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PIKApp/libpikamath/pikamatrix.c

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/* LIBPIKA - The PIKA Library
* Copyright (C) 1995-1997 Peter Mattis and Spencer Kimball
*
* pikamatrix.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 "pikamath.h"
/**
* SECTION: pikamatrix
* @title: PikaMatrix
* @short_description: Utilities to set up and manipulate 3x3
* transformation matrices.
* @see_also: #PikaVector2, #PikaVector3, #PikaVector4
*
* 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 PikaMatrix2 * matrix2_copy (const PikaMatrix2 *matrix);
G_DEFINE_BOXED_TYPE (PikaMatrix2, pika_matrix2, matrix2_copy, g_free)
/*
* PIKA_TYPE_PARAM_MATRIX2
*/
#define PIKA_PARAM_SPEC_MATRIX2(pspec) (G_TYPE_CHECK_INSTANCE_CAST ((pspec), PIKA_TYPE_PARAM_MATRIX2, PikaParamSpecMatrix2))
static void pika_param_matrix2_class_init (GParamSpecClass *class);
static void pika_param_matrix2_init (GParamSpec *pspec);
static void pika_param_matrix2_set_default (GParamSpec *pspec,
GValue *value);
static gint pika_param_matrix2_values_cmp (GParamSpec *pspec,
const GValue *value1,
const GValue *value2);
typedef struct _PikaParamSpecMatrix2 PikaParamSpecMatrix2;
struct _PikaParamSpecMatrix2
{
GParamSpecBoxed parent_instance;
PikaMatrix2 default_value;
};
/**
* pika_param_matrix2_get_type:
*
* Reveals the object type
*
* Returns: the #GType for a PikaMatrix2 object
*
* Since: 2.4
**/
GType
pika_param_matrix2_get_type (void)
{
static GType spec_type = 0;
if (!spec_type)
{
static const GTypeInfo type_info =
{
sizeof (GParamSpecClass),
NULL, NULL,
(GClassInitFunc) pika_param_matrix2_class_init,
NULL, NULL,
sizeof (PikaParamSpecMatrix2),
0,
(GInstanceInitFunc) pika_param_matrix2_init
};
spec_type = g_type_register_static (G_TYPE_PARAM_BOXED,
"PikaParamMatrix2",
&type_info, 0);
}
return spec_type;
}
static void
pika_param_matrix2_class_init (GParamSpecClass *class)
{
class->value_type = PIKA_TYPE_MATRIX2;
class->value_set_default = pika_param_matrix2_set_default;
class->values_cmp = pika_param_matrix2_values_cmp;
}
static void
pika_param_matrix2_init (GParamSpec *pspec)
{
PikaParamSpecMatrix2 *cspec = PIKA_PARAM_SPEC_MATRIX2 (pspec);
pika_matrix2_identity (&cspec->default_value);
}
static void
pika_param_matrix2_set_default (GParamSpec *pspec,
GValue *value)
{
PikaParamSpecMatrix2 *cspec = PIKA_PARAM_SPEC_MATRIX2 (pspec);
g_value_set_static_boxed (value, &cspec->default_value);
}
static gint
pika_param_matrix2_values_cmp (GParamSpec *pspec,
const GValue *value1,
const GValue *value2)
{
PikaMatrix2 *matrix1;
PikaMatrix2 *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;
}
/**
* pika_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 #PikaMatrix2 value.
* See g_param_spec_internal() for more information.
*
* Returns: (transfer full): a newly allocated #GParamSpec instance
*
* Since: 2.4
**/
GParamSpec *
pika_param_spec_matrix2 (const gchar *name,
const gchar *nick,
const gchar *blurb,
const PikaMatrix2 *default_value,
GParamFlags flags)
{
PikaParamSpecMatrix2 *cspec;
g_return_val_if_fail (default_value != NULL, NULL);
cspec = g_param_spec_internal (PIKA_TYPE_PARAM_MATRIX2,
name, nick, blurb, flags);
cspec->default_value = *default_value;
return G_PARAM_SPEC (cspec);
}
static PikaMatrix2 *
matrix2_copy (const PikaMatrix2 *matrix)
{
return (PikaMatrix2 *) g_memdup2 (matrix, sizeof (PikaMatrix2));
}
/**
* pika_matrix2_identity:
* @matrix: A matrix.
*
* Sets the matrix to the identity matrix.
*/
void
pika_matrix2_identity (PikaMatrix2 *matrix)
{
static const PikaMatrix2 identity = { { { 1.0, 0.0 },
{ 0.0, 1.0 } } };
*matrix = identity;
}
/**
* pika_matrix2_mult:
* @left: The first input matrix.
