geomlib/ellipse.h File Reference

GEOMLIB - Ellipses and elliptic arcs. More...

#include "geomlib/curve.h"
#include "geomlib/vector.h"

Go to the source code of this file.

Defines
#define	geom_elliptic_arc_VMT   geom_curve_VMT
#define	geom_elliptic_arc_INIT
Functions
	GEOM_CLASS_HEAD (elliptic_arc, curve)
void	geom_elliptic_arc_create (struct geom_elliptic_arc *arc)
void	geom_elliptic_arc_destroy (struct geom_elliptic_arc *arc)
void	geom_elliptic_arc_after_change (struct geom_elliptic_arc *arc)
void	geom_elliptic_arc_copy (struct geom_elliptic_arc *arc, struct geom_elliptic_arc *src)
void	geom_elliptic_arc_set (struct geom_elliptic_arc *arc, struct geom_point *center, real rotation, real a_radius, real b_radius, real start, real dif)
	Sets elliptic arc from given center point, rotation, radii and endpoints angles.
void	geom_elliptic_arc_set_closed (struct geom_elliptic_arc *arc, struct geom_point *center, real rotation, real a_radius, real b_radius)
	Sets entire ellipse from given center point, rotation and radii.
int	geom_elliptic_arc_set_endpoints (struct geom_elliptic_arc *arc, struct geom_point *start, struct geom_point *end, struct geom_point *mid, real st, real dif, uns flags)
	Sets new endpoints to ellipse or elliptic arc.
int	geom_elliptic_arc_from_foci_major (struct geom_elliptic_arc *arc, struct geom_point *focus1, struct geom_point *focus2, real major)
	Sets the ellipse from 2 foci and major axis.
int	geom_elliptic_arc_from_foci_point (struct geom_elliptic_arc *arc, struct geom_point *focus1, struct geom_point *focus2, struct geom_point *point)
	Sets the ellipse from 2 foci going through given point.
int	geom_elliptic_arc_from_3_points_smallest (struct geom_elliptic_arc *arc, struct geom_point *point1, struct geom_point *point2, struct geom_point *point3)
	Sets the ellipse with smallest area going through 3 given points.
int	geom_elliptic_arc_from_3_points_circle (struct geom_elliptic_arc *arc, struct geom_point *point1, struct geom_point *point2, struct geom_point *point3)
	Sets the ellipse to be circle going through 3 given points.
int	geom_elliptic_arc_from_3_points_rotation_eccentricity (struct geom_elliptic_arc *arc, struct geom_point *point1, struct geom_point *point2, struct geom_point *point3, real rotation, real eccentricity)
	Sets the ellipse from 3 points, rotation and eccentricity.
int	geom_elliptic_arc_from_center_point_circle (struct geom_elliptic_arc *arc, struct geom_point *center, struct geom_point *point)
	Sets the ellipse to be circle with given center and one point.
int	geom_elliptic_arc_from_center_point_rotation_eccentricity (struct geom_elliptic_arc *arc, struct geom_point *center, struct geom_point *point, real rotation, real eccentricity)
	Sets the ellipse with given center, one point, rotation and eccentricity.
real	geom_elliptic_arc_time_to_btime (struct geom_elliptic_arc *arc, struct geom_expansion *expansion, real time)
real	geom_elliptic_arc_btime_to_time (struct geom_elliptic_arc *arc, struct geom_expansion *expansion, real btime)
int	geom_elliptic_arc_expansion_append (struct geom_elliptic_arc *arc, struct geom_fpath *path)
int	geom_elliptic_arc_to_bezier (struct geom_elliptic_arc *arc, struct geom_bezier *bezier)
int	geom_elliptic_arc_conversion_append (struct geom_elliptic_arc *arc, uns flags, struct geom_fpath *result)
int	geom_elliptic_arc_from_arc (struct geom_elliptic_arc *elliptic_arc, struct geom_arc *arc)
	Converts circular arc to elliptic arc.
int	geom_elliptic_arc_to_poly (struct geom_elliptic_arc *arc, real poly[6])
	Converts ellipse to form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
int	geom_elliptic_arc_transform (struct geom_elliptic_arc *arc, struct geom_transform *transform, struct geom_elliptic_arc *result)
	Apply affine transformation to given elliptic arc.
int	geom_elliptic_arc_normalize (struct geom_elliptic_arc *arc)
	Normalize elliptic arc structure.
int	geom_elliptic_arc_point_start (struct geom_elliptic_arc *arc, struct geom_point *result)
	Returns starting point of given elliptic arc.
int	geom_elliptic_arc_point_end (struct geom_elliptic_arc *arc, struct geom_point *result)
	Returns ending point of given elliptic arc.
int	geom_elliptic_arc_points (struct geom_elliptic_arc *arc, struct geom_point *start, struct geom_point *end)
	Returns starting and ending points of given elliptic arc.
int	geom_elliptic_arc_point_at_time (struct geom_elliptic_arc *arc, real time, struct geom_point *result)
	Returns point of given elliptic arc.
int	geom_elliptic_arc_derivation_start (struct geom_elliptic_arc *arc, struct geom_vector *result)
	Returns first derivation in starting point of given elliptic arc.
int	geom_elliptic_arc_derivation_end (struct geom_elliptic_arc *arc, struct geom_vector *result)
	Returns first derivation in ending point of given elliptic arc.
int	geom_elliptic_arc_derivation_at_time (struct geom_elliptic_arc *arc, real time, struct geom_vector *result)
	Returns first derivation in point of given elliptic arc.
int	geom_elliptic_arc_is_closed (struct geom_elliptic_arc UNUSED *arc)
	Returns whether the structure contains entire ellipse.
int	geom_elliptic_arc_is_singular (struct geom_elliptic_arc *arc)
	Returns whether the elliptic arc is singular (zero radius or radii).
real	geom_elliptic_arc_semimajor (struct geom_elliptic_arc *arc)
	Returns semimajor axis of given ellipse.
real	geom_elliptic_arc_semiminor (struct geom_elliptic_arc *arc)
	Returns semiminor axis of given ellipse.
real	geom_elliptic_arc_eccentricity (struct geom_elliptic_arc *arc)
	Returns eccentricity of given ellipse.
real	geom_elliptic_arc_focal_parameter (struct geom_elliptic_arc *arc)
	Returns focal parameter of given ellipse (distance of focus to directrix).
int	geom_elliptic_arc_foci (struct geom_elliptic_arc *arc, struct geom_point *focus1, struct geom_point *focus2)
	Returns foci of given ellipse.
int	geom_elliptic_arc_directrices (struct geom_elliptic_arc *arc, struct geom_point *point1, struct geom_point *point2, struct geom_vector *vector)
	Returns directrices of given ellipse.
real	geom_elliptic_arc_point_error (struct geom_elliptic_arc *arc, struct geom_point *point)
	Returns value near zero for points near the ellipse.
int	geom_elliptic_arc_bbox (struct geom_elliptic_arc *arc, struct geom_rectangle *bbox)

