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/*************************************************************************
* Copyright (c) 2011 AT&T Intellectual Property
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* which accompanies this distribution, and is available at
* https://www.eclipse.org/legal/epl-v10.html
*
* Contributors: Details at https://graphviz.org
*************************************************************************/
#include <math.h>
#include "simple.h"
#include <stdlib.h>
#include <util/unreachable.h>
static int sign(double v) {
if (v < 0)
return -1;
if (v > 0)
return 1;
return 0;
}
/* find the sign of the area of each of the triangles
formed by adding a vertex of m to l
also find the sign of their product */
static void sgnarea(struct vertex *l, struct vertex *m, int i[])
{
const double a = l->pos.x;
const double b = l->pos.y;
const double c = after(l)->pos.x - a;
const double d = after(l)->pos.y - b;
const double e = m->pos.x - a;
const double f = m->pos.y - b;
const double g = after(m)->pos.x - a;
const double h = after(m)->pos.y - b;
double t = c * f - d * e;
i[0] = sign(t);
t = c * h - d * g;
i[1] = sign(t);
i[2] = i[0] * i[1];
}
/** where is `g` relative to the interval delimited by `f` and `h`?
*
* The order of `f` and `h` is not assumed. That is, the interval defined may be
* `(f, h)` or `(h, f)` depending on whether `f` is less than or greater than
* `h`.
*
* \param f First boundary of the interval
* \param g Value to test
* \param h Second boundary of the interval
* \return -1 if g is not in the interval, 1 if g is in the interval, 0 if g is
* on the boundary (that is, equal to f or equal to h)
*/
static int between(double f, double g, double h) {
if (f < g) {
if (g < h) {
return 1;
}
if (g > h) {
return -1;
}
return 0;
}
if (f > g) {
if (g > h) {
return 1;
}
if (g < h) {
return -1;
}
return 0;
}
return 0;
}
/* determine if vertex i of line m is on line l */
static int online(struct vertex *l, struct vertex *m, int i)
{
struct position a, b, c;
a = l->pos;
b = after(l)->pos;
c = i == 0 ? m->pos : after(m)->pos;
return a.x == b.x ? (a.x == c.x && -1 != between(a.y, c.y, b.y))
: between(a.x, c.x, b.x);
}
/* determine point of detected intersections */
static int intpoint(struct vertex *l, struct vertex *m, double *x, double *y,
int cond) {
struct position ls, le, ms, me, pt1, pt2;
if (cond <= 0)
return (0);
ls = l->pos;
le = after(l)->pos;
ms = m->pos;
me = after(m)->pos;
switch (cond) {
case 3: /* a simple intersection */
if (ls.x == le.x) {
*x = ls.x;
*y = me.y + SLOPE(ms, me) * (*x - me.x);
} else if (ms.x == me.x) {
*x = ms.x;
*y = le.y + SLOPE(ls, le) * (*x - le.x);
} else {
const double m1 = SLOPE(ms, me);
const double m2 = SLOPE(ls, le);
const double c1 = ms.y - m1 * ms.x;
const double c2 = ls.y - m2 * ls.x;
*x = (c2 - c1) / (m1 - m2);
*y = (m1 * c2 - c1 * m2) / (m1 - m2);
}
break;
case 2: /* the two lines have a common segment */
if (online(l, m, 0) == -1) { /* ms between ls and le */
pt1 = ms;
pt2 = online(m, l, 1) == -1 ? (online(m, l, 0 == -1) ? le : ls) : me;
} else if (online(l, m, 1) == -1) { /* me between ls and le */
pt1 = me;
pt2 = online(l, m, 0) == -1 ? (online(m, l, 0) == -1 ? le : ls) : ms;
} else {
/* may be degenerate? */
if (online(m, l, 0) != -1)
return 0;
pt1 = ls;
pt2 = le;
}
*x = (pt1.x + pt2.x) / 2;
*y = (pt1.y + pt2.y) / 2;
break;
case 1: /* a vertex of line m is on line l */
if ((ls.x - le.x) * (ms.y - ls.y) == (ls.y - le.y) * (ms.x - ls.x)) {
*x = ms.x;
*y = ms.y;
} else {
*x = me.x;
*y = me.y;
}
break;
default:
UNREACHABLE();
} /* end switch */
return 1;
}
void find_intersection(struct vertex *l, struct vertex *m,
intersections_t *ilist) {
double x, y;
int i[3];
sgnarea(l, m, i);
if (i[2] > 0)
return;
if (i[2] < 0) {
sgnarea(m, l, i);
if (i[2] > 0)
return;
if (!intpoint(l, m, &x, &y, i[2] < 0 ? 3 : online(m, l, abs(i[0]))))
return;
}
else if (!intpoint(l, m, &x, &y, i[0] == i[1] ? 2 * MAX(online(l, m, 0),
online(l, m, 1)) : online(l, m, abs(i[0]))))
return;
struct intersection inter = {
.firstv = l,
.secondv = m,
.firstp = l->poly,
.secondp = m->poly,
.x = x,
.y = y
};
LIST_APPEND(ilist, inter);
}
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