6b62cce03b
... which is the same as gimp_transform_polygon(), but using GimpCoords for the vertices, instead of GimpVector2. Specify when the input and output arguments may alias, in the description of gimp_transform_polygon().
735 lines
21 KiB
C
735 lines
21 KiB
C
/* GIMP - The GNU Image Manipulation Program
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* Copyright (C) 1995-2001 Spencer Kimball, Peter Mattis, and others
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "config.h"
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#include <glib-object.h>
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#include "libgimpmath/gimpmath.h"
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#include "core-types.h"
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#include "gimp-transform-utils.h"
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#include "gimpcoords.h"
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#define EPSILON 1e-6
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void
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gimp_transform_get_rotate_center (gint x,
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gint y,
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gint width,
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gint height,
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gboolean auto_center,
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gdouble *center_x,
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gdouble *center_y)
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{
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g_return_if_fail (center_x != NULL);
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g_return_if_fail (center_y != NULL);
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if (auto_center)
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{
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*center_x = (gdouble) x + (gdouble) width / 2.0;
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*center_y = (gdouble) y + (gdouble) height / 2.0;
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}
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}
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void
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gimp_transform_get_flip_axis (gint x,
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gint y,
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gint width,
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gint height,
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GimpOrientationType flip_type,
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gboolean auto_center,
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gdouble *axis)
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{
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g_return_if_fail (axis != NULL);
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if (auto_center)
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{
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switch (flip_type)
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{
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case GIMP_ORIENTATION_HORIZONTAL:
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*axis = ((gdouble) x + (gdouble) width / 2.0);
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break;
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case GIMP_ORIENTATION_VERTICAL:
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*axis = ((gdouble) y + (gdouble) height / 2.0);
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break;
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default:
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g_return_if_reached ();
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break;
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}
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}
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}
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void
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gimp_transform_matrix_flip (GimpMatrix3 *matrix,
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GimpOrientationType flip_type,
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gdouble axis)
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{
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g_return_if_fail (matrix != NULL);
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switch (flip_type)
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{
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case GIMP_ORIENTATION_HORIZONTAL:
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gimp_matrix3_translate (matrix, - axis, 0.0);
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gimp_matrix3_scale (matrix, -1.0, 1.0);
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gimp_matrix3_translate (matrix, axis, 0.0);
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break;
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case GIMP_ORIENTATION_VERTICAL:
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gimp_matrix3_translate (matrix, 0.0, - axis);
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gimp_matrix3_scale (matrix, 1.0, -1.0);
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gimp_matrix3_translate (matrix, 0.0, axis);
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break;
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case GIMP_ORIENTATION_UNKNOWN:
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break;
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}
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}
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void
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gimp_transform_matrix_flip_free (GimpMatrix3 *matrix,
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gdouble x1,
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gdouble y1,
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gdouble x2,
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gdouble y2)
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{
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gdouble angle;
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g_return_if_fail (matrix != NULL);
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angle = atan2 (y2 - y1, x2 - x1);
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gimp_matrix3_identity (matrix);
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gimp_matrix3_translate (matrix, -x1, -y1);
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gimp_matrix3_rotate (matrix, -angle);
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gimp_matrix3_scale (matrix, 1.0, -1.0);
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gimp_matrix3_rotate (matrix, angle);
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gimp_matrix3_translate (matrix, x1, y1);
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}
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void
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gimp_transform_matrix_rotate (GimpMatrix3 *matrix,
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GimpRotationType rotate_type,
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gdouble center_x,
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gdouble center_y)
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{
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gdouble angle = 0;
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switch (rotate_type)
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{
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case GIMP_ROTATE_90:
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angle = G_PI_2;
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break;
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case GIMP_ROTATE_180:
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angle = G_PI;
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break;
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case GIMP_ROTATE_270:
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angle = - G_PI_2;
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break;
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}
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gimp_transform_matrix_rotate_center (matrix, center_x, center_y, angle);
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}
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void
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gimp_transform_matrix_rotate_rect (GimpMatrix3 *matrix,
