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gimp/libgimpmath/gimpmatrix.c

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/* LIBGIMP - The GIMP Library
* Copyright (C) 1995-1997 Peter Mattis and Spencer Kimball
*
* gimpmatrix.c
* Copyright (C) 1998 Jay Cox <jaycox@earthlink.net>
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Library General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#include "config.h"
#include <glib.h>
#include "gimpmath.h"
#define EPSILON 1e-6
/**
* gimp_matrix2_identity:
* @matrix: A matrix.
*
* Sets the matrix to the identity matrix.
*/
void
gimp_matrix2_identity (GimpMatrix2 *matrix)
{
static const GimpMatrix2 identity = { { { 1.0, 0.0 },
{ 0.0, 1.0 } } };
*matrix = identity;
}
/**
* gimp_matrix2_mult:
* @matrix1: The first input matrix.
* @matrix2: The second input matrix which will be overwritten by the result.
*
* Multiplies two matrices and puts the result into the second one.
*/
void
gimp_matrix2_mult (const GimpMatrix2 *matrix1,
GimpMatrix2 *matrix2)
{
GimpMatrix2 tmp;
tmp.coeff[0][0] = (matrix1->coeff[0][0] * matrix2->coeff[0][0] +
matrix1->coeff[0][1] * matrix2->coeff[1][0]);
tmp.coeff[0][1] = (matrix1->coeff[0][0] * matrix2->coeff[0][1] +
matrix1->coeff[0][1] * matrix2->coeff[1][1]);
tmp.coeff[1][0] = (matrix1->coeff[1][0] * matrix2->coeff[0][0] +
matrix1->coeff[1][1] * matrix2->coeff[1][0]);
tmp.coeff[1][1] = (matrix1->coeff[1][0] * matrix2->coeff[0][1] +
matrix1->coeff[1][1] * matrix2->coeff[1][1]);
*matrix2 = tmp;
}
/**
* gimp_matrix3_identity:
* @matrix: A matrix.
*
* Sets the matrix to the identity matrix.
*/
void
gimp_matrix3_identity (GimpMatrix3 *matrix)
{
static const GimpMatrix3 identity = { { { 1.0, 0.0, 0.0 },
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 } } };
*matrix = identity;
}
/**
* gimp_matrix3_transform_point:
* @matrix: The transformation matrix.
* @x: The source X coordinate.
* @y: The source Y coordinate.
* @newx: The transformed X coordinate.
* @newy: The transformed Y coordinate.
*
* Transforms a point in 2D as specified by the transformation matrix.
*/
void
gimp_matrix3_transform_point (const GimpMatrix3 *matrix,
gdouble x,
gdouble y,
gdouble *newx,
gdouble *newy)
{
gdouble w;
w = matrix->coeff[2][0] * x + matrix->coeff[2][1] * y + matrix->coeff[2][2];
if (w == 0.0)
w = 1.0;
else
w = 1.0/w;
*newx = (matrix->coeff[0][0] * x +
matrix->coeff[0][1] * y +
matrix->coeff[0][2]) * w;
*newy = (matrix->coeff[1][0] * x +
matrix->coeff[1][1] * y +
matrix->coeff[1][2]) * w;
}
/**
* gimp_matrix3_mult:
* @matrix1: The first input matrix.
* @matrix2: The second input matrix which will be overwritten by the result.
*
* Multiplies two matrices and puts the result into the second one.
*/
void
gimp_matrix3_mult (const GimpMatrix3 *matrix1,
GimpMatrix3 *matrix2)
{
gint i, j;
GimpMatrix3 tmp;
gdouble t1, t2, t3;
for (i = 0; i < 3; i++)
{
t1 = matrix1->coeff[i][0];
t2 = matrix1->coeff[i][1];
t3 = matrix1->coeff[i][2];
for (j = 0; j < 3; j++)
{
tmp.coeff[i][j] = t1 * matrix2->coeff[0][j];
tmp.coeff[i][j] += t2 * matrix2->coeff[1][j];
tmp.coeff[i][j] += t3 * matrix2->coeff[2][j];
}
}
*matrix2 = tmp;
}
/**
* gimp_matrix3_translate:
* @matrix: The matrix that is to be translated.
* @x: Translation in X direction.
* @y: Translation in Y direction.
*
* Translates the matrix by x and y.
