geomlib/conic.h File Reference

GEOMLIB - Handling conic curves and their sections. More...

#include "lib/lib.h"
#include "geomlib/types.h"
#include "geomlib/numeric.h"
#include "geomlib/vector.h"

Go to the source code of this file.

Defines
#define	GEOM_PARABOLIC_ARC_ASSERT(a)
	Makes assertions to test validity of geom_parabolic_arc structure.
#define	GEOM_HYPERBOLIC_ARC_ASSERT(a)
	Makes assertions to test validity of geom_hyperbolic_arc structure.
#define	GEOM_CONIC_ASSERT(a)
	Makes assertions to test validity of geom_conic structure.
Enumerations
enum	geom_conic_arc_type {   GEOM_CONIC_ARC_START_ENTIRE, GEOM_CONIC_ARC_START_DIF, GEOM_CONIC_ARC_POINT_ENTIRE, GEOM_CONIC_ARC_POINT_DIF,   GEOM_CONIC_ARC_CCW, GEOM_CONIC_ARC_CW, GEOM_CONIC_ARC_SMALLER, GEOM_CONIC_ARC_BIGGER,   GEOM_CONIC_ARC_MIDDLE, GEOM_CONIC_ARC_OPPOSITE, GEOM_CONIC_ARC_ENTIRE, GEOM_CONIC_ARC_MAX,   GEOM_CONIC_ARC_0P = GEOM_CONIC_ARC_START_DIF, GEOM_CONIC_ARC_1P = GEOM_CONIC_ARC_POINT_DIF, GEOM_CONIC_ARC_2P = GEOM_CONIC_ARC_BIGGER, GEOM_CONIC_ARC_3P = GEOM_CONIC_ARC_OPPOSITE }
Functions
int	geom_parabolic_arc_valid (const struct geom_parabolic_arc *arc)
	Test validity of geom_parabolic_arc structure.
void	geom_parabolic_arc_dump (const struct geom_parabolic_arc *arc)
	Dumps geom_parabolic_arc structure data.
void	geom_parabolic_arc_set (struct geom_parabolic_arc *arc, const struct geom_point *center, const real rotation, const real distance, const real start, const real end)
	Initialize parabolic arc.
void	geom_parabolic_arc_set_unit (struct geom_parabolic_arc *arc, const struct geom_point *center, const real rotation, const real distance)
	Initialize "unit" parabolic arc.
int	geom_parabolic_arc_normalize (struct geom_parabolic_arc *arc)
	Normalize parabolic arc structure. Rotation angle is aligned to [0, 2 * PI].
int	geom_parabolic_arc_set_endpoints (struct geom_parabolic_arc *arc, const struct geom_point *start, const struct geom_point *end)
	Sets parabolic arc endpoints. Given points should be near the parabola.
int	geom_parabolic_arc_point_at (const struct geom_parabolic_arc *arc, const real time, struct geom_point *point)
	Returns point on parabola for given parameter (see parabola in parametric form).
int	geom_parabolic_arc_focus (const struct geom_parabolic_arc *arc, struct geom_point *focus)
	Compute focus point of given parabola.
int	geom_parabolic_arc_directrix (const struct geom_parabolic_arc *arc, struct geom_point *point, struct geom_vector *vector)
	Compute directrix of given parabola.
real	geom_parabolic_arc_focal_parameter (const struct geom_parabolic_arc *arc)
	Compute focal parameter of given parabola (distance of focus to directrix).
real	geom_parabolic_arc_latus_rectum (const struct geom_parabolic_arc *arc)
	Compute latus rectum of given parabola.
int	geom_parabolic_arc_to_poly (const struct geom_parabolic_arc *arc, real *poly)
	Converts parabola to form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
int	geom_parabolic_arc_to_bezier (const struct geom_parabolic_arc *arc, struct geom_bezier *bezier)
	Converts parabolic arc to single bezier curve.