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gint x,
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gint y,
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gint width,
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gint height,
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gdouble angle)
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{
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gdouble center_x;
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gdouble center_y;
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g_return_if_fail (matrix != NULL);
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center_x = (gdouble) x + (gdouble) width / 2.0;
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center_y = (gdouble) y + (gdouble) height / 2.0;
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gimp_matrix3_translate (matrix, -center_x, -center_y);
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gimp_matrix3_rotate (matrix, angle);
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gimp_matrix3_translate (matrix, +center_x, +center_y);
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}
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void
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gimp_transform_matrix_rotate_center (GimpMatrix3 *matrix,
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gdouble center_x,
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gdouble center_y,
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gdouble angle)
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{
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g_return_if_fail (matrix != NULL);
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gimp_matrix3_translate (matrix, -center_x, -center_y);
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gimp_matrix3_rotate (matrix, angle);
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gimp_matrix3_translate (matrix, +center_x, +center_y);
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}
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void
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gimp_transform_matrix_scale (GimpMatrix3 *matrix,
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gint x,
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gint y,
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gint width,
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gint height,
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gdouble t_x,
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gdouble t_y,
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gdouble t_width,
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gdouble t_height)
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{
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gdouble scale_x = 1.0;
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gdouble scale_y = 1.0;
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g_return_if_fail (matrix != NULL);
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if (width > 0)
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scale_x = t_width / (gdouble) width;
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if (height > 0)
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scale_y = t_height / (gdouble) height;
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gimp_matrix3_identity (matrix);
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gimp_matrix3_translate (matrix, -x, -y);
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gimp_matrix3_scale (matrix, scale_x, scale_y);
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gimp_matrix3_translate (matrix, t_x, t_y);
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}
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void
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gimp_transform_matrix_shear (GimpMatrix3 *matrix,
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gint x,
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gint y,
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gint width,
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gint height,
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GimpOrientationType orientation,
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gdouble amount)
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{
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gdouble center_x;
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gdouble center_y;
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g_return_if_fail (matrix != NULL);
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if (width == 0)
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width = 1;
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if (height == 0)
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height = 1;
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center_x = (gdouble) x + (gdouble) width / 2.0;
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center_y = (gdouble) y + (gdouble) height / 2.0;
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gimp_matrix3_identity (matrix);
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gimp_matrix3_translate (matrix, -center_x, -center_y);
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if (orientation == GIMP_ORIENTATION_HORIZONTAL)
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gimp_matrix3_xshear (matrix, amount / height);
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else
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gimp_matrix3_yshear (matrix, amount / width);
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gimp_matrix3_translate (matrix, +center_x, +center_y);
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}
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void
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gimp_transform_matrix_perspective (GimpMatrix3 *matrix,
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gint x,
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gint y,
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gint width,
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gint height,
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gdouble t_x1,
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gdouble t_y1,
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gdouble t_x2,
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gdouble t_y2,
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gdouble t_x3,
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gdouble t_y3,
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gdouble t_x4,
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gdouble t_y4)
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{
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GimpMatrix3 trafo;
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gdouble scalex;
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gdouble scaley;
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g_return_if_fail (matrix != NULL);
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scalex = scaley = 1.0;
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if (width > 0)
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scalex = 1.0 / (gdouble) width;
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if (height > 0)
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scaley = 1.0 / (gdouble) height;
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gimp_matrix3_translate (matrix, -x, -y);
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gimp_matrix3_scale (matrix, scalex, scaley);
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/* Determine the perspective transform that maps from
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* the unit cube to the transformed coordinates
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*/
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{
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gdouble dx1, dx2, dx3, dy1, dy2, dy3;
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dx1 = t_x2 - t_x4;
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dx2 = t_x3 - t_x4;
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dx3 = t_x1 - t_x2 + t_x4 - t_x3;
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dy1 = t_y2 - t_y4;
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dy2 = t_y3 - t_y4;
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dy3 = t_y1 - t_y2 + t_y4 - t_y3;
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/* Is the mapping affine? */
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if ((dx3 == 0.0) && (dy3 == 0.0))
