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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@gimp.org>
+ *
+ * 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 3 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, see
+ * <https://www.gnu.org/licenses/>.
+ */
+
+#include "config.h"
+
+#include <glib-object.h>
+
+#include "gimpmath.h"
+
+
+/**
+ * SECTION: gimpmatrix
+ * @title: GimpMatrix
+ * @short_description: Utilities to set up and manipulate 3x3
+ * transformation matrices.
+ * @see_also: #GimpVector2, #GimpVector3, #GimpVector4
+ *
+ * When doing image manipulation you will often need 3x3
+ * transformation matrices that define translation, rotation, scaling,
+ * shearing and arbitrary perspective transformations using a 3x3
+ * matrix. Here you'll find a set of utility functions to set up those
+ * matrices and to perform basic matrix manipulations and tests.
+ *
+ * Each matrix class has a 2 dimensional gdouble coeff member. The
+ * element for row r and column c of the matrix is coeff[r][c].
+ **/
+
+
+#define EPSILON 1e-6
+
+
+static GimpMatrix2 * matrix2_copy (const GimpMatrix2 *matrix);
+
+/**
+ * gimp_matrix2_get_type:
+ *
+ * Reveals the object type
+ *
+ * Returns: the #GType for Matrix2 objects
+ *
+ * Since: 2.4
+ **/
+GType
+gimp_matrix2_get_type (void)
+{
+ static GType matrix_type = 0;
+
+ if (!matrix_type)
+ matrix_type = g_boxed_type_register_static ("GimpMatrix2",
+ (GBoxedCopyFunc) matrix2_copy,
+ (GBoxedFreeFunc) g_free);
+
+ return matrix_type;
+}
+
+
+/*
+ * GIMP_TYPE_PARAM_MATRIX2
+ */
+
+#define GIMP_PARAM_SPEC_MATRIX2(pspec) (G_TYPE_CHECK_INSTANCE_CAST ((pspec), GIMP_TYPE_PARAM_MATRIX2, GimpParamSpecMatrix2))
+
+static void gimp_param_matrix2_class_init (GParamSpecClass *class);
+static void gimp_param_matrix2_init (GParamSpec *pspec);
+static void gimp_param_matrix2_set_default (GParamSpec *pspec,
+ GValue *value);
+static gint gimp_param_matrix2_values_cmp (GParamSpec *pspec,
+ const GValue *value1,
+ const GValue *value2);
+
+typedef struct _GimpParamSpecMatrix2 GimpParamSpecMatrix2;
+
+struct _GimpParamSpecMatrix2
+{
+ GParamSpecBoxed parent_instance;
+
+ GimpMatrix2 default_value;
+};
+
+/**
+ * gimp_param_matrix2_get_type:
+ *
+ * Reveals the object type
+ *
+ * Returns: the #GType for a GimpMatrix2 object
+ *
+ * Since: 2.4
+ **/
+GType
+gimp_param_matrix2_get_type (void)
+{
+ static GType spec_type = 0;
+
+ if (!spec_type)
+ {
+ static const GTypeInfo type_info =
+ {
+ sizeof (GParamSpecClass),
+ NULL, NULL,
+ (GClassInitFunc) gimp_param_matrix2_class_init,
+ NULL, NULL,
+ sizeof (GimpParamSpecMatrix2),
+ 0,
+ (GInstanceInitFunc) gimp_param_matrix2_init
+ };
+
+ spec_type = g_type_register_static (G_TYPE_PARAM_BOXED,
+ "GimpParamMatrix2",
+ &type_info, 0);
+ }
+
+ return spec_type;
+}
+
+static void
+gimp_param_matrix2_class_init (GParamSpecClass *class)
+{
+ class->value_type = GIMP_TYPE_MATRIX2;
+ class->value_set_default = gimp_param_matrix2_set_default;
+ class->values_cmp = gimp_param_matrix2_values_cmp;
+}
+
+static void
+gimp_param_matrix2_init (GParamSpec *pspec)
+{
+ GimpParamSpecMatrix2 *cspec = GIMP_PARAM_SPEC_MATRIX2 (pspec);
+
+ gimp_matrix2_identity (&cspec->default_value);
+}
+
+static void
+gimp_param_matrix2_set_default (GParamSpec *pspec,
+ GValue *value)
+{
+ GimpParamSpecMatrix2 *cspec = GIMP_PARAM_SPEC_MATRIX2 (pspec);
+
+ g_value_set_static_boxed (value, &cspec->default_value);
+}
+
+static gint
+gimp_param_matrix2_values_cmp (GParamSpec *pspec,
+ const GValue *value1,
+ const GValue *value2)
+{
+ GimpMatrix2 *matrix1;
+ GimpMatrix2 *matrix2;
+ gint i, j;
+
+ matrix1 = value1->data[0].v_pointer;
+ matrix2 = value2->data[0].v_pointer;
+
+ /* try to return at least *something*, it's useless anyway... */
+
+ if (! matrix1)
+ return matrix2 != NULL ? -1 : 0;
+ else if (! matrix2)
+ return matrix1 != NULL;
+
+ for (i = 0; i < 2; i++)
+ for (j = 0; j < 2; j++)
+ if (matrix1->coeff[i][j] != matrix2->coeff[i][j])
+ return 1;
+
+ return 0;
+}
+
+/**
+ * gimp_param_spec_matrix2:
+ * @name: Canonical name of the param
+ * @nick: Nickname of the param
+ * @blurb: Brief description of param.
