parallel.

Parameters

x	First line.
y	Second line.
tol	Tolerance.

Returns

true when parallel.

c_is_parallel_planes()

bool c_is_parallel_planes	(	const c_plane *	x,
		const c_plane *	y,
		double	tol
	)

Test whether two planes are parallel.

Parameters

x	First plane.
y	Second plane.
tol	Tolerance.

Returns

true when parallel.

c_is_point_on_plane()

bool c_is_point_on_plane	(	const double	pt[3],
		const c_plane *	pln,
		double	tol
	)

Test whether a point lies on a plane.

Parameters

pt	Point.
pln	Plane.
tol	Tolerance.

Returns

true when on the plane.

c_is_point_on_line()

bool c_is_point_on_line	(	const double	pt[3],
		const c_line *	ln,
		double	tol
	)

Test whether a point lies on a line.

Parameters

pt	Point.
ln	Line.
tol	Tolerance.

Returns

true when on the line.

c_nearest_point_on_line()

double c_nearest_point_on_line	(	const double	pt[3],
		const c_line *	ln
	)

Find the parameter of the nearest point on a line.

Parameters

pt	Point.
ln	Line.

Returns

Line parameter.

c_point_to_line_distance()

double c_point_to_line_distance	(	const double	pt[3],
		const c_line *	ln
	)

Compute the distance from a point to a line.

Parameters

pt	Point.
ln	Line.

Returns

Distance.

c_point_to_plane_distance()

double c_point_to_plane_distance	(	const double	pt[3],
		const c_plane *	pln
	)

Compute the distance from a point to a plane.

Parameters

pt	Point.
pln	Plane.

Returns

Distance.

c_vector_plane_projection()

void c_vector_plane_projection	(	const double	x[3],
		const c_plane *	pln,
		double	px[3]
	)

Project a vector onto a plane.

Parameters

x	Input vector.
pln	Plane.
px	Output projection.

c_point_plane_projection()

void c_point_plane_projection	(	const double	pt[3],
		const c_plane *	pln,
		double	ppt[3]
	)

Project a point onto a plane.

Parameters

pt	Input point.
pln	Plane.
ppt	Output projected point.

c_plucker_line_from_2_points()

void c_plucker_line_from_2_points	(	const double	pt1[3],
		const double	pt2[3],
		c_plucker_line *	ln
	)

Construct a Pluecker line through two points.

Parameters

pt1	First point.
pt2	Second point.
ln	Output Pluecker line.

c_plucker_line_from_line()

void c_plucker_line_from_line	(	const c_line *	src,
		c_plucker_line *	ln
	)

Convert a line to Pluecker coordinates.

Parameters

src	Input line.
ln	Output Pluecker line.

c_plucker_line_from_2_planes()

void c_plucker_line_from_2_planes	(	const c_plane *	p1,
		const c_plane *	p2,
		c_plucker_line *	ln
	)

Construct a Pluecker line from two planes.

Parameters

p1	First plane.
p2	Second plane.
ln	Output line.

c_plucker_line_from_array()

void c_plucker_line_from_array	(	const double	x[6],
		c_plucker_line *	ln
	)

Construct a Pluecker line from six coordinates.

Parameters

x	Six coordinates.
ln	Output line.

c_plucker_line_mtx_mult()

void c_plucker_line_mtx_mult	(	int	n,
		const double *	x,
		int	ldx,
		const c_plucker_line *	ln,
		double *	y
	)

Apply a matrix to a Pluecker line.

Parameters

n	Matrix row count.
x	Matrix.
ldx	Leading dimension of x.
ln	Pluecker line.
y	Output vector.

c_plucker_line_to_array()

void c_plucker_line_to_array	(	const c_plucker_line *	ln,
		double	x[6]
	)

Convert a Pluecker line to six coordinates.

Parameters

ln	Input line.
x	Output coordinates.

c_line_common_normal()

void c_line_common_normal	(	const c_line *	ln1,
		const c_line *	ln2,
		c_line *	ln
	)

Compute the common normal of two lines.

Parameters

ln1	First line.
ln2	Second line.
ln	Output common normal.

c_do_lines_intersect()

void c_do_lines_intersect	(	const c_line *	ln1,
		const c_line *	ln2,
		bool *	intersect,
		double *	t1,
		double *	t2,
		double	tol
	)

Determine whether two lines intersect and return their parameters.

Parameters

ln1	First line.
ln2	Second line.
intersect	Output intersection flag.
t1	Output parameter on ln1.
t2	Output parameter on ln2.
tol	Tolerance.

c_line_from_point_and_vector()

void c_line_from_point_and_vector	(	const double	pt[3],
		const double	v[3],
		c_line *	ln
	)

Construct a line from a point and direction.

Parameters

pt	Point.
v	Direction vector.
ln	Output line.

c_poincare_map()

void c_poincare_map	(	int	n,
		const double *	x,
		const double *	y,
		const double *	z,
		const c_plane *	pln,
		int	side,
		int	nbuffer,
		double *	xbuffer,
		double *	ybuffer,
		double *	zbuffer,
		int *	nactual
	)

Compute a Poincare section map from sampled trajectories.

Parameters

n	Sample count.
x	X samples.
y	Y samples.
z	Z samples.
pln	Section plane.
side	Section orientation selector.
nbuffer	Buffer capacity.
xbuffer	Output section x values.
ybuffer	Output section y values.
zbuffer	Output section z values.
nactual	Output number of intersections.

c_poincare_map_ode()

void c_poincare_map_ode	(	c_ode_equations	fcn,
		const double	tspan[2],
		int	n,
		const double *	iv,
		int	sample_count,
		const c_plane *	pln,
		int	side,
		int	solver,
		c_poincare_coordinates	coordinates,
		int	nbuffer,
		double *	xbuffer,
		double *	ybuffer,
		double *	zbuffer,
		int *	nactual,
		void *	user_data
	)

Compute a Poincare section map by integrating an ODE and intersecting uniformly spaced solution samples with a plane.

The coordinate callback is held per thread for the duration of the call, so this routine must not be re-entered from within its own callbacks.

Parameters

fcn	ODE callback.
tspan	Increasing start and end times.
n	State dimension. At least 3 if coordinates is NULL.
iv	n-element initial state at tspan[0].
sample_count	Number of uniformly spaced samples across tspan, including both endpoints; at least 2.
pln	Section plane.
side	Section orientation selector.
solver	ODE integration method (e.g. DYN_RUNGE_KUTTA_45).
coordinates	Optional callback mapping each sample onto section coordinates; pass NULL to use the first three state components.
nbuffer	Buffer capacity.
xbuffer	Output section x values.
ybuffer	Output section y values.
zbuffer	Output section z values.
nactual	Output number of intersections stored, at most nbuffer.
user_data	Opaque caller data forwarded to fcn and coordinates.