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{
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trafo.coeff[0][0] = t_x2 - t_x1;
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trafo.coeff[0][1] = t_x4 - t_x2;
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trafo.coeff[0][2] = t_x1;
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trafo.coeff[1][0] = t_y2 - t_y1;
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trafo.coeff[1][1] = t_y4 - t_y2;
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trafo.coeff[1][2] = t_y1;
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trafo.coeff[2][0] = 0.0;
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trafo.coeff[2][1] = 0.0;
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}
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else
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{
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gdouble det1, det2;
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det1 = dx3 * dy2 - dy3 * dx2;
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det2 = dx1 * dy2 - dy1 * dx2;
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trafo.coeff[2][0] = (det2 == 0.0) ? 1.0 : det1 / det2;
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det1 = dx1 * dy3 - dy1 * dx3;
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trafo.coeff[2][1] = (det2 == 0.0) ? 1.0 : det1 / det2;
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trafo.coeff[0][0] = t_x2 - t_x1 + trafo.coeff[2][0] * t_x2;
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trafo.coeff[0][1] = t_x3 - t_x1 + trafo.coeff[2][1] * t_x3;
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trafo.coeff[0][2] = t_x1;
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trafo.coeff[1][0] = t_y2 - t_y1 + trafo.coeff[2][0] * t_y2;
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trafo.coeff[1][1] = t_y3 - t_y1 + trafo.coeff[2][1] * t_y3;
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trafo.coeff[1][2] = t_y1;
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}
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trafo.coeff[2][2] = 1.0;
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}
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gimp_matrix3_mult (&trafo, matrix);
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}
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/* modified gaussian algorithm
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* solves a system of linear equations
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*
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* Example:
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* 1x + 2y + 4z = 25
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* 2x + 1y = 4
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* 3x + 5y + 2z = 23
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* Solution: x=1, y=2, z=5
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*
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* Input:
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* matrix = { 1,2,4,25,2,1,0,4,3,5,2,23 }
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* s = 3 (Number of variables)
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* Output:
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* return value == TRUE (TRUE, if there is a single unique solution)
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* solution == { 1,2,5 } (if the return value is FALSE, the content
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* of solution is of no use)
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*/
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static gboolean
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mod_gauss (gdouble matrix[],
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gdouble solution[],
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gint s)
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{
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gint p[s]; /* row permutation */
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gint i, j, r, temp;
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gdouble q;
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gint t = s + 1;
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for (i = 0; i < s; i++)
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{
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p[i] = i;
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}
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for (r = 0; r < s; r++)
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{
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/* make sure that (r,r) is not 0 */
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if (fabs (matrix[p[r] * t + r]) <= EPSILON)
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{
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/* we need to permutate rows */
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for (i = r + 1; i <= s; i++)
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{
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if (i == s)
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{
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/* if this happens, the linear system has zero or
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* more than one solutions.
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*/
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return FALSE;
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}
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if (fabs (matrix[p[i] * t + r]) > EPSILON)
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break;
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}
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temp = p[r];
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p[r] = p[i];
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p[i] = temp;
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}
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/* make (r,r) == 1 */
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q = 1.0 / matrix[p[r] * t + r];
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matrix[p[r] * t + r] = 1.0;
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for (j = r + 1; j < t; j++)
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{
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matrix[p[r] * t + j] *= q;
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}
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/* make that all entries in column r are 0 (except (r,r)) */
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for (i = 0; i < s; i++)
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{
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if (i == r)
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continue;
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for (j = r + 1; j < t ; j++)
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{
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matrix[p[i] * t + j] -= matrix[p[r] * t + j] * matrix[p[i] * t + r];
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}
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/* we don't need to execute the following line
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* since we won't access this element again:
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*
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* matrix[p[i] * t + r] = 0.0;
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*/
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}
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}
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for (i = 0; i < s; i++)
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{
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solution[i] = matrix[p[i] * t + s];
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}
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return TRUE;
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}
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/* multiplies 'matrix' by the matrix that transforms a set of 4 'input_points'
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* to corresponding 'output_points', if such matrix exists, and is valid (i.e.,
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* keeps the output points in front of the camera).
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*
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* returns TRUE if successful.