*/
void
gimp_matrix3_translate (GimpMatrix3 *matrix,
gdouble x,
gdouble y)
{
gdouble g, h, i;
g = matrix->coeff[2][0];
h = matrix->coeff[2][1];
i = matrix->coeff[2][2];
matrix->coeff[0][0] += x * g;
matrix->coeff[0][1] += x * h;
matrix->coeff[0][2] += x * i;
matrix->coeff[1][0] += y * g;
matrix->coeff[1][1] += y * h;
matrix->coeff[1][2] += y * i;
}
/**
* gimp_matrix3_scale:
* @matrix: The matrix that is to be scaled.
* @x: X scale factor.
* @y: Y scale factor.
*
* Scales the matrix by x and y
*/
void
gimp_matrix3_scale (GimpMatrix3 *matrix,
gdouble x,
gdouble y)
{
matrix->coeff[0][0] *= x;
matrix->coeff[0][1] *= x;
matrix->coeff[0][2] *= x;
matrix->coeff[1][0] *= y;
matrix->coeff[1][1] *= y;
matrix->coeff[1][2] *= y;
}
/**
* gimp_matrix3_rotate:
* @matrix: The matrix that is to be rotated.
* @theta: The angle of rotation (in radians).
*
* Rotates the matrix by theta degrees.
*/
void
gimp_matrix3_rotate (GimpMatrix3 *matrix,
gdouble theta)
{
gdouble t1, t2;
gdouble cost, sint;
cost = cos (theta);
sint = sin (theta);
t1 = matrix->coeff[0][0];
t2 = matrix->coeff[1][0];
matrix->coeff[0][0] = cost * t1 - sint * t2;
matrix->coeff[1][0] = sint * t1 + cost * t2;
t1 = matrix->coeff[0][1];
t2 = matrix->coeff[1][1];
matrix->coeff[0][1] = cost * t1 - sint * t2;
matrix->coeff[1][1] = sint * t1 + cost * t2;
t1 = matrix->coeff[0][2];
t2 = matrix->coeff[1][2];
matrix->coeff[0][2] = cost * t1 - sint * t2;
matrix->coeff[1][2] = sint * t1 + cost * t2;
}
/**
* gimp_matrix3_xshear:
* @matrix: The matrix that is to be sheared.
* @amount: X shear amount.
*
* Shears the matrix in the X direction.
*/
void
gimp_matrix3_xshear (GimpMatrix3 *matrix,
gdouble amount)
{
matrix->coeff[0][0] += amount * matrix->coeff[1][0];
matrix->coeff[0][1] += amount * matrix->coeff[1][1];
matrix->coeff[0][2] += amount * matrix->coeff[1][2];
}
/**
* gimp_matrix3_yshear:
* @matrix: The matrix that is to be sheared.
* @amount: Y shear amount.
*
* Shears the matrix in the Y direction.
*/
void
gimp_matrix3_yshear (GimpMatrix3 *matrix,
gdouble amount)
{
matrix->coeff[1][0] += amount * matrix->coeff[0][0];
matrix->coeff[1][1] += amount * matrix->coeff[0][1];
matrix->coeff[1][2] += amount * matrix->coeff[0][2];
}
/**
* gimp_matrix3_affine:
* @matrix: The input matrix.
* @a:
* @b:
* @c:
* @d:
* @e:
* @f:
*
* Applies the affine transformation given by six values to @matrix.
* The six values form define an affine transformation matrix as
* illustrated below:
*
* ( a c e )
* ( b d f )
* ( 0 0 1 )
**/
void
gimp_matrix3_affine (GimpMatrix3 *matrix,
gdouble a,
gdouble b,
gdouble c,
gdouble d,
gdouble e,
gdouble f)
{
GimpMatrix3 affine;
affine.coeff[0][0] = a;
affine.coeff[1][0] = b;
affine.coeff[2][0] = 0.0;
affine.coeff[0][1] = c;
affine.coeff[1][1] = d;
affine.coeff[2][1] = 0.0;
affine.coeff[0][2] = e;
affine.coeff[1][2] = f;
affine.coeff[2][2] = 1.0;
gimp_matrix3_mult (&affine, matrix);
}
/**
* gimp_matrix3_determinant:
* @matrix: The input matrix.
*
* Calculates the determinant of the given matrix.
*
* Returns: The determinant.
*/
gdouble
gimp_matrix3_determinant (const GimpMatrix3 *matrix)
{
gdouble determinant;
determinant = (matrix->coeff[0][0] *
(matrix->coeff[1][1] * matrix->coeff[2][2] -
matrix->coeff[1][2] * matrix->coeff[2][1]));
determinant -= (matrix->coeff[1][0] *
(matrix->coeff[0][1] * matrix->coeff[2][2] -
matrix->coeff[0][2] * matrix->coeff[2][1]));
determinant += (matrix->coeff[2][0] *
(matrix->coeff[0][1] * matrix->coeff[1][2] -
matrix->coeff[0][2] * matrix->coeff[1][1]));
return determinant;
}
/**
* gimp_matrix3_invert:
* @matrix: The matrix that is to be inverted.