* @right: The second input matrix which will be overwritten by the result.
*
* Multiplies two matrices and puts the result into the second one.
*/
void
pika_matrix2_mult (const PikaMatrix2 *left,
PikaMatrix2 *right)
{
gdouble r00 = right->coeff[0][0];
gdouble r01 = right->coeff[0][1];
right->coeff[0][0] = (left->coeff[0][0] * r00 +
left->coeff[0][1] * right->coeff[1][0]);
right->coeff[0][1] = (left->coeff[0][0] * r01 +
left->coeff[0][1] * right->coeff[1][1]);
right->coeff[1][0] = (left->coeff[1][0] * r00 +
left->coeff[1][1] * right->coeff[1][0]);
right->coeff[1][1] = (left->coeff[1][0] * r01 +
left->coeff[1][1] * right->coeff[1][1]);
}
/**
* pika_matrix2_determinant:
* @matrix: The input matrix.
*
* Calculates the determinant of the given matrix.
*
* Returns: The determinant.
*
* Since: 2.10.16
*/
gdouble
pika_matrix2_determinant (const PikaMatrix2 *matrix)
{
return matrix->coeff[0][0] * matrix->coeff[1][1] -
matrix->coeff[0][1] * matrix->coeff[1][0];
}
/**
* pika_matrix2_invert:
* @matrix: The matrix that is to be inverted.
*
* Inverts the given matrix.
*
* Since: 2.10.16
*/
void
pika_matrix2_invert (PikaMatrix2 *matrix)
{
gdouble det = pika_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;
}
/**
* pika_matrix2_transform_point:
* @matrix: The transformation matrix.
* @x: The source X coordinate.
* @y: The source Y coordinate.
* @newx: (out): The transformed X coordinate.
* @newy: (out): The transformed Y coordinate.
*
* Transforms a point in 2D as specified by the transformation matrix.
*
* Since: 2.10.16
*/
void
pika_matrix2_transform_point (const PikaMatrix2 *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 PikaMatrix3 * matrix3_copy (const PikaMatrix3 *matrix);
G_DEFINE_BOXED_TYPE (PikaMatrix3, pika_matrix3, matrix3_copy, g_free)
/*
* PIKA_TYPE_PARAM_MATRIX3
*/
#define PIKA_PARAM_SPEC_MATRIX3(pspec) (G_TYPE_CHECK_INSTANCE_CAST ((pspec), PIKA_TYPE_PARAM_MATRIX3, PikaParamSpecMatrix3))
static void pika_param_matrix3_class_init (GParamSpecClass *class);
static void pika_param_matrix3_init (GParamSpec *pspec);
static void pika_param_matrix3_set_default (GParamSpec *pspec,
GValue *value);
static gint pika_param_matrix3_values_cmp (GParamSpec *pspec,
const GValue *value1,
const GValue *value2);
typedef struct _PikaParamSpecMatrix3 PikaParamSpecMatrix3;
struct _PikaParamSpecMatrix3
{
GParamSpecBoxed parent_instance;
PikaMatrix3 default_value;
};
/**
* pika_param_matrix3_get_type:
*
* Reveals the object type
*
* Returns: the #GType for a PikaMatrix3 object
*
* Since: 2.8
**/
GType
pika_param_matrix3_get_type (void)
{
static GType spec_type = 0;
if (!spec_type)
{
static const GTypeInfo type_info =
{
sizeof (GParamSpecClass),
NULL, NULL,
(GClassInitFunc) pika_param_matrix3_class_init,
NULL, NULL,
sizeof (PikaParamSpecMatrix3),
0,
(GInstanceInitFunc) pika_param_matrix3_init
};
spec_type = g_type_register_static (G_TYPE_PARAM_BOXED,
"PikaParamMatrix3",
&type_info, 0);
}
return spec_type;
}
static void
pika_param_matrix3_class_init (GParamSpecClass *class)
{
class->value_type = PIKA_TYPE_MATRIX3;
class->value_set_default = pika_param_matrix3_set_default;
class->values_cmp = pika_param_matrix3_values_cmp;
}
static void
pika_param_matrix3_init (GParamSpec *pspec)
{
PikaParamSpecMatrix3 *cspec = PIKA_PARAM_SPEC_MATRIX3 (pspec);
pika_matrix3_identity (&cspec->default_value);
}
static void
pika_param_matrix3_set_default (GParamSpec *pspec,
GValue *value)
{
PikaParamSpecMatrix3 *cspec = PIKA_PARAM_SPEC_MATRIX3 (pspec);
g_value_set_static_boxed (value, &cspec->default_value);
}
static gint
pika_param_matrix3_values_cmp (GParamSpec *pspec,
const GValue *value1,
const GValue *value2)
{
PikaMatrix3 *matrix1;
PikaMatrix3 *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;
}
/**
* pika_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 #PikaMatrix3 value.