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*/
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gboolean
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gimp_transform_matrix_generic (GimpMatrix3 *matrix,
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const GimpVector2 input_points[4],
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const GimpVector2 output_points[4])
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{
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GimpMatrix3 trafo;
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gdouble coeff[8 * 9];
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gboolean negative;
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gint i;
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g_return_val_if_fail (matrix != NULL, FALSE);
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g_return_val_if_fail (input_points != NULL, FALSE);
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g_return_val_if_fail (output_points != NULL, FALSE);
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/* find the matrix that transforms 'input_points' to 'output_points', whose
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* (3, 3) coeffcient is 1, by solving a system of linear equations whose
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* solution is the remaining 8 coefficients.
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*/
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for (i = 0; i < 4; i++)
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{
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coeff[i * 9 + 0] = input_points[i].x;
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coeff[i * 9 + 1] = input_points[i].y;
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coeff[i * 9 + 2] = 1.0;
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coeff[i * 9 + 3] = 0.0;
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coeff[i * 9 + 4] = 0.0;
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coeff[i * 9 + 5] = 0.0;
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coeff[i * 9 + 6] = -input_points[i].x * output_points[i].x;
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coeff[i * 9 + 7] = -input_points[i].y * output_points[i].x;
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coeff[i * 9 + 8] = output_points[i].x;
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coeff[(i + 4) * 9 + 0] = 0.0;
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coeff[(i + 4) * 9 + 1] = 0.0;
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coeff[(i + 4) * 9 + 2] = 0.0;
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coeff[(i + 4) * 9 + 3] = input_points[i].x;
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coeff[(i + 4) * 9 + 4] = input_points[i].y;
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coeff[(i + 4) * 9 + 5] = 1.0;
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coeff[(i + 4) * 9 + 6] = -input_points[i].x * output_points[i].y;
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coeff[(i + 4) * 9 + 7] = -input_points[i].y * output_points[i].y;
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coeff[(i + 4) * 9 + 8] = output_points[i].y;
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}
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/* if there is no solution, bail */
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if (! mod_gauss (coeff, (gdouble *) trafo.coeff, 8))
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return FALSE;
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trafo.coeff[2][2] = 1.0;
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/* make sure that none of the input points maps to a point at infinity, and
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* that all output points are on the same side of the camera.
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*/
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for (i = 0; i < 4; i++)
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{
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gdouble w;
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gboolean neg;
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w = trafo.coeff[2][0] * input_points[i].x +
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trafo.coeff[2][1] * input_points[i].y +
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trafo.coeff[2][2];
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if (fabs (w) <= EPSILON)
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return FALSE;
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neg = (w < 0.0);
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if (i == 0)
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negative = neg;
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else if (neg != negative)
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return FALSE;
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}
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/* if the output points are all behind the camera, negate the matrix, which
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* would map the input points to the corresponding points in front of the
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* camera.
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*/
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if (negative)
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{
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gint r;
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gint c;
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for (r = 0; r < 3; r++)
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{
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for (c = 0; c < 3; c++)
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{
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trafo.coeff[r][c] = -trafo.coeff[r][c];
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}
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}
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}
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/* append the transformation to 'matrix' */
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gimp_matrix3_mult (&trafo, matrix);
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return TRUE;
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}
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gboolean
|
|
gimp_transform_polygon_is_convex (gdouble x1,
|
|
gdouble y1,
|
|
gdouble x2,
|
|
gdouble y2,
|
|
gdouble x3,
|
|
gdouble y3,
|
|
gdouble x4,
|
|
gdouble y4)
|
|
{
|
|
gdouble z1, z2, z3, z4;
|
|
|
|
/* We test if the transformed polygon is convex. if z1 and z2 have
|
|
* the same sign as well as z3 and z4 the polygon is convex.
|
|
*/
|
|
z1 = ((x2 - x1) * (y4 - y1) -
|
|
(x4 - x1) * (y2 - y1));
|
|
z2 = ((x4 - x1) * (y3 - y1) -
|
|
(x3 - x1) * (y4 - y1));
|
|
z3 = ((x4 - x2) * (y3 - y2) -
|
|
(x3 - x2) * (y4 - y2));
|
|
z4 = ((x3 - x2) * (y1 - y2) -
|
|
(x1 - x2) * (y3 - y2));
|
|
|
|
return (z1 * z2 > 0) && (z3 * z4 > 0);
|
|
}
|
|
|
|
/* transforms the polygon or polyline, whose vertices are given by 'vertices',
|
|
* by 'matrix', performing clipping by the near plane. 'closed' indicates
|
|
* whether the vertices represent a polygon ('closed == TRUE') or a polyline
|
|
* ('closed == FALSE').