*
* Inverts the given matrix.
*/
void
gimp_matrix3_invert (GimpMatrix3 *matrix)
{
GimpMatrix3 inv;
gdouble det;
det = gimp_matrix3_determinant (matrix);
if (det == 0.0)
return;
det = 1.0 / det;
inv.coeff[0][0] = (matrix->coeff[1][1] * matrix->coeff[2][2] -
matrix->coeff[1][2] * matrix->coeff[2][1]) * det;
inv.coeff[1][0] = - (matrix->coeff[1][0] * matrix->coeff[2][2] -
matrix->coeff[1][2] * matrix->coeff[2][0]) * det;
inv.coeff[2][0] = (matrix->coeff[1][0] * matrix->coeff[2][1] -
matrix->coeff[1][1] * matrix->coeff[2][0]) * det;
inv.coeff[0][1] = - (matrix->coeff[0][1] * matrix->coeff[2][2] -
matrix->coeff[0][2] * matrix->coeff[2][1]) * det;
inv.coeff[1][1] = (matrix->coeff[0][0] * matrix->coeff[2][2] -
matrix->coeff[0][2] * matrix->coeff[2][0]) * det;
inv.coeff[2][1] = - (matrix->coeff[0][0] * matrix->coeff[2][1] -
matrix->coeff[0][1] * matrix->coeff[2][0]) * det;
inv.coeff[0][2] = (matrix->coeff[0][1] * matrix->coeff[1][2] -
matrix->coeff[0][2] * matrix->coeff[1][1]) * det;
inv.coeff[1][2] = - (matrix->coeff[0][0] * matrix->coeff[1][2] -
matrix->coeff[0][2] * matrix->coeff[1][0]) * det;
inv.coeff[2][2] = (matrix->coeff[0][0] * matrix->coeff[1][1] -
matrix->coeff[0][1] * matrix->coeff[1][0]) * det;
*matrix = inv;
}
/* functions to test for matrix properties */
/**
* gimp_matrix3_is_diagonal:
* @matrix: The matrix that is to be tested.
*
* Checks if the given matrix is diagonal.
*
* Returns: TRUE if the matrix is diagonal.
*/
gboolean
gimp_matrix3_is_diagonal (const GimpMatrix3 *matrix)
{
gint i, j;
for (i = 0; i < 3; i++)
{
for (j = 0; j < 3; j++)
{
if (i != j && fabs (matrix->coeff[i][j]) > EPSILON)
return FALSE;
}
}
return TRUE;
}
/**
* gimp_matrix3_is_identity:
* @matrix: The matrix that is to be tested.
*
* Checks if the given matrix is the identity matrix.
*
* Returns: TRUE if the matrix is the identity matrix.
*/
gboolean
gimp_matrix3_is_identity (const GimpMatrix3 *matrix)
{
gint i, j;
for (i = 0; i < 3; i++)
{
for (j = 0; j < 3; j++)
{
if (i == j)
{
if (fabs (matrix->coeff[i][j] - 1.0) > EPSILON)
return FALSE;
}
else
{
if (fabs (matrix->coeff[i][j]) > EPSILON)
return FALSE;
}
}
}
return TRUE;
}
/* Check if we'll need to interpolate when applying this matrix.
This function returns TRUE if all entries of the upper left
2x2 matrix are either 0 or 1
*/
/**
* gimp_matrix3_is_simple:
* @matrix: The matrix that is to be tested.
*
* Checks if we'll need to interpolate when applying this matrix as
* a transformation.
*
* Returns: TRUE if all entries of the upper left 2x2 matrix are either
* 0 or 1
*/
gboolean
gimp_matrix3_is_simple (const GimpMatrix3 *matrix)
{
gdouble absm;
gint i, j;
for (i = 0; i < 2; i++)
{
for (j = 0; j < 2; j++)
{
absm = fabs (matrix->coeff[i][j]);
if (absm > EPSILON && fabs (absm - 1.0) > EPSILON)
return FALSE;
}
}
return TRUE;
}
void
gimp_matrix4_to_deg (const GimpMatrix4 *matrix,
gdouble *a,
gdouble *b,
gdouble *c)
{
*a = 180 * (asin (matrix->coeff[1][0]) / G_PI_2);
*b = 180 * (asin (matrix->coeff[2][0]) / G_PI_2);
*c = 180 * (asin (matrix->coeff[2][1]) / G_PI_2);
}
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