* See g_param_spec_internal() for more information.
*
* Returns: (transfer full): a newly allocated #GParamSpec instance
*
* Since: 2.8
**/
GParamSpec *
pika_param_spec_matrix3 (const gchar *name,
const gchar *nick,
const gchar *blurb,
const PikaMatrix3 *default_value,
GParamFlags flags)
{
PikaParamSpecMatrix3 *cspec;
cspec = g_param_spec_internal (PIKA_TYPE_PARAM_MATRIX3,
name, nick, blurb, flags);
if (default_value)
cspec->default_value = *default_value;
return G_PARAM_SPEC (cspec);
}
static PikaMatrix3 *
matrix3_copy (const PikaMatrix3 *matrix)
{
return (PikaMatrix3 *) g_memdup2 (matrix, sizeof (PikaMatrix3));
}
/**
* pika_matrix3_identity:
* @matrix: A matrix.
*
* Sets the matrix to the identity matrix.
*/
void
pika_matrix3_identity (PikaMatrix3 *matrix)
{
static const PikaMatrix3 identity = { { { 1.0, 0.0, 0.0 },
{ 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 } } };
*matrix = identity;
}
/**
* pika_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
pika_matrix3_transform_point (const PikaMatrix3 *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;
}
/**
* pika_matrix3_mult:
* @left: The first input matrix.
* @right: The second input matrix which will be overwritten by the result.
*
* Multiplies two matrices and puts the result into the second one.
*/
void
pika_matrix3_mult (const PikaMatrix3 *left,
PikaMatrix3 *right)
{
gint i;
gdouble li0, li1, li2;
gdouble r00 = right->coeff[0][0];
gdouble r01 = right->coeff[0][1];
gdouble r02 = right->coeff[0][2];
gdouble r10 = right->coeff[1][0];
gdouble r11 = right->coeff[1][1];
gdouble r12 = right->coeff[1][2];
gdouble r20 = right->coeff[2][0];
gdouble r21 = right->coeff[2][1];
gdouble r22 = right->coeff[2][2];
for (i = 0; i < 3; i++)
{
li0 = left->coeff[i][0];
li1 = left->coeff[i][1];
li2 = left->coeff[i][2];
right->coeff[i][0] = li0 * r00 + li1 * r10 + li2 * r20;
right->coeff[i][1] = li0 * r01 + li1 * r11 + li2 * r21;
right->coeff[i][2] = li0 * r02 + li1 * r12 + li2 * r22;
}
}
/**
* pika_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
pika_matrix3_translate (PikaMatrix3 *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;
}
/**
* pika_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
pika_matrix3_scale (PikaMatrix3 *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;
}
/**
* pika_matrix3_rotate:
* @matrix: The matrix that is to be rotated.
* @theta: The angle of rotation (in radians).
*
* Rotates the matrix by theta degrees.
*/
void
pika_matrix3_rotate (PikaMatrix3 *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;
}
/**
* pika_matrix3_xshear:
* @matrix: The matrix that is to be sheared.
* @amount: X shear amount.
*
* Shears the matrix in the X direction.
*/
void
pika_matrix3_xshear (PikaMatrix3 *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];
}
/**
* pika_matrix3_yshear:
* @matrix: The matrix that is to be sheared.
* @amount: Y shear amount.
*
* Shears the matrix in the Y direction.
*/
void
pika_matrix3_yshear (PikaMatrix3 *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];
}
/**
* pika_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
pika_matrix3_affine (PikaMatrix3 *matrix,
gdouble a,
gdouble b,
gdouble c,
gdouble d,
gdouble e,
gdouble f)
{
PikaMatrix3 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;
pika_matrix3_mult (&affine, matrix);
}
/**
* pika_matrix3_determinant:
* @matrix: The input matrix.
*
* Calculates the determinant of the given matrix.
*
* Returns: The determinant.
*/
gdouble
pika_matrix3_determinant (const PikaMatrix3 *matrix)
{
gdouble m01 = matrix->coeff[0][1];
gdouble m02 = matrix->coeff[0][2];
gdouble m11 = matrix->coeff[1][1];
gdouble m12 = matrix->coeff[1][2];
gdouble m21 = matrix->coeff[2][1];
gdouble m22 = matrix->coeff[2][2];
return matrix->coeff[0][0] * (m11 * m22 - m12 * m21)
- matrix->coeff[1][0] * (m01 * m22 - m02 * m21)
+ matrix->coeff[2][0] * (m01 * m12 - m02 * m11);
}
/**
* pika_matrix3_invert:
* @matrix: The matrix that is to be inverted.