|
|
*
|
|
* returns the transformed vertices in 't_vertices', and their count in
|
|
* 'n_t_vertices'. the minimal possible number of transformed vertices is 0,
|
|
* which happens when the entire input is clipped. in general, the maximal
|
|
* possible number of transformed vertices is '3 * n_vertices / 2' (rounded
|
|
* down), however, for convex polygons the number is 'n_vertices + 1', and for
|
|
* a single line segment ('n_vertices == 2' and 'closed == FALSE') the number
|
|
* is 2.
|
|
*
|
|
* 't_vertices' may not alias 'vertices', except when transforming a single
|
|
* line segment.
|
|
*/
|
|
void
|
|
gimp_transform_polygon (const GimpMatrix3 *matrix,
|
|
const GimpVector2 *vertices,
|
|
gint n_vertices,
|
|
gboolean closed,
|
|
GimpVector2 *t_vertices,
|
|
gint *n_t_vertices)
|
|
{
|
|
GimpVector3 curr;
|
|
gboolean curr_visible;
|
|
gint i;
|
|
|
|
g_return_if_fail (matrix != NULL);
|
|
g_return_if_fail (vertices != NULL);
|
|
g_return_if_fail (n_vertices >= 0);
|
|
g_return_if_fail (t_vertices != NULL);
|
|
g_return_if_fail (n_t_vertices != NULL);
|
|
|
|
*n_t_vertices = 0;
|
|
|
|
if (n_vertices == 0)
|
|
return;
|
|
|
|
curr.x = matrix->coeff[0][0] * vertices[0].x +
|
|
matrix->coeff[0][1] * vertices[0].y +
|
|
matrix->coeff[0][2];
|
|
curr.y = matrix->coeff[1][0] * vertices[0].x +
|
|
matrix->coeff[1][1] * vertices[0].y +
|
|
matrix->coeff[1][2];
|
|
curr.z = matrix->coeff[2][0] * vertices[0].x +
|
|
matrix->coeff[2][1] * vertices[0].y +
|
|
matrix->coeff[2][2];
|
|
|
|
curr_visible = (curr.z >= GIMP_TRANSFORM_NEAR_Z);
|
|
|
|
for (i = 0; i < n_vertices; i++)
|
|
{
|
|
if (curr_visible)
|
|
{
|
|
t_vertices[(*n_t_vertices)++] = (GimpVector2) { curr.x / curr.z,
|
|
curr.y / curr.z };
|
|
}
|
|
|
|
if (i < n_vertices - 1 || closed)
|
|
{
|
|
GimpVector3 next;
|
|
gboolean next_visible;
|
|
gint j = (i + 1) % n_vertices;
|
|
|
|
next.x = matrix->coeff[0][0] * vertices[j].x +
|
|
matrix->coeff[0][1] * vertices[j].y +
|
|
matrix->coeff[0][2];
|
|
next.y = matrix->coeff[1][0] * vertices[j].x +
|
|
matrix->coeff[1][1] * vertices[j].y +
|
|
matrix->coeff[1][2];
|
|
next.z = matrix->coeff[2][0] * vertices[j].x +
|
|
matrix->coeff[2][1] * vertices[j].y +
|
|
matrix->coeff[2][2];
|
|
|
|
next_visible = (next.z >= GIMP_TRANSFORM_NEAR_Z);
|
|
|
|
if (next_visible != curr_visible)
|
|
{
|
|
gdouble ratio = (curr.z - GIMP_TRANSFORM_NEAR_Z) / (curr.z - next.z);
|
|
|
|
t_vertices[(*n_t_vertices)++] =
|
|
(GimpVector2) { (curr.x + (next.x - curr.x) * ratio) / GIMP_TRANSFORM_NEAR_Z,
|
|
(curr.y + (next.y - curr.y) * ratio) / GIMP_TRANSFORM_NEAR_Z };
|
|
}
|
|
|
|
curr = next;
|
|
curr_visible = next_visible;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* same as gimp_transform_polygon(), but using GimpCoords as the vertex type,
|
|
* instead of GimpVector2.
