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/*
* Copyright © 2016 Red Hat, Inc.
*
* Permission to use, copy, modify, distribute, and sell this software
* and its documentation for any purpose is hereby granted without
* fee, provided that the above copyright notice appear in all copies
* and that both that copyright notice and this permission notice
* appear in supporting documentation, and that the name of Red Hat
* not be used in advertising or publicity pertaining to distribution
* of the software without specific, written prior permission. Red
* Hat makes no representations about the suitability of this software
* for any purpose. It is provided "as is" without express or implied
* warranty.
*
* THE AUTHORS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
* INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN
* NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY SPECIAL, INDIRECT OR
* CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
* OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
* NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include "bezier.h"
const struct bezier_control_point bezier_defaults[4] = {
{ 0.0, 0.0 },
{ 0.0, 0.0 },
{ 1.0, 1.0 },
{ 1.0, 1.0 },
};
struct point {
int x, y;
};
/**
* de Casteljau's algorithm. See this page here
* https://pomax.github.io/bezierinfo/#extended
*
* To play with bezier curve shapes, I used
* http://cubic-bezier.com/
*/
static struct point
decasteljau(const struct point *controls,
size_t ncontrols,
double t)
{
struct point new_controls[ncontrols];
if (ncontrols == 1)
return controls[0];
for (int i = 0; i < ncontrols - 1; i++) {
new_controls[i].x = (1.0 - t) * controls[i].x + t * controls[i + 1].x;
new_controls[i].y = (1.0 - t) * controls[i].y + t * controls[i + 1].y;
}
return decasteljau(new_controls, ncontrols - 1, t);
}
/**
* Given a Bézier curve defined by the control points, reduce the curve to
* one with ncurve_points.
*/
static void
flatten_curve(const struct point *controls,
size_t ncontrols,
struct point *curve,
size_t ncurve_points)
{
ncurve_points--; /* make sure we end up with 100/100 as last point */
for (int i = 0; i <= ncurve_points; i++) {
double t = 1.0 * i/ncurve_points;
struct point p;
p = decasteljau(controls, ncontrols, t);
curve[i] = p;
}
}
/**
* Calculate line through a and b, set curve[x] for each x between
* [a.x, b.x].
*
* Note: pcurve must be at least b.x size.
*/
static void
line_between(struct point a, struct point b,
struct point *curve, size_t curve_sz)
{
double slope;
double offset;
assert(b.x < curve_sz);
if (a.x == b.x) {
curve[a.x].x = a.x;
curve[a.x].y = a.y;
return;
}
slope = (double)(b.y - a.y)/(b.x - a.x);
offset = a.y - slope * a.x;
for (int x = a.x; x <= b.x; x++) {
struct point p;
p.x = x;
p.y = slope * x + offset;
curve[x] = p;
}
}
bool
cubic_bezier(const struct bezier_control_point controls[4],
int *bezier_out,
size_t bezier_sz)
{
const int nsegments = 50;
const int range = bezier_sz - 1;
struct point curve[nsegments];
struct point bezier[bezier_sz];
struct point zero = { 0, 0 },
max = { range, range};
/* Scale control points into the [0, bezier_sz) range */
struct point ctrls[4];
for (int i = 0; i < 4; i++) {
if (controls[i].x < 0.0 || controls[i].x > 1.0 ||
controls[i].y < 0.0 || controls[i].y > 1.0)
return false;
ctrls[i].x = controls[i].x * range;
ctrls[i].y = controls[i].y * range;
}
for (int i = 0; i < 3; i++) {
if (ctrls[i].x > ctrls[i+1].x)
return false;
}
/* Reduce curve to nsegments, because this isn't a drawing program */
flatten_curve(ctrls, 4, curve, nsegments);
/* we now have nsegments points in curve that represent the bezier
curve (already in the [0, bezier_sz) range). Run through the
points and draw a straight line between each point and voila, we
have our curve.
If the first control points (x0/y0) is not at x == 0 or the last
control point (x3/y3) is not at the max value, draw a line
between from 0/0 to x0/y0 and from x3/y3 to xmax/y3.
*/
line_between(zero, curve[0], bezier, bezier_sz);
for (int i = 0; i < nsegments - 1; i++)
line_between(curve[i], curve[i+1], bezier, bezier_sz);
if (curve[nsegments - 1].x < max.x)
line_between(curve[nsegments - 1], max, bezier, bezier_sz);
for (int i = 0; i < bezier_sz; i++)
bezier_out[i] = bezier[i].y;
return true;
}
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