---

Detailed Description

GEOMLIB - Ellipses and elliptic arcs.

See also:

Ellipses and elliptic arcs

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

---

Define Documentation

#define geom_elliptic_arc_INIT

Value: geom_curve_INIT \ \ .time_to_btime = (real (*)(void *, struct geom_expansion *, real)) &geom_elliptic_arc_time_to_btime, \ .btime_to_time = (real (*)(void *, struct geom_expansion *, real)) &geom_elliptic_arc_btime_to_time, \ \ .expansion_append = (int (*)(void *, struct geom_fpath *)) &geom_elliptic_arc_expansion_append, \ .to_bezier = (int (*)(void *, struct geom_bezier *)) &geom_elliptic_arc_to_bezier, \ .conversion_append = (int (*)(void *, uns, struct geom_fpath *)) &geom_elliptic_arc_conversion_append, \

---

Function Documentation

int geom_elliptic_arc_derivation_at_time (  struct geom_elliptic_arc *  arc, real  time, struct geom_vector *  result )

Returns first derivation in point of given elliptic arc. Parameters: arc  Elliptic arc. time  TIME parameter. result  Resulting derivation vector. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_derivation_end (  struct geom_elliptic_arc *  arc, struct geom_vector *  result )

Returns first derivation in ending point of given elliptic arc. Parameters: arc  Elliptic arc. result  Resulting derivation vector. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_derivation_start (  struct geom_elliptic_arc *  arc, struct geom_vector *  result )

Returns first derivation in starting point of given elliptic arc. Parameters: arc  Elliptic arc. result  Resulting derivation vector. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_directrices (  struct geom_elliptic_arc *  arc, struct geom_point *  point1, struct geom_point *  point2, struct geom_vector *  vector )