+ * @default_value: Value to use if none is assigned.
+ * @flags: a combination of #GParamFlags
+ *
+ * Creates a param spec to hold a #GimpMatrix2 value.
+ * See g_param_spec_internal() for more information.
+ *
+ * Returns: a newly allocated #GParamSpec instance
+ *
+ * Since: 2.4
+ **/
+GParamSpec *
+gimp_param_spec_matrix2 (const gchar *name,
+ const gchar *nick,
+ const gchar *blurb,
+ const GimpMatrix2 *default_value,
+ GParamFlags flags)
+{
+ GimpParamSpecMatrix2 *cspec;
+
+ g_return_val_if_fail (default_value != NULL, NULL);
+
+ cspec = g_param_spec_internal (GIMP_TYPE_PARAM_MATRIX2,
+ name, nick, blurb, flags);
+
+ cspec->default_value = *default_value;
+
+ return G_PARAM_SPEC (cspec);
+}
+
+
+static GimpMatrix2 *
+matrix2_copy (const GimpMatrix2 *matrix)
+{
+ return (GimpMatrix2 *) g_memdup (matrix, sizeof (GimpMatrix2));
+}
+
+
+/**
+ * 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_matrix2_determinant:
+ * @matrix: The input matrix.
+ *
+ * Calculates the determinant of the given matrix.
+ *
+ * Returns: The determinant.
+ *
+ * Since: 2.10.16
+ */
+
+gdouble
+gimp_matrix2_determinant (const GimpMatrix2 *matrix)
+{
+ return matrix->coeff[0][0] * matrix->coeff[1][1] -
+ matrix->coeff[0][1] * matrix->coeff[1][0];
+}
+
+/**
+ * gimp_matrix2_invert:
+ * @matrix: The matrix that is to be inverted.
+ *
+ * Inverts the given matrix.
+ *
+ * Since: 2.10.16
+ */
+void
+gimp_matrix2_invert (GimpMatrix2 *matrix)
+{
+ gdouble det = gimp_matrix2_determinant (matrix);
+ gdouble temp;
+
+ if (fabs (det) <= EPSILON)
+ return;
+
+ temp = matrix->coeff[0][0];
+
+ matrix->coeff[0][0] = matrix->coeff[1][1] / det;
+ matrix->coeff[0][1] /= -det;
+ matrix->coeff[1][0] /= -det;
+ matrix->coeff[1][1] = temp / det;
+}
+
+/**
+ * gimp_matrix2_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.
+ *
+ * Since: 2.10.16
+ */
+void
+gimp_matrix2_transform_point (const GimpMatrix2 *matrix,
+ gdouble x,
+ gdouble y,
+ gdouble *newx,
+ gdouble *newy)
+{
+ *newx = matrix->coeff[0][0] * x + matrix->coeff[0][1] * y;
+ *newy = matrix->coeff[1][0] * x + matrix->coeff[1][1] * y;
+}
+
+
+static GimpMatrix3 * matrix3_copy (const GimpMatrix3 *matrix);
+
+/**
+ * gimp_matrix3_get_type:
+ *
+ * Reveals the object type
+ *
+ * Returns: the #GType for Matrix3 objects
+ *
+ * Since: 2.8
+ **/
+GType
+gimp_matrix3_get_type (void)
+{
+ static GType matrix_type = 0;
+
+ if (!matrix_type)
+ matrix_type = g_boxed_type_register_static ("GimpMatrix3",
+ (GBoxedCopyFunc) matrix3_copy,
+ (GBoxedFreeFunc) g_free);
+
+ return matrix_type;
+}
+
+
+/*
+ * GIMP_TYPE_PARAM_MATRIX3
+ */
+
+#define GIMP_PARAM_SPEC_MATRIX3(pspec) (G_TYPE_CHECK_INSTANCE_CAST ((pspec), GIMP_TYPE_PARAM_MATRIX3, GimpParamSpecMatrix3))
+
+static void gimp_param_matrix3_class_init (GParamSpecClass *class);
+static void gimp_param_matrix3_init (GParamSpec *pspec);
+static void gimp_param_matrix3_set_default (GParamSpec *pspec,
+ GValue *value);
+static gint gimp_param_matrix3_values_cmp (GParamSpec *pspec,
+ const GValue *value1,
+ const GValue *value2);
+
+typedef struct _GimpParamSpecMatrix3 GimpParamSpecMatrix3;
+
+struct _GimpParamSpecMatrix3
+{
+ GParamSpecBoxed parent_instance;
+
+ GimpMatrix3 default_value;
+};
+
+/**
+ * gimp_param_matrix3_get_type:
+ *
+ * Reveals the object type
+ *
