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/*
ppedit - A pattern plate editor for Spiro splines.
Copyright (C) 2007 Raph Levien
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 2
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, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.
*/
#include "zmisc.h"
#include "bezctx.h"
#include "bezctx_hittest.h"
#include <math.h>
typedef struct {
bezctx base;
double x, y;
double x0, y0;
int knot_idx;
int knot_idx_min;
double r_min;
} bezctx_hittest;
static void
bezctx_hittest_moveto(bezctx *z, double x, double y, int is_open) {
bezctx_hittest *bc = (bezctx_hittest *)z;
bc->x0 = x;
bc->y0 = y;
}
static void
bezctx_hittest_lineto(bezctx *z, double x, double y) {
bezctx_hittest *bc = (bezctx_hittest *)z;
double x0 = bc->x0;
double y0 = bc->y0;
double dx = x - x0;
double dy = y - y0;
double dotp = (bc->x - x0) * dx + (bc->y - y0) * dy;
double lin_dotp = dx * dx + dy * dy;
double r_min, r;
r = hypot(bc->x - x0, bc->y - y0);
r_min = r;
r = hypot(bc->x - x, bc->y - y);
if (r < r_min) r_min = r;
if (dotp >= 0 && dotp <= lin_dotp) {
double norm = (bc->x - x0) * dy - (bc->y - y0) * dx;
r = fabs(norm / sqrt(lin_dotp));
if (r < r_min) r_min = r;
}
if (r_min < bc->r_min) {
bc->r_min = r_min;
bc->knot_idx_min = bc->knot_idx;
}
bc->x0 = x;
bc->y0 = y;
}
#define cube(x) ((x) * (x) * (x))
static double
my_cbrt(double x)
{
if (x >= 0)
return pow(x, 1.0 / 3.0);
else
return -pow(-x, 1.0 / 3.0);
}
/**
* Give real roots to eqn c0 + c1 * x + c2 * x^2 + c3 * x^3 == 0.
* Return value is number of roots found.
**/
static int
solve_cubic(double c0, double c1, double c2, double c3, double root[3])
{
double p, q, r, a, b, Q, x0;
p = c2 / c3;
q = c1 / c3;
r = c0 / c3;
a = (3 * q - p * p) / 3;
b = (2 * cube(p) - 9 * p * q + 27 * r) / 27;
Q = b * b / 4 + cube(a) / 27;
x0 = p / 3;
if (Q > 0) {
double sQ = sqrt(Q);
double t1 = my_cbrt(-b/2 + sQ) + my_cbrt(-b/2 - sQ);
root[0] = t1 - x0;
return 1;
} else if (Q == 0) {
double t1 = my_cbrt(b / 2);
double x1 = t1 - x0;
root[0] = x1;
root[1] = x1;
root[2] = -2 * t1 - x0;
return 3;
} else {
double sQ = sqrt(-Q);
double rho = hypot(-b/2, sQ);
double th = atan2(sQ, -b/2);
double cbrho = my_cbrt(rho);
double c = cos(th / 3);
double s = sin(th / 3);
double sqr3 = sqrt(3);
root[0] = 2 * cbrho * c - x0;
root[1] = -cbrho * (c + sqr3 * s) - x0;
root[2] = -cbrho * (c - sqr3 * s) - x0;
return 3;
}
}
static double
dist_to_quadratic(double x, double y,
double x0, double y0,
double x1, double y1,
double x2, double y2)
{
double u0, u1, t0, t1, t2, c0, c1, c2, c3;
double roots[3];
int n_roots;
double ts[4];
int n_ts;
int i;
double minerr = 0;
u0 = x1 - x0;
u1 = x0 - 2 * x1 + x2;
t0 = x0 - x;
t1 = 2 * u0;
t2 = u1;
c0 = t0 * u0;
c1 = t1 * u0 + t0 * u1;
c2 = t2 * u0 + t1 * u1;
c3 = t2 * u1;
u0 = y1 - y0;
u1 = y0 - 2 * y1 + y2;
t0 = y0 - y;
t1 = 2 * u0;
t2 = u1;
c0 += t0 * u0;
c1 += t1 * u0 + t0 * u1;
c2 += t2 * u0 + t1 * u1;
c3 += t2 * u1;
n_roots = solve_cubic(c0, c1, c2, c3, roots);
n_ts = 0;
for (i = 0; i < n_roots; i++) {
double t = roots[i];
if (t > 0 && t < 1)
ts[n_ts++] = t;
}
if (n_ts < n_roots) {
ts[n_ts++] = 0;
ts[n_ts++] = 1;
}
for (i = 0; i < n_ts; i++) {
double t = ts[i];
double xa = x0 * (1 - t) * (1 - t) + 2 * x1 * (1 - t) * t + x2 * t * t;
double ya = y0 * (1 - t) * (1 - t) + 2 * y1 * (1 - t) * t + y2 * t * t;
double err = hypot(xa - x, ya - y);
if (i == 0 || err < minerr) {
minerr = err;
}
}
return minerr;
}
static void
bezctx_hittest_quadto(bezctx *z, double x1, double y1, double x2, double y2)
{
bezctx_hittest *bc = (bezctx_hittest *)z;
double r = dist_to_quadratic(bc->x, bc->y,
bc->x0, bc->y0, x1, y1, x2, y2);
if (r < bc->r_min) {
bc->r_min = r;
bc->knot_idx_min = bc->knot_idx;
}
bc->x0 = x2;
bc->y0 = y2;
}
static void
bezctx_hittest_curveto(bezctx *z, double x1, double y1, double x2, double y2,
double x3, double y3)
{
bezctx_hittest *bc = (bezctx_hittest *)z;
double x0 = bc->x0;
double y0 = bc->y0;
int n_subdiv = 32;
int i;
double xq2, yq2;
/* todo: subdivide to quadratics rather than lines */
for (i = 0; i < n_subdiv; i++) {
double t = (1. / n_subdiv) * (i + 1);
double mt = 1 - t;
xq2 = x0 * mt * mt * mt + 3 * x1 * mt * t * t + 3 * x2 * mt * mt * t +
x3 * t * t * t;
yq2 = y0 * mt * mt * mt + 3 * y1 * mt * t * t + 3 * y2 * mt * mt * t +
y3 * t * t * t;
bezctx_hittest_lineto(z, xq2, yq2);
}
}
static void
bezctx_hittest_mark_knot(bezctx *z, int knot_idx) {
bezctx_hittest *bc = (bezctx_hittest *)z;
bc->knot_idx = knot_idx;
}
bezctx *
new_bezctx_hittest(double x, double y) {
bezctx_hittest *result = znew(bezctx_hittest, 1);
result->base.moveto = bezctx_hittest_moveto;
result->base.lineto = bezctx_hittest_lineto;
result->base.quadto = bezctx_hittest_quadto;
result->base.curveto = bezctx_hittest_curveto;
result->base.mark_knot = bezctx_hittest_mark_knot;
result->x = x;
result->y = y;
result->knot_idx_min = -1;
result->r_min = 1e12;
return &result->base;
}
double
bezctx_hittest_report(bezctx *z, int *p_knot_idx)
{
bezctx_hittest *bc = (bezctx_hittest *)z;
double r_min = bc->r_min;
if (p_knot_idx)
*p_knot_idx = bc->knot_idx_min;
zfree(z);
return r_min;
}
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