Returns directrices of given ellipse. Parameters: arc  Ellipse. point1  Rotated point on right directrix (possibly NULL). point2  Rotated point on left directrix (possibly NULL). vertex  Direction vector of directrices, ellipse is to the left of vector from point1 (possibly NULL). Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

real geom_elliptic_arc_eccentricity (  struct geom_elliptic_arc *  arc  )  [inline, static]

Returns eccentricity of given ellipse. Parameters: arc  Ellipse. Return values: finite  Eccentricity (in interval [0, 1]). otherwise  Numeric error.

real geom_elliptic_arc_focal_parameter (  struct geom_elliptic_arc *  arc  )  [inline, static]

Returns focal parameter of given ellipse (distance of focus to directrix). Parameters: arc  Ellipse. Return values: finite  Focal parameter (>=0). otherwise  Numeric error.

int geom_elliptic_arc_foci (  struct geom_elliptic_arc *  arc, struct geom_point *  focus1, struct geom_point *  focus2 )

Returns foci of given ellipse. Parameters: arc  Ellipse. focus1  Rotated right (possibly NULL). focus2  Rotated left focus (possibly NULL). Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_3_points_circle (  struct geom_elliptic_arc *  arc, struct geom_point *  point1, struct geom_point *  point2, struct geom_point *  point3 )

Sets the ellipse to be circle going through 3 given points. Parameters: arc  Resulting ellipse (initialized). point1  First point. point2  Second point. point3  Third point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_3_points_rotation_eccentricity (  struct geom_elliptic_arc *  arc, struct geom_point *  point1, struct geom_point *  point2, struct geom_point *  point3, real  rotation, real  eccentricity )

Sets the ellipse from 3 points, rotation and eccentricity. Parameters: arc  Resulting ellipse (initialized). point1  First point. point2  Second point. point3  Third point. rotation  Rotation of major axis. eccentricity  Ellipse eccentricity. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_3_points_smallest (  struct geom_elliptic_arc *  arc, struct geom_point *  point1, struct geom_point *  point2, struct geom_point *  point3 )

Sets the ellipse with smallest area going through 3 given points. Parameters: arc  Resulting ellipse (initialized). point1  First point. point2  Second point. point3  Third point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_arc (  struct geom_elliptic_arc *  elliptic_arc, struct geom_arc *  arc )

Converts circular arc to elliptic arc. Parameters: elliptic_arc  Resulting elliptic arc. arc  Circular arc to convert. Return values: zero  Always.

int geom_elliptic_arc_from_center_point_circle (  struct geom_elliptic_arc *  arc, struct geom_point *  center, struct geom_point *  point )

Sets the ellipse to be circle with given center and one point. Parameters: arc  Resulting ellipse (initialized). center  Center. point  Point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_center_point_rotation_eccentricity (  struct geom_elliptic_arc *  arc, struct geom_point *  center, struct geom_point *  point, real  rotation, real  eccentricity )

Sets the ellipse with given center, one point, rotation and eccentricity. Parameters: arc  Resulting ellipse (initialized). center  Center. point  Point. rotation  Rotation of major axis. eccentricity  Ellipse eccentricity. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_foci_major (  struct geom_elliptic_arc *  arc, struct geom_point *  focus1, struct geom_point *  focus2, real  major )

Sets the ellipse from 2 foci and major axis. If axis is too short, resulting ellipse is singular. Parameters: arc  Resulting ellipse (initialized). focus1  First focus. focus2  Second focus. major  Length of major axis (>=0). Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_from_foci_point (  struct geom_elliptic_arc *  arc, struct geom_point *  focus1, struct geom_point *  focus2, struct geom_point *  point )

Sets the ellipse from 2 foci going through given point. Parameters: arc  Resulting ellipse (initialized). focus1  First focus. focus2  Second focus. point  Point on resulting ellipse. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_is_closed (  struct geom_elliptic_arc UNUSED *  arc  )  [inline, static]

Returns whether the structure contains entire ellipse. Parameters: arc  Ellipse or elliptic arc. Return values: nonzero  Ellipse. zero  Elliptic arc.

int geom_elliptic_arc_is_singular (  struct geom_elliptic_arc *  arc  )  [inline, static]