*
* Inverts the given matrix.
*/
void
pika_matrix3_invert (PikaMatrix3 *matrix)
{
gdouble det;
gdouble m00 = matrix->coeff[0][0];
gdouble m01 = matrix->coeff[0][1];
gdouble m02 = matrix->coeff[0][2];
gdouble m10 = matrix->coeff[1][0];
gdouble m11 = matrix->coeff[1][1];
gdouble m12 = matrix->coeff[1][2];
gdouble m20 = matrix->coeff[2][0];
gdouble m21 = matrix->coeff[2][1];
gdouble m22 = matrix->coeff[2][2];
/* To avoid redundant access to the coefficients, inline the determinant
* formula.
*
* See: https://gitlab.gnome.org/GNOME/gimp/-/merge_requests/880#note_1727051
*/
det = m00 * (m11 * m22 - m12 * m21)
- m10 * (m01 * m22 - m02 * m21)
+ m20 * (m01 * m12 - m02 * m11);
if (det == 0.0)
return;
det = 1.0 / det;
matrix->coeff[0][0] = (m11 * m22 - m12 * m21) * det;
matrix->coeff[1][0] = - (m10 * m22 - m12 * m20) * det;
matrix->coeff[2][0] = (m10 * m21 - m11 * m20) * det;
matrix->coeff[0][1] = - (m01 * m22 - m02 * m21) * det;
matrix->coeff[1][1] = (m00 * m22 - m02 * m20) * det;
matrix->coeff[2][1] = - (m00 * m21 - m01 * m20) * det;
matrix->coeff[0][2] = (m01 * m12 - m02 * m11) * det;
matrix->coeff[1][2] = - (m00 * m12 - m02 * m10) * det;
matrix->coeff[2][2] = (m00 * m11 - m01 * m10) * det;
}
/* functions to test for matrix properties */
/**
* pika_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
pika_matrix3_is_identity (const PikaMatrix3 *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;
}
/**
* pika_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
pika_matrix3_is_diagonal (const PikaMatrix3 *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;
}
/**
* pika_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
pika_matrix3_is_affine (const PikaMatrix3 *matrix)
{
return (fabs (matrix->coeff[2][0]) < EPSILON &&
fabs (matrix->coeff[2][1]) < EPSILON &&
fabs (matrix->coeff[2][2] - 1.0) < EPSILON);
}
/**
* pika_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
pika_matrix3_is_simple (const PikaMatrix3 *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;
}
/**
* pika_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
pika_matrix3_equal (const PikaMatrix3 *matrix1,
const PikaMatrix3 *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;
}
/**
* pika_matrix4_identity:
* @matrix: A matrix.
*
* Sets the matrix to the identity matrix.
*
* Since: 2.10.16
*/
void
pika_matrix4_identity (PikaMatrix4 *matrix)
{
gint i, j;
for (i = 0; i < 4; i++)
{
for (j = 0; j < 4; j++)
matrix->coeff[i][j] = i == j;
}
}
/**
* pika_matrix4_mult:
* @left: The first input matrix.
* @right: 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
pika_matrix4_mult (const PikaMatrix4 *left,
PikaMatrix4 *right)
{
PikaMatrix4 result = {};
gint i, j;
gdouble li0, li1, li2, li3;
for (i = 0; i < 4; i++)
{
li0 = left->coeff[i][0];
li1 = left->coeff[i][1];
li2 = left->coeff[i][2];
li3 = left->coeff[i][3];
for (j = 0; j < 4; j++)
{
result.coeff[i][j] = li0 * right->coeff[0][j]
+ li1 * right->coeff[1][j]
+ li2 * right->coeff[2][j]
+ li3 * right->coeff[3][j];
}
}
*right = result;
}
/**
* pika_matrix4_to_deg:
* @matrix:
* @a: (out):
* @b: (out):
* @c: (out):
*
**/
void
pika_matrix4_to_deg (const PikaMatrix4 *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);
}
/**
* pika_matrix4_transform_point:
* @matrix: The transformation matrix.
* @x: The source X coordinate.
* @y: The source Y coordinate.
* @z: The source Z coordinate.
* @newx: (out): The transformed X coordinate.
* @newy: (out): The transformed Y coordinate.
* @newz: (out): 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
pika_matrix4_transform_point (const PikaMatrix4 *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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