+ * Returns: the #GType for a GimpMatrix3 object
+ *
+ * Since: 2.8
+ **/
+GType
+gimp_param_matrix3_get_type (void)
+{
+ static GType spec_type = 0;
+
+ if (!spec_type)
+ {
+ static const GTypeInfo type_info =
+ {
+ sizeof (GParamSpecClass),
+ NULL, NULL,
+ (GClassInitFunc) gimp_param_matrix3_class_init,
+ NULL, NULL,
+ sizeof (GimpParamSpecMatrix3),
+ 0,
+ (GInstanceInitFunc) gimp_param_matrix3_init
+ };
+
+ spec_type = g_type_register_static (G_TYPE_PARAM_BOXED,
+ "GimpParamMatrix3",
+ &type_info, 0);
+ }
+
+ return spec_type;
+}
+
+static void
+gimp_param_matrix3_class_init (GParamSpecClass *class)
+{
+ class->value_type = GIMP_TYPE_MATRIX3;
+ class->value_set_default = gimp_param_matrix3_set_default;
+ class->values_cmp = gimp_param_matrix3_values_cmp;
+}
+
+static void
+gimp_param_matrix3_init (GParamSpec *pspec)
+{
+ GimpParamSpecMatrix3 *cspec = GIMP_PARAM_SPEC_MATRIX3 (pspec);
+
+ gimp_matrix3_identity (&cspec->default_value);
+}
+
+static void
+gimp_param_matrix3_set_default (GParamSpec *pspec,
+ GValue *value)
+{
+ GimpParamSpecMatrix3 *cspec = GIMP_PARAM_SPEC_MATRIX3 (pspec);
+
+ g_value_set_static_boxed (value, &cspec->default_value);
+}
+
+static gint
+gimp_param_matrix3_values_cmp (GParamSpec *pspec,
+ const GValue *value1,
+ const GValue *value2)
+{
+ GimpMatrix3 *matrix1;
+ GimpMatrix3 *matrix2;
+ gint i, j;
+
+ matrix1 = value1->data[0].v_pointer;
+ matrix2 = value2->data[0].v_pointer;
+
+ /* try to return at least *something*, it's useless anyway... */
+
+ if (! matrix1)
+ return matrix2 != NULL ? -1 : 0;
+ else if (! matrix2)
+ return matrix1 != NULL;
+
+ for (i = 0; i < 3; i++)
+ for (j = 0; j < 3; j++)
+ if (matrix1->coeff[i][j] != matrix2->coeff[i][j])
+ return 1;
+
+ return 0;
+}
+
+/**
+ * gimp_param_spec_matrix3:
+ * @name: Canonical name of the param
+ * @nick: Nickname of the param
+ * @blurb: Brief description of param.
+ * @default_value: Value to use if none is assigned.
+ * @flags: a combination of #GParamFlags
+ *
+ * Creates a param spec to hold a #GimpMatrix3 value.
+ * See g_param_spec_internal() for more information.
+ *
+ * Returns: a newly allocated #GParamSpec instance
+ *
+ * Since: 2.8
+ **/
+GParamSpec *
+gimp_param_spec_matrix3 (const gchar *name,
+ const gchar *nick,
+ const gchar *blurb,
+ const GimpMatrix3 *default_value,
+ GParamFlags flags)
+{
+ GimpParamSpecMatrix3 *cspec;
+
+ cspec = g_param_spec_internal (GIMP_TYPE_PARAM_MATRIX3,
+ name, nick, blurb, flags);
+
+ if (default_value)
+ cspec->default_value = *default_value;
+
+ return G_PARAM_SPEC (cspec);
+}
+
+
+static GimpMatrix3 *
+matrix3_copy (const GimpMatrix3 *matrix)
+{
+ return (GimpMatrix3 *) g_memdup (matrix, sizeof (GimpMatrix3));
+}
+
+
+/**
+ * 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: the 'a' coefficient
+ * @b: the 'b' coefficient
+ * @c: the 'c' coefficient
+ * @d: the 'd' coefficient
+ * @e: the 'e' coefficient
+ * @f: the 'f' coefficient
+ *
+ * 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_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, %FALSE otherwise
+ */
+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;
+}
+
+/**
+ * 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, %FALSE otherwise
+ */
+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_affine:
+ * @matrix: The matrix that is to be tested.
