552 lines
11 KiB
C
552 lines
11 KiB
C
/*
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* path.c - 2D path operations
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*
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* Written 2011 by Werner Almesberger
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* Copyright 2011 by Werner Almesberger
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*/
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#include <stdlib.h>
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#include <assert.h>
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#include "ptrude.h"
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#include "path.h"
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#define alloc_type(t) ((t *) malloc(sizeof(t)))
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#define stralloc(s) strdup(s)
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static double deg(double rad)
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{
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return rad/M_PI*180.0;
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}
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static struct path *alloc_path(void)
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{
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struct path *path;
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path = alloc_type(struct path);
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path->vertices = NULL;
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path->last = &path->vertices;
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return path;
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}
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static struct vertex *alloc_vertex(void)
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{
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struct vertex *v;
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v = alloc_type(struct vertex);
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v->r = 0;
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v->d = 0;
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v->tag = NULL;
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v->next = NULL;
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v->len = 0;
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return v;
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}
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static void free_vertex(struct vertex *v)
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{
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free(v);
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}
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void free_path(struct path *path)
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{
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struct vertex *v, *next;
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for (v = path->vertices; v; v = next) {
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next = v->next;
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free_vertex(v);
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}
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free(path);
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}
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static struct vertex *clone_vertex(const struct vertex *v)
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{
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struct vertex *new;
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new = alloc_type(struct vertex);
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*new = *v;
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new->next = NULL;
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return new;
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}
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static void append_vertex(struct path *path, struct vertex *v)
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{
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*path->last = v;
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path->last = &v->next;
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}
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static struct vertex *add_vertex(struct path *path, double x, double y,
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double r, double d, const char *tag)
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{
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struct vertex *v;
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v = alloc_vertex();
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v->x = x;
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v->y = y;
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v->r = r;
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v->d = d;
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v->tag = tag;
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append_vertex(path, v);
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return v;
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}
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double path_set_length(struct path *path)
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{
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struct vertex *v;
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double sum = 0;
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if (!path->vertices)
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return 0;
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for (v = path->vertices; v->next; v = v->next) {
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v->len = hypot(v->x-v->next->x, v->y-v->next->y);
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sum += v->len;
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}
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v->len = 0;
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return sum;
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}
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static void adjust_length(struct vertex *from, struct vertex *to, double len)
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{
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struct vertex *v;
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double sum, f;
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if (from == to)
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return;
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sum = 0;
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for (v = from->next; v != to; v = v->next) {
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v->len = hypot(v->x-v->next->x, v->y-v->next->y);
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sum += v->len;
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}
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f = len/sum;
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for (v = from->next; v != to; v = v->next)
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v->len *= f;
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}
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/*
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* "corner" replaces a corner with a ploygon if the corner is too sharp to be
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* within distance "d" of the bend radius. This may change the point from
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* where we resume drawing (originally the corner point, "b"). "corner"
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* therefore returns the new end of the arc.
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*/
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static struct vertex *corner(struct path *path, struct vertex *a,
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const struct vertex *b, const struct vertex *c, double r, double d)
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{
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/* points to vectors */
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double ax = b->x-a->x;
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double ay = b->y-a->y;
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double bx = c->x-b->x;
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double by = c->y-b->y;
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/* vector length */
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double aa = hypot(ax, ay);
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double bb = hypot(bx, by);
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/* dot and cross product */
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double dp = ax*bx+ay*by; /* a * b = a*b*cos 2t */
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double cp = ax*by-ay*bx; /* |a x b| = a*b*sin 2t */
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double dir = copysign(1, cp);
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/* see corner.fig */
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double dd; /* "d" of the given vectors */
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double tt; /* tan t */
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double s; /* distance between start of arc and corner */
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double t2; /* angle, t*2 */
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/* see arc.fig */
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double p; /* half-angle of border side of border segment */
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double q; /* half-angle of connecting segment */