int	geom_parabolic_arc_to_path (const struct geom_parabolic_arc *arc, struct geom_path *path)
	Converts parabolic arc to single bezier curve and adds it to end of given path.
int	geom_hyperbolic_arc_valid (const struct geom_hyperbolic_arc *arc)
	Test validity of geom_hyperbolic_arc structure.
void	geom_hyperbolic_arc_dump (const struct geom_hyperbolic_arc *arc)
	Dumps geom_hyperbolic_arc structure data.
void	geom_hyperbolic_arc_set (struct geom_hyperbolic_arc *arc, const struct geom_point *center, const real rotation, const real major, const real minor, const real start, const real end)
	Initialize hyperbolic arc.
void	geom_hyperbolic_arc_set_unit (struct geom_hyperbolic_arc *arc, const struct geom_point *center, const real rotation, const real major, const real minor)
	Initialize "unit" hyperbolic arc.
int	geom_hyperbolic_arc_normalize (struct geom_hyperbolic_arc *arc)
	Normalize hyperbolic arc structure. Rotation angle is aligned to [0, 2 * PI].
int	geom_hyperbolic_arc_set_endpoints (struct geom_hyperbolic_arc *arc, const struct geom_point *start, const struct geom_point *end)
	Sets hyperbolic arc endpoints. Given points should be near one branch of hyperbola.
int	geom_hyperbolic_arc_point_at (const struct geom_hyperbolic_arc *arc, const real time, struct geom_point *point)
	Returns point on hyperbola for given parameter (see hyperbola in parametric form).
int	geom_hyperbolic_arc_to_poly (const struct geom_hyperbolic_arc *arc, real *poly)
	Converts hyperbola to form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
int	geom_hyperbolic_arc_to_bezier (const struct geom_hyperbolic_arc *arc, struct geom_bezier *bezier)
	Converts hyperbolic arc to single bezier curve.
int	geom_hyperbolic_arc_to_path (const struct geom_hyperbolic_arc *arc, struct geom_path *path)
	Converts hyperbolic arc to single bezier curve and adds it to end of given path.
int	geom_conic_valid (struct geom_conic *conic)
	Test validity of geom_conic structure.
void	geom_conic_dump (struct geom_conic *conic)
	Dumps geom_conic structure data.
int	geom_conic_to_poly (struct geom_conic *conic, real *poly)
	Converts conic to form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
int	geom_conic_to_bezier (struct geom_conic *conic, struct geom_bezier *bezier)
	Converts conic to single bezier curve.
int	geom_conic_to_path (struct geom_conic *conic, struct geom_path *path)
	Converts conic to list of bezier curves and adds them to end of given path.
int	geom_conic_from_poly (struct geom_conic *conic, const real *poly)
	Convers form AX^2 + Bxy + Cy^2 + Dx + Ey + F = 0 to conic curve.
int	geom_conic_from_5_points (struct geom_conic *conic, const struct geom_point *points)
	Find conic containing 5 given points.
int	geom_conic_from_rotation_and_4_points (struct geom_conic *conic, const real rotation, const struct geom_point *points)
	Find conic containing 4 given points and with axis in given angle.
int	geom_conic_from_2_tangents_and_point (struct geom_conic *conic, const real *angles, const struct geom_point *points)
	Finds conic for 3 given points and 2 tangential angles in first 2 of them.

