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DEFINITIONS
This source file includes following definitions.
- gdAffineApplyToPointF
- gdAffineInvert
- gdAffineFlip
- gdAffineConcat
- gdAffineIdentity
- gdAffineScale
- gdAffineRotate
- gdAffineShearHorizontal
- gdAffineShearVertical
- gdAffineTranslate
- gdAffineExpansion
- gdAffineRectilinear
- gdAffineEqual
#include "gd.h"
#include <math.h>
#ifndef M_PI
# define M_PI 3.14159265358979323846
#endif
/**
* Title: Matrix
* Group: Affine Matrix
*/
/**
* Function: gdAffineApplyToPointF
* Applies an affine transformation to a point (floating point
* gdPointF)
*
*
* Parameters:
* dst - Where to store the resulting point
* affine - Source Point
* flip_horz - affine matrix
*
* Returns:
* GD_TRUE if the affine is rectilinear or GD_FALSE
*/
int gdAffineApplyToPointF (gdPointFPtr dst, const gdPointFPtr src,
const double affine[6])
{
double x = src->x;
double y = src->y;
x = src->x;
y = src->y;
dst->x = x * affine[0] + y * affine[2] + affine[4];
dst->y = x * affine[1] + y * affine[3] + affine[5];
return GD_TRUE;
}
/**
* Function: gdAffineInvert
* Find the inverse of an affine transformation.
*
* All non-degenerate affine transforms are invertible. Applying the
* inverted matrix will restore the original values. Multiplying <src>
* by <dst> (commutative) will return the identity affine (rounding
* error possible).
*
* Parameters:
* dst - Where to store the resulting affine transform
* src_affine - Original affine matrix
* flip_horz - Whether or not to flip horizontally
* flip_vert - Whether or not to flip vertically
*
* See also:
* <gdAffineIdentity>
*
* Returns:
* GD_TRUE if the affine is rectilinear or GD_FALSE
*/
int gdAffineInvert (double dst[6], const double src[6])
{
double r_det = (src[0] * src[3] - src[1] * src[2]);
if (r_det <= 0.0) {
return GD_FALSE;
}
r_det = 1.0 / r_det;
dst[0] = src[3] * r_det;
dst[1] = -src[1] * r_det;
dst[2] = -src[2] * r_det;
dst[3] = src[0] * r_det;
dst[4] = -src[4] * dst[0] - src[5] * dst[2];
dst[5] = -src[4] * dst[1] - src[5] * dst[3];
return GD_TRUE;
}
/**
* Function: gdAffineFlip
* Flip an affine transformation horizontally or vertically.
*
* Flips the affine transform, giving GD_FALSE for <flip_horz> and
* <flip_vert> will clone the affine matrix. GD_TRUE for both will
* copy a 180° rotation.
*
* Parameters:
* dst - Where to store the resulting affine transform
* src_affine - Original affine matrix
* flip_h - Whether or not to flip horizontally
* flip_v - Whether or not to flip vertically
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineFlip (double dst[6], const double src[6], const int flip_h, const int flip_v)
{
dst[0] = flip_h ? - src[0] : src[0];
dst[1] = flip_h ? - src[1] : src[1];
dst[2] = flip_v ? - src[2] : src[2];
dst[3] = flip_v ? - src[3] : src[3];
dst[4] = flip_h ? - src[4] : src[4];
dst[5] = flip_v ? - src[5] : src[5];
return GD_TRUE;
}
/**
* Function: gdAffineConcat
* Concat (Multiply) two affine transformation matrices.
*
* Concats two affine transforms together, i.e. the result
* will be the equivalent of doing first the transformation m1 and then
* m2. All parameters can be the same matrix (safe to call using
* the same array for all three arguments).
*
* Parameters:
* dst - Where to store the resulting affine transform
* m1 - First affine matrix
* m2 - Second affine matrix
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineConcat (double dst[6], const double m1[6], const double m2[6])
{
double dst0, dst1, dst2, dst3, dst4, dst5;
dst0 = m1[0] * m2[0] + m1[1] * m2[2];
dst1 = m1[0] * m2[1] + m1[1] * m2[3];
dst2 = m1[2] * m2[0] + m1[3] * m2[2];
dst3 = m1[2] * m2[1] + m1[3] * m2[3];
dst4 = m1[4] * m2[0] + m1[5] * m2[2] + m2[4];
dst5 = m1[4] * m2[1] + m1[5] * m2[3] + m2[5];
dst[0] = dst0;
dst[1] = dst1;
dst[2] = dst2;
dst[3] = dst3;
dst[4] = dst4;
dst[5] = dst5;
return GD_TRUE;
}
/**
* Function: gdAffineIdentity
* Set up the identity matrix.