Returns whether the elliptic arc is singular (zero radius or radii). Parameters: arc  Elliptic arc. Return values: nonzero  Elliptic arc is singular. zero  Elliptic arc is not singular.

int geom_elliptic_arc_normalize (  struct geom_elliptic_arc *  arc  )

Normalize elliptic arc structure. Input: rotation, a_radius, b_radius, start and dif must be finite Output: rotation in [0, R_PI] a_radius >= b_radius start in [0, R_2PI] dif in [-R_2PI, R_2PI] Parameters: arc  Elliptic arc to normalize. Return values: zero  Always.

int geom_elliptic_arc_point_at_time (  struct geom_elliptic_arc *  arc, real  time, struct geom_point *  result )

Returns point of given elliptic arc. Parameters: arc  Elliptic arc. time  TIME parameter. result  Resulting point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_point_end (  struct geom_elliptic_arc *  arc, struct geom_point *  result )

Returns ending point of given elliptic arc. Parameters: arc  Elliptic arc. result  Resulting ending point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

real geom_elliptic_arc_point_error (  struct geom_elliptic_arc *  arc, struct geom_point *  point )

Returns value near zero for points near the ellipse. Parameters: arc  Ellipse. point  Point to test. Return values: ~zero  Point is near the ellipse. ~nonzero  Point is far from the ellipse. not_finite  Numeric error.

int geom_elliptic_arc_point_start (  struct geom_elliptic_arc *  arc, struct geom_point *  result )

Returns starting point of given elliptic arc. Parameters: arc  Elliptic arc. result  Resulting starting point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_points (  struct geom_elliptic_arc *  arc, struct geom_point *  start, struct geom_point *  end )

Returns starting and ending points of given elliptic arc. Parameters: arc  Elliptic arc. start  Resulting starting point. end  Resulting ending point. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

real geom_elliptic_arc_semimajor (  struct geom_elliptic_arc *  arc  )  [inline, static]

Returns semimajor axis of given ellipse. Parameters: arc  Ellipse. Return values: finite  Semimajor axis.

real geom_elliptic_arc_semiminor (  struct geom_elliptic_arc *  arc  )  [inline, static]

Returns semiminor axis of given ellipse. Parameters: arc  Ellipse. Return values: finite  Semiminor axis.

void geom_elliptic_arc_set (  struct geom_elliptic_arc *  arc, struct geom_point *  center, real  rotation, real  a_radius, real  b_radius, real  start, real  dif )

Sets elliptic arc from given center point, rotation, radii and endpoints angles. Parameters: arc  Resulting elliptic arc (initialized). center  Center point. rotation  CCW rotation around the center point. a_radius  First radius (>=0). b_radius  Second radius (>=0). start  Angle of starting point in unit circle. dif  CCW angles difference in unit circle. Return values: zero  Always.

void geom_elliptic_arc_set_closed (  struct geom_elliptic_arc *  arc, struct geom_point *  center, real  rotation, real  a_radius, real  b_radius )  [inline, static]

Sets entire ellipse from given center point, rotation and radii. Parameters: arc  Resulting elliptic arc (initialized). center  Center point. rotation  CCW rotation around the center point. a_radius  First radius (>=0). b_radius  Second radius (>=0). Return values: zero  Always.

int geom_elliptic_arc_set_endpoints (  struct geom_elliptic_arc *  arc, struct geom_point *  start, struct geom_point *  end, struct geom_point *  mid, real  st, real  dif, uns  flags )

Sets new endpoints to ellipse or elliptic arc. Parameters: arc  Ellipse or elliptic arc. start  Point very near to ellipse (or NULL). end  Point very near to ellipse (or NULL). mid  Point very near to ellipse (or NULL). dif  Angle difference, if needed. flags  Flags describing the arc to select (see GEOM_CONIC_ARC_...). Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_to_poly (  struct geom_elliptic_arc *  arc, real  poly[6] )

Converts ellipse to form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. Parameters: arc  Elliptic arc to convert. poly  Resulting coefficents. Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

int geom_elliptic_arc_transform (  struct geom_elliptic_arc *  arc, struct geom_transform *  transform, struct geom_elliptic_arc *  result )

Apply affine transformation to given elliptic arc. Parameters: arc  Elliptic arc to transform. transform  Affine transformation. result  Resulting elliptic arc (possibly result = arc). Return values: zero  Success. GEOM_ERR_NUMERIC  Numeric error.

---