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Detailed Description

GEOMLIB - Handling conic curves and their sections.

Copyright (c) 2004-2005 The VRR Team <vrr@ucw.cz> This program is distributed under GNU General Public License, see COPYING.

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Define Documentation

#define GEOM_CONIC_ASSERT (  a   )

Value: do{ \ GEOM_BASSERT((a) != NULL); \ switch ((a)->type) { \ case GEOM_CONIC_PARABOLIC_ARC: GEOM_PARABOLIC_ARC_ASSERT(&(a)->data.parabolic_arc); break; \ case GEOM_CONIC_ARC: GEOM_ARC_ASSERT(&(a)->data.arc); break; \ case GEOM_CONIC_ELLIPTIC_ARC: GEOM_ELLIPTIC_ARC_ASSERT(&(a)->data.elliptic_arc); break; \ case GEOM_CONIC_HYPERBOLIC_ARC: GEOM_HYPERBOLIC_ARC_ASSERT(&(a)->data.hyperbolic_arc); break; \ default: GEOM_BASSERT(0); \ } \ }while(0) Makes assertions to test validity of geom_conic structure. Parameters: a  Pointer to geom_conic structure.

#define GEOM_HYPERBOLIC_ARC_ASSERT (  a   )

Value: do{ \ GEOM_BASSERT((a) != NULL); \ GEOM_POINT_ASSERT(&(a)->center); \ GEOM_BASSERT(isfinite((a)->rotation)); \ GEOM_BASSERT(isfinite((a)->major)); \ GEOM_BASSERT((a)->major >= 0); \ GEOM_BASSERT(isfinite((a)->minor)); \ GEOM_BASSERT((a)->minor >= 0); \ GEOM_BASSERT(isfinite((a)->start)); \ GEOM_BASSERT(isfinite((a)->end)); \ }while(0) Makes assertions to test validity of geom_hyperbolic_arc structure. Parameters: a  Pointer to geom_hyperbolic_arc structure.

#define GEOM_PARABOLIC_ARC_ASSERT (  a   )

Value: do{ \ GEOM_BASSERT((a) != NULL); \ GEOM_POINT_ASSERT(&(a)->center); \ GEOM_BASSERT(isfinite((a)->rotation)); \ GEOM_BASSERT(isfinite((a)->distance)); \ GEOM_BASSERT((a)->distance >= 0); \ GEOM_BASSERT(isfinite((a)->start)); \ GEOM_BASSERT(isfinite((a)->end)); \ }while(0) Makes assertions to test validity of geom_parabolic_arc structure. Parameters: a  Pointer to geom_parabolic_arc structure.

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Function Documentation

void geom_conic_dump (  struct geom_conic *  conic  )

Dumps geom_conic structure data. Parameters: conic  Pointer to geom_conic structure (could has invalid data).

int geom_conic_from_2_tangents_and_point (  struct geom_conic *  conic, const real *  angles, const struct geom_point *  points )

Finds conic for 3 given points and 2 tangential angles in first 2 of them. Parameters: conic  Resulting Conic. angles  Array of 2 angles. points  Array of 3 points. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error. GEOM_ERR_CONIC_DEGENERATED  Degenerated case of conic. GEOM_ERR_CONIC_AMBIGUOUS  More solutions.

int geom_conic_from_5_points (  struct geom_conic *  conic, const struct geom_point *  points )

Find conic containing 5 given points. Parameters: conic  Resulting conic. points  Array of 5 points. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error. GEOM_ERR_CONIC_DEGENERATED  Degenerated case of conic. GEOM_ERR_CONIC_AMBIGUOUS  More solutions.

int geom_conic_from_poly (  struct geom_conic *  conic, const real *  poly )

Convers form AX^2 + Bxy + Cy^2 + Dx + Ey + F = 0 to conic curve. Parameters: conic  Resulting conic. poly  Coefficients to convert (A, B, C, D, E, F). Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error. GEOM_ERR_CONIC_DEGENERATED  Degenerated case of conic.

int geom_conic_from_rotation_and_4_points (  struct geom_conic *  conic, const real  rotation, const struct geom_point *  points )

Find conic containing 4 given points and with axis in given angle. Parameters: conic  Resulting Conic. rotation  Angle of one axis (periode = PI / 2). points  Array of 4 points. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error. GEOM_ERR_CONIC_DEGENERATED  Degenerated case of conic. GEOM_ERR_CONIC_AMBIGUOUS  More solutions.

int geom_conic_to_bezier (  struct geom_conic *  conic, struct geom_bezier *  bezier )

Converts conic to single bezier curve. Parameters: arc  Conic to convert. bezier  Resulting bezier curve. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error. GEOM_ERR_CONIC_TOO_LONG  Arc or elliptic arc angle too big.

int geom_conic_to_path (  struct geom_conic *  conic, struct geom_path *  path )

