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gimp/app/core/gimpcoords-interpolate.c

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/* 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 <https://www.gnu.org/licenses/>.
*/
#include "config.h"
#include <glib-object.h>
#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);
}
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