/* GIMP - The GNU Image Manipulation Program * Copyright (C) 1995 Spencer Kimball and Peter Mattis * * gimpcoords-interpolate.c * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or * (at your option) any later version. * * This program 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 General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program. If not, see . */ #include "config.h" #include #include "libgimpmath/gimpmath.h" #include "core-types.h" #include "gimpcoords.h" #include "gimpcoords-interpolate.h" /* Local helper functions declarations*/ static void gimp_coords_interpolate_bezier_internal (const GimpCoords bezier_pt[4], const gdouble start_t, const gdouble end_t, const gdouble precision, GArray *ret_coords, GArray *ret_params, gint depth); static gdouble gimp_coords_get_catmull_spline_point (const gdouble t, const gdouble p0, const gdouble p1, const gdouble p2, const gdouble p3); /* Functions for bezier subdivision */ void gimp_coords_interpolate_bezier (const GimpCoords bezier_pt[4], const gdouble precision, GArray *ret_coords, GArray *ret_params) { g_return_if_fail (bezier_pt != NULL); g_return_if_fail (precision > 0.0); g_return_if_fail (ret_coords != NULL); gimp_coords_interpolate_bezier_internal (bezier_pt, 0.0, 1.0, precision, ret_coords, ret_params, 10); } /* Recursive subdivision helper function */ static void gimp_coords_interpolate_bezier_internal (const GimpCoords bezier_pt[4], const gdouble start_t, const gdouble end_t, const gdouble precision, GArray *ret_coords, GArray *ret_params, gint depth) { /* * bezier_pt has to contain four GimpCoords with the four control points * of the bezier segment. We subdivide it at the parameter 0.5. */ GimpCoords subdivided[8]; gdouble middle_t = (start_t + end_t) / 2; subdivided[0] = bezier_pt[0]; subdivided[6] = bezier_pt[3]; /* if (!depth) g_printerr ("Hit recursion depth limit!\n"); */ gimp_coords_average (&bezier_pt[0], &bezier_pt[1], &subdivided[1]); gimp_coords_average (&bezier_pt[1], &bezier_pt[2], &subdivided[7]); gimp_coords_average (&bezier_pt[2], &bezier_pt[3], &subdivided[5]); gimp_coords_average (&subdivided[1], &subdivided[7], &subdivided[2]); gimp_coords_average (&subdivided[7], &subdivided[5], &subdivided[4]); gimp_coords_average (&subdivided[2], &subdivided[4], &subdivided[3]); /* * We now have the coordinates of the two bezier segments in * subdivided [0-3] and subdivided [3-6] */ /* * Here we need to check, if we have sufficiently subdivided, i.e. * if the stroke is sufficiently close to a straight line. */ if (! depth || gimp_coords_bezier_is_straight (subdivided, precision)) /* 1st half */ { g_array_append_vals (ret_coords, subdivided, 3); if (ret_params) { gdouble params[3]; params[0] = start_t; params[1] = (2 * start_t + middle_t) / 3; params[2] = (start_t + 2 * middle_t) / 3; g_array_append_vals (ret_params, params, 3); } } else { gimp_coords_interpolate_bezier_internal (subdivided, start_t, (start_t + end_t) / 2, precision, ret_coords, ret_params, depth - 1); } if (! depth || gimp_coords_bezier_is_straight (subdivided + 3, precision)) /* 2nd half */ { g_array_append_vals (ret_coords, subdivided + 3, 3); if (ret_params) { gdouble params[3]; params[0] = middle_t; params[1] = (2 * middle_t + end_t) / 3; params[2] = (middle_t + 2 * end_t) / 3; g_array_append_vals (ret_params, params, 3); } } else { gimp_coords_interpolate_bezier_internal (subdivided + 3, (start_t + end_t) / 2, end_t, precision, ret_coords, ret_params, depth - 1); } } /* * Returns the position and/or velocity of a Bezier curve at time 't'. */ void gimp_coords_interpolate_bezier_at (const GimpCoords bezier_pt[4], gdouble t, GimpCoords *position, GimpCoords *velocity) { gdouble u = 1.0 - t; g_return_if_fail (bezier_pt != NULL); if (position) { GimpCoords a; GimpCoords b; gimp_coords_mix ( u * u * u, &bezier_pt[0], 3.0 * u * u * t, &bezier_pt[1], &a); gimp_coords_mix (3.0 * u * t * t, &bezier_pt[2], t * t * t, &bezier_pt[3], &b); gimp_coords_add (&a, &b, position); } if (velocity) { GimpCoords a; GimpCoords b; gimp_coords_mix (-3.0 * u * u, &bezier_pt[0], 3.0 * (u - 2.0 * t) * u, &bezier_pt[1], &a); gimp_coords_mix (-3.0 * (t - 2.0 * u) * t, &bezier_pt[2], 3.0 * t * t, &bezier_pt[3], &b); gimp_coords_add (&a, &b, velocity); } } /* * a helper function that determines if a bezier segment is "straight * enough" to be approximated by a line. * * To be more exact, it also checks for the control points to be distributed * evenly along the line. This makes it easier to reconstruct parameters for * a given point along the segment. * * Needs four GimpCoords in an array. */ gboolean gimp_coords_bezier_is_straight (const GimpCoords bezier_pt[4], gdouble precision) { GimpCoords pt1, pt2; g_return_val_if_fail (bezier_pt != NULL, FALSE); g_return_val_if_fail (precision > 0.0, FALSE); /* calculate the "ideal" positions for the control points */ gimp_coords_mix (2.0 / 3.0, &bezier_pt[0], 1.0 / 3.0, &bezier_pt[3], &pt1); gimp_coords_mix (1.0 / 3.0, &bezier_pt[0], 2.0 / 3.0, &bezier_pt[3], &pt2); /* calculate the deviation of the actual control points */ return (gimp_coords_manhattan_dist (&bezier_pt[1], &pt1) < precision && gimp_coords_manhattan_dist (&bezier_pt[2], &pt2) < precision); } /* Functions for catmull-rom interpolation */ void gimp_coords_interpolate_catmull (const GimpCoords catmull_pt[4], gdouble precision, GArray *ret_coords, GArray *ret_params) { gdouble delta_x, delta_y; gdouble distance; gdouble dir_step; gdouble delta_dir; gint num_points; gint n; GimpCoords past_coords; GimpCoords start_coords; GimpCoords end_coords; GimpCoords future_coords; g_return_if_fail (catmull_pt != NULL); g_return_if_fail (precision > 0.0); g_return_if_fail (ret_coords != NULL); delta_x = catmull_pt[2].x - catmull_pt[1].x; delta_y = catmull_pt[2].y - catmull_pt[1].y; /* Catmull-Rom interpolation requires 4 points. * Two endpoints plus one more at each end. */ past_coords = catmull_pt[0]; start_coords = catmull_pt[1]; end_coords = catmull_pt[2]; future_coords = catmull_pt[3]; distance = sqrt (SQR (delta_x) + SQR (delta_y)); num_points = distance / precision; delta_dir = end_coords.direction - start_coords.direction; if (delta_dir <= -0.5) delta_dir += 1.0; else if (delta_dir >= 0.5) delta_dir -= 1.0; dir_step = delta_dir / num_points; for (n = 1; n <= num_points; n++) { GimpCoords coords = past_coords; /* Make sure we carry over things * we do not interpolate */ gdouble velocity; gdouble pressure; gdouble p = (gdouble) n / num_points; coords.x = gimp_coords_get_catmull_spline_point (p, past_coords.x, start_coords.x, end_coords.x, future_coords.x); coords.y = gimp_coords_get_catmull_spline_point (p, past_coords.y, start_coords.y, end_coords.y, future_coords.y); pressure = gimp_coords_get_catmull_spline_point (p, past_coords.pressure, start_coords.pressure, end_coords.pressure, future_coords.pressure); coords.pressure = CLAMP (pressure, 0.0, 1.0); coords.xtilt = gimp_coords_get_catmull_spline_point (p, past_coords.xtilt, start_coords.xtilt, end_coords.xtilt, future_coords.xtilt); coords.ytilt = gimp_coords_get_catmull_spline_point (p, past_coords.ytilt, start_coords.ytilt, end_coords.ytilt, future_coords.ytilt); coords.wheel = gimp_coords_get_catmull_spline_point (p, past_coords.wheel, start_coords.wheel, end_coords.wheel, future_coords.wheel); velocity = gimp_coords_get_catmull_spline_point (p, past_coords.velocity, start_coords.velocity, end_coords.velocity, future_coords.velocity); coords.velocity = CLAMP (velocity, 0.0, 1.0); coords.direction = start_coords.direction + dir_step * n; coords.direction = coords.direction - floor (coords.direction); coords.xscale = end_coords.xscale; coords.yscale = end_coords.yscale; coords.angle = end_coords.angle; coords.reflect = end_coords.reflect; g_array_append_val (ret_coords, coords); if (ret_params) g_array_append_val (ret_params, p); } } static gdouble gimp_coords_get_catmull_spline_point (const gdouble t, const gdouble p0, const gdouble p1, const gdouble p2, const gdouble p3) { return ((((-t + 2.0) * t - 1.0) * t / 2.0) * p0 + ((((3.0 * t - 5.0) * t) * t + 2.0) / 2.0) * p1 + (((-3.0 * t + 4.0) * t + 1.0) * t / 2.0) * p2 + (((t - 1) * t * t) / 2.0) * p3); }