|
|
*/
|
|
void
|
|
gimp_transform_polygon_coords (const GimpMatrix3 *matrix,
|
|
const GimpCoords *vertices,
|
|
gint n_vertices,
|
|
gboolean closed,
|
|
GimpCoords *t_vertices,
|
|
gint *n_t_vertices)
|
|
{
|
|
GimpVector3 curr;
|
|
gboolean curr_visible;
|
|
gint i;
|
|
|
|
g_return_if_fail (matrix != NULL);
|
|
g_return_if_fail (vertices != NULL);
|
|
g_return_if_fail (n_vertices >= 0);
|
|
g_return_if_fail (t_vertices != NULL);
|
|
g_return_if_fail (n_t_vertices != NULL);
|
|
|
|
*n_t_vertices = 0;
|
|
|
|
if (n_vertices == 0)
|
|
return;
|
|
|
|
curr.x = matrix->coeff[0][0] * vertices[0].x +
|
|
matrix->coeff[0][1] * vertices[0].y +
|
|
matrix->coeff[0][2];
|
|
curr.y = matrix->coeff[1][0] * vertices[0].x +
|
|
matrix->coeff[1][1] * vertices[0].y +
|
|
matrix->coeff[1][2];
|
|
curr.z = matrix->coeff[2][0] * vertices[0].x +
|
|
matrix->coeff[2][1] * vertices[0].y +
|
|
matrix->coeff[2][2];
|
|
|
|
curr_visible = (curr.z >= GIMP_TRANSFORM_NEAR_Z);
|
|
|
|
for (i = 0; i < n_vertices; i++)
|
|
{
|
|
if (curr_visible)
|
|
{
|
|
t_vertices[*n_t_vertices] = vertices[i];
|
|
t_vertices[*n_t_vertices].x = curr.x / curr.z;
|
|
t_vertices[*n_t_vertices].y = curr.y / curr.z;
|
|
|
|
(*n_t_vertices)++;
|
|
}
|
|
|
|
if (i < n_vertices - 1 || closed)
|
|
{
|
|
GimpVector3 next;
|
|
gboolean next_visible;
|
|
gint j = (i + 1) % n_vertices;
|
|
|
|
next.x = matrix->coeff[0][0] * vertices[j].x +
|
|
matrix->coeff[0][1] * vertices[j].y +
|
|
matrix->coeff[0][2];
|
|
next.y = matrix->coeff[1][0] * vertices[j].x +
|
|
matrix->coeff[1][1] * vertices[j].y +
|
|
matrix->coeff[1][2];
|
|
next.z = matrix->coeff[2][0] * vertices[j].x +
|
|
matrix->coeff[2][1] * vertices[j].y +
|
|
matrix->coeff[2][2];
|
|
|
|
next_visible = (next.z >= GIMP_TRANSFORM_NEAR_Z);
|
|
|
|
if (next_visible != curr_visible)
|
|
{
|
|
gdouble ratio = (curr.z - GIMP_TRANSFORM_NEAR_Z) / (curr.z - next.z);
|
|
|
|
gimp_coords_mix (1.0 - ratio, &vertices[i],
|
|
ratio, &vertices[j],
|
|
&t_vertices[*n_t_vertices]);
|
|
|
|
t_vertices[*n_t_vertices].x = (curr.x + (next.x - curr.x) * ratio) /
|
|
GIMP_TRANSFORM_NEAR_Z;
|
|
t_vertices[*n_t_vertices].y = (curr.y + (next.y - curr.y) * ratio) /
|
|
GIMP_TRANSFORM_NEAR_Z;
|
|
|
|
(*n_t_vertices)++;
|
|
}
|
|
|
|
curr = next;
|
|
curr_visible = next_visible;
|
|
}
|
|
}
|
|
}
|