*
* Parameters:
* dst - Where to store the resulting affine transform
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineIdentity (double dst[6])
{
dst[0] = 1;
dst[1] = 0;
dst[2] = 0;
dst[3] = 1;
dst[4] = 0;
dst[5] = 0;
return GD_TRUE;
}
/**
* Function: gdAffineScale
* Set up a scaling matrix.
*
* Parameters:
* scale_x - X scale factor
* scale_y - Y scale factor
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineScale (double dst[6], const double scale_x, const double scale_y)
{
dst[0] = scale_x;
dst[1] = 0;
dst[2] = 0;
dst[3] = scale_y;
dst[4] = 0;
dst[5] = 0;
return GD_TRUE;
}
/**
* Function: gdAffineRotate
* Set up a rotation affine transform.
*
* Like the other angle in libGD, in which increasing y moves
* downward, this is a counterclockwise rotation.
*
* Parameters:
* dst - Where to store the resulting affine transform
* angle - Rotation angle in degrees
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineRotate (double dst[6], const double angle)
{
const double sin_t = sin (angle * M_PI / 180.0);
const double cos_t = cos (angle * M_PI / 180.0);
dst[0] = cos_t;
dst[1] = sin_t;
dst[2] = -sin_t;
dst[3] = cos_t;
dst[4] = 0;
dst[5] = 0;
return GD_TRUE;
}
/**
* Function: gdAffineShearHorizontal
* Set up a horizontal shearing matrix || becomes \\.
*
* Parameters:
* dst - Where to store the resulting affine transform
* angle - Shear angle in degrees
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineShearHorizontal(double dst[6], const double angle)
{
dst[0] = 1;
dst[1] = 0;
dst[2] = tan(angle * M_PI / 180.0);
dst[3] = 1;
dst[4] = 0;
dst[5] = 0;
return GD_TRUE;
}
/**
* Function: gdAffineShearVertical
* Set up a vertical shearing matrix, columns are untouched.
*
* Parameters:
* dst - Where to store the resulting affine transform
* angle - Shear angle in degrees
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineShearVertical(double dst[6], const double angle)
{
dst[0] = 1;
dst[1] = tan(angle * M_PI / 180.0);;
dst[2] = 0;
dst[3] = 1;
dst[4] = 0;
dst[5] = 0;
return GD_TRUE;
}
/**
* Function: gdAffineTranslate
* Set up a translation matrix.
*
* Parameters:
* dst - Where to store the resulting affine transform
* offset_x - Horizontal translation amount
* offset_y - Vertical translation amount
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineTranslate (double dst[6], const double offset_x, const double offset_y)
{
dst[0] = 1;
dst[1] = 0;
dst[2] = 0;
dst[3] = 1;
dst[4] = offset_x;
dst[5] = offset_y;
return GD_TRUE;
}
/**
* gdAffineexpansion: Find the affine's expansion factor.
* @src: The affine transformation.
*
* Finds the expansion factor, i.e. the square root of the factor
* by which the affine transform affects area. In an affine transform
* composed of scaling, rotation, shearing, and translation, returns
* the amount of scaling.
*
* GD_SUCCESS on success or GD_FAILURE
**/
double gdAffineExpansion (const double src[6])
{
return sqrt (fabs (src[0] * src[3] - src[1] * src[2]));
}
/**
* Function: gdAffineRectilinear
* Determines whether the affine transformation is axis aligned. A
* tolerance has been implemented using GD_EPSILON.
*
* Parameters:
* m - The affine transformation
*
* Returns:
* GD_TRUE if the affine is rectilinear or GD_FALSE
*/
int gdAffineRectilinear (const double m[6])
{
return ((fabs (m[1]) < GD_EPSILON && fabs (m[2]) < GD_EPSILON) ||
(fabs (m[0]) < GD_EPSILON && fabs (m[3]) < GD_EPSILON));
}
/**
* Function: gdAffineEqual
* Determines whether two affine transformations are equal. A tolerance
* has been implemented using GD_EPSILON.
*
* Parameters:
* m1 - The first affine transformation
* m2 - The first affine transformation
*
* Returns:
* GD_SUCCESS on success or GD_FAILURE
*/
int gdAffineEqual (const double m1[6], const double m2[6])
{
return (fabs (m1[0] - m2[0]) < GD_EPSILON &&
fabs (m1[1] - m2[1]) < GD_EPSILON &&
fabs (m1[2] - m2[2]) < GD_EPSILON &&
fabs (m1[3] - m2[3]) < GD_EPSILON &&
fabs (m1[4] - m2[4]) < GD_EPSILON &&
fabs (m1[5] - m2[5]) < GD_EPSILON);
}