Converts conic to list of bezier curves and adds them to end of given path. Parameters: arc  Conic to convert. path  Resulting path. Return values: >0  Success, number of beziers added. GEOM_ERR_NUMERIC  Numeric error. GEOM_ERR_CONIC_TOO_LONG  Arc or elliptic arc angle too big.

int geom_conic_to_poly (  struct geom_conic *  conic, real *  poly )

Converts conic to form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. Parameters: arc  Conic to convert. poly  Resulting coefficients (A, B, C, D, E, F). Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_conic_valid (  struct geom_conic *  conic  )

Test validity of geom_conic structure. Parameters: conic  Pointer to geom_conic structure. Return values: nonzero  Structure is valid. zero  Structure is invalid.

void geom_hyperbolic_arc_dump (  const struct geom_hyperbolic_arc *  arc  )

Dumps geom_hyperbolic_arc structure data. Parameters: arc  Pointer to geom_hyperbolic_arc structure (could has invalid data).

int geom_hyperbolic_arc_normalize (  struct geom_hyperbolic_arc *  arc  )

Normalize hyperbolic arc structure. Rotation angle is aligned to [0, 2 * PI]. Parameters: arc  Hyperbolic arc to normalize. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_hyperbolic_arc_point_at (  const struct geom_hyperbolic_arc *  arc, const real  time, struct geom_point *  point )

Returns point on hyperbola for given parameter (see hyperbola in parametric form). Parameters: arc  Hyperbola. time  Finite parameter. point  Resulting point. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

void geom_hyperbolic_arc_set (  struct geom_hyperbolic_arc *  arc, const struct geom_point *  center, const real  rotation, const real  major, const real  minor, const real  start, const real  end )

Initialize hyperbolic arc. Parameters: arc  Resulting hyperbolic arc. center  Center point. rotation  Rotation around the center point (CCW in radians). major  Semimajor axis (major >= 0). minor  Semiminor axis (minor >= 0). start  Parameter of hyperbolic arc starting point (-1 for entire hyperbola). end  Parameter of hyperbolic arc ending point (+1 for entire hyperbola).

int geom_hyperbolic_arc_set_endpoints (  struct geom_hyperbolic_arc *  arc, const struct geom_point *  start, const struct geom_point *  end )

Sets hyperbolic arc endpoints. Given points should be near one branch of hyperbola. Parameters: arc  Hyperbolic arc structure to change. start  Starting point. end  Ending point. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

void geom_hyperbolic_arc_set_unit (  struct geom_hyperbolic_arc *  arc, const struct geom_point *  center, const real  rotation, const real  major, const real  minor )  [inline, static]

Initialize "unit" hyperbolic arc. Parameters: arc  Resulting hyperbola. center  Center point. rotation  Rotation around the center point (CCW in radians). major  Semimajor axis (major >= 0). minor  Semiminor axis (minor >= 0).

int geom_hyperbolic_arc_to_bezier (  const struct geom_hyperbolic_arc *  arc, struct geom_bezier *  bezier )

Converts hyperbolic arc to single bezier curve. Parameters: arc  Hyperbolic arc to convert. bezier  Resulting bezier curve. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_hyperbolic_arc_to_path (  const struct geom_hyperbolic_arc *  arc, struct geom_path *  path )

Converts hyperbolic arc to single bezier curve and adds it to end of given path. Parameters: arc  Hyperbolic arc to convert. path  Resulting path. Return values: 1  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_hyperbolic_arc_to_poly (  const struct geom_hyperbolic_arc *  arc, real *  poly )

Converts hyperbola to form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. Parameters: arc  Hyperbola to convert. poly  Resulting coefficients (A, B, C, D, E, F). Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_hyperbolic_arc_valid (  const struct geom_hyperbolic_arc *  arc  )

Test validity of geom_hyperbolic_arc structure. Parameters: arc  Pointer to geom_hyperbolic_arc structure. Return values: nonzero  Structure is valid. zero  Structure is invalid.

int geom_parabolic_arc_directrix (  const struct geom_parabolic_arc *  arc, struct geom_point *  point, struct geom_vector *  vector )