+ *
+ * Checks if the given matrix defines an affine transformation.
+ *
+ * Returns: %TRUE if the matrix defines an affine transformation,
+ * %FALSE otherwise
+ *
+ * Since: 2.4
+ */
+gboolean
+gimp_matrix3_is_affine (const GimpMatrix3 *matrix)
+{
+ return (fabs (matrix->coeff[2][0]) < EPSILON &&
+ fabs (matrix->coeff[2][1]) < EPSILON &&
+ fabs (matrix->coeff[2][2] - 1.0) < EPSILON);
+}
+
+/**
+ * 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, %FALSE otherwise
+ */
+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;
+}
+
+/**
+ * gimp_matrix3_equal:
+ * @matrix1: The first matrix
+ * @matrix2: The second matrix
+ *
+ * Checks if two matrices are equal.
+ *
+ * Returns: %TRUE the matrices are equal, %FALSE otherwise
+ *
+ * Since: 2.10.16
+ */
+gboolean
+gimp_matrix3_equal (const GimpMatrix3 *matrix1,
+ const GimpMatrix3 *matrix2)
+{
+ gint i, j;
+
+ for (i = 0; i < 3; i++)
+ {
+ for (j = 0; j < 3; j++)
+ {
+ if (fabs (matrix1->coeff[i][j] - matrix2->coeff[i][j]) > EPSILON)
+ return FALSE;
+ }
+ }
+
+ return TRUE;
+}
+
+/**
+ * gimp_matrix4_identity:
+ * @matrix: A matrix.
+ *
+ * Sets the matrix to the identity matrix.
+ *
+ * Since: 2.10.16
+ */
+void
+gimp_matrix4_identity (GimpMatrix4 *matrix)
+{
+ gint i, j;
+
+ for (i = 0; i < 4; i++)
+ {
+ for (j = 0; j < 4; j++)
+ matrix->coeff[i][j] = i == j;
+ }
+}
+
+/**
+ * gimp_matrix4_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.
+ *
+ * Since: 2.10.16
+ */
+void
+gimp_matrix4_mult (const GimpMatrix4 *matrix1,
+ GimpMatrix4 *matrix2)
+{
+ GimpMatrix4 result = {};
+ gint i, j, k;
+
+ for (i = 0; i < 4; i++)
+ {
+ for (j = 0; j < 4; j++)
+ {
+ for (k = 0; k < 4; k++)
+ result.coeff[i][j] += matrix1->coeff[i][k] * matrix2->coeff[k][j];
+ }
+ }
+
+ *matrix2 = result;
+}
+
+/**
+ * gimp_matrix4_to_deg:
+ * @matrix:
+ * @a:
+ * @b:
+ * @c:
+ *
+ *
+ **/
+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);
+}
+
+/**
+ * gimp_matrix4_transform_point:
+ * @matrix: The transformation matrix.
+ * @x: The source X coordinate.
+ * @y: The source Y coordinate.
+ * @z: The source Z coordinate.
+ * @newx: The transformed X coordinate.
+ * @newy: The transformed Y coordinate.
+ * @newz: The transformed Z coordinate.
+ *
+ * Transforms a point in 3D as specified by the transformation matrix.
+ *
+ * Returns: The transformed W coordinate.
+ *
+ * Since: 2.10.16
+ */
+gdouble
+gimp_matrix4_transform_point (const GimpMatrix4 *matrix,
+ gdouble x,
+ gdouble y,
+ gdouble z,
+ gdouble *newx,
+ gdouble *newy,
+ gdouble *newz)
+{
+ gdouble neww;
+
+ *newx = matrix->coeff[0][0] * x +
+ matrix->coeff[0][1] * y +
+ matrix->coeff[0][2] * z +
+ matrix->coeff[0][3];
+ *newy = matrix->coeff[1][0] * x +
+ matrix->coeff[1][1] * y +
+ matrix->coeff[1][2] * z +
+ matrix->coeff[1][3];
+ *newz = matrix->coeff[2][0] * x +
+ matrix->coeff[2][1] * y +
+ matrix->coeff[2][2] * z +
+ matrix->coeff[2][3];
+ neww = matrix->coeff[3][0] * x +
+ matrix->coeff[3][1] * y +
+ matrix->coeff[3][2] * z +
+ matrix->coeff[3][3];
+
+ *newx /= neww;
+ *newy /= neww;
+ *newz /= neww;
+
+ return neww;
+}
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