Compute directrix of given parabola. Parameters: arc  Parabolic arc. point  Resulting point on parabola directrix (nearest to focus). vector  Line direction vector (unit, parabola is to the left of this vector). Return values: 0  Success (always, if point = NULL). GEOM_ERR_NUMERIC  Numeric error.

void geom_parabolic_arc_dump (  const struct geom_parabolic_arc *  arc  )

Dumps geom_parabolic_arc structure data. Parameters: arc  Pointer to geom_parabolic_arc structure (could has invalid data).

real geom_parabolic_arc_focal_parameter (  const struct geom_parabolic_arc *  arc  )  [inline, static]

Compute focal parameter of given parabola (distance of focus to directrix). Parameters: arc  Parabolic arc. Returns: Focal parameter (infinite for numeric overflow).

int geom_parabolic_arc_focus (  const struct geom_parabolic_arc *  arc, struct geom_point *  focus )

Compute focus point of given parabola. Parameters: arc  Parabolic arc. focus  Resulting parabola focus. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

real geom_parabolic_arc_latus_rectum (  const struct geom_parabolic_arc *  arc  )  [inline, static]

Compute latus rectum of given parabola. Parameters: arc  Parabolic arc. Returns: Latus rectum (infinite for numeric overflow).

int geom_parabolic_arc_normalize (  struct geom_parabolic_arc *  arc  )

Normalize parabolic arc structure. Rotation angle is aligned to [0, 2 * PI]. Parameters: arc  Parabolic arc to normalize. Return values: 0  Always.

int geom_parabolic_arc_point_at (  const struct geom_parabolic_arc *  arc, const real  time, struct geom_point *  point )

Returns point on parabola for given parameter (see parabola in parametric form). Parameters: arc  Parabolic arc. time  Finite parameter. point  Resulting point. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

void geom_parabolic_arc_set (  struct geom_parabolic_arc *  arc, const struct geom_point *  center, const real  rotation, const real  distance, const real  start, const real  end )

Initialize parabolic arc. Parameters: arc  Resulting parabolic arc. center  Center point. rotation  Rotation around the center point (CCW in radians). distance  Distance of center point to parabola focus and directrix (distance >= 0). start  Parameter of parabolic arc starting point. end  Parameter of parabolic arc ending point.

int geom_parabolic_arc_set_endpoints (  struct geom_parabolic_arc *  arc, const struct geom_point *  start, const struct geom_point *  end )

Sets parabolic arc endpoints. Given points should be near the parabola. Parameters: arc  Parabolic arc structure to change. start  Starting point. end  Ending point. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

void geom_parabolic_arc_set_unit (  struct geom_parabolic_arc *  arc, const struct geom_point *  center, const real  rotation, const real  distance )  [inline, static]

Initialize "unit" parabolic arc. Parameters: arc  Resulting parabola. center  Center point. rotation  Rotation around the center point (CCW in radians). distance  Distance of center point to parabola focus and directrix (distance >= 0).

int geom_parabolic_arc_to_bezier (  const struct geom_parabolic_arc *  arc, struct geom_bezier *  bezier )

Converts parabolic arc to single bezier curve. Parameters: arc  Parabolic arc to convert. bezier  Resulting bezier curve. Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_parabolic_arc_to_path (  const struct geom_parabolic_arc *  arc, struct geom_path *  path )

Converts parabolic arc to single bezier curve and adds it to end of given path. Parameters: arc  Parabolic arc to convert. path  Resulting path. Return values: 1  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_parabolic_arc_to_poly (  const struct geom_parabolic_arc *  arc, real *  poly )

Converts parabola to form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. Parameters: arc  Parabola to convert. poly  Resulting coefficients (A, B, C, D, E, F). Return values: 0  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_parabolic_arc_valid (  const struct geom_parabolic_arc *  arc  )

Test validity of geom_parabolic_arc structure. Parameters: arc  Pointer to geom_parabolic_arc structure. Return values: nonzero  Structure is valid. zero  Structure is invalid.

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