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double u; /* length of border side of border segment */
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double v; /* half-length of connecting segment */
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int n; /* number of connecting segments (0 if none) */
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double f; /* scale factor; various uses */
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double fa, fb; /* scale factors for first and last vertex */
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double ang; /* current angle, for iteration */
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double x, y; /* current position; for iteration */
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int i; /* segment; for iteration */
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struct vertex *v0; /* first vertex of arc */
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struct vertex *v1; /* last vertex of arc */
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/*
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* http://en.wikipedia.org/wiki/Dot_product
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* dp = a*b*cos 2t
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*
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* http://en.wikipedia.org/wiki/Cross_product
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* cp = a*b*sin 2t
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*
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* http://en.wikipedia.org/wiki/Tangent_half-angle_formula
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* tan t = sin 2t/(1+cos 2t)
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*/
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tt = cp/(aa*bb+dp);
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/*
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* From s = r*tan t
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*/
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s = fabs(r*tt);
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/*
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* From r^2+s^2 = (r+d)^2
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*/
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dd = hypot(r, s)-r;
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if (debug) {
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fprintf(stderr, "a = (%g, %g)-(%g, %g) = (%g, %g); |a| = %g\n",
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b->x, b->y, a->x, a->y, ax, ay, aa);
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fprintf(stderr, "b = (%g, %g)-(%g, %g) = (%g, %g); |b| = %g\n",
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c->x, c->y, b->x, b->y, bx, by, bb);
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fprintf(stderr, "sin 2t = %g, cos 2t = %g, tan t = %g\n",
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cp/aa/bb, dp/aa/bb, tt);
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fprintf(stderr, "r = %g, d = %g, s = %g, dd = %g\n",
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r, d, s, dd);
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}
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/*
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* We only know how to make a rounded corner if two vectors are
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* involved. They therefore have to be long enough to accommodate the
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* entire arc, from beginning to end. Furthermore, we split the
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* available length in half, one for the inbound arc, the other for the
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* outbound arc.
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*/
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/*
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* @@@ Our error checking is a bit overzealous and doesn't provide
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* enough information to debug any problems. Turn errors into warnings
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* for now.
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*/
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if (aa/2 < s) {
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fprintf(stderr, "first vector is too short (%g/2 < %g)\n",
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aa, s);
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// exit(1);
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}
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if (bb/2 < s) {
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fprintf(stderr, "second vector is too short (%g/2 < %g)\n",
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bb, s);
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// exit(1);
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}
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/*
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* If the corner is already smooth enough, we just keep what we have.
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*/
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if (dd <= d) {
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v1 = clone_vertex(b);
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append_vertex(path, v1);
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return v1;
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}
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/* Step 1: determine the total angle (2*t) */
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t2 = acos(dp/aa/bb);
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/*
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* Step 2: determine the maximum angle of the first and last segment.
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*
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* We use
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* r*cos p = r-d
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* cos p = 1-d/r
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*/
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p = acos(1-d/r);
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/*
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* Step 3: determine the maximum angle of intermediate segments (if
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* there are any).
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*
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* We use
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* (r+d)*cos q = r-d
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* cos q = r-q/(r+d)
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*/
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q = acos((r-d)/(r+d));
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if (debug)
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fprintf(stderr, "t2 = %g, p(max) = %g, q(max) = %g\n",
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deg(t2), deg(p), deg(q));
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/*
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* Step 4: emit the starting point of the arc
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*/
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fa = s/aa;
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x = b->x-fa*ax;
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y = b->y-fa*ay;
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v0 = add_vertex(path, x, y, b->r, b->d, b->tag);
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v0->len = a->len*(1-fa);
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/*
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* Step 5: determine if we need intermediate points. If yes, how many,
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* and then proceed to add them.
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*/
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if (t2 > 2*p) {
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n = (int) ceil((t2-2*(p+q))/(2*q));
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/*
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* We could evenly distribute the slack and try to pick a
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* smaller value for d, but that seems difficult.
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*
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* A drawback of reducing p would be that we may make the
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* corner unnecessarily sharp, possibly even turning against
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* the general direction of the turn. We'd still respect the
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* bend radius and the tolerance, but the result may look weird
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* anyway.
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*
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* For now, we just center the polygon.
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*/
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q = (t2/2-p)/(n+1);
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if (n)
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ang = p+q;
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else {
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ang = t2/2;
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/*
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* @@@ To do: adjust the radius such that we always hug
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* the r-d circle (see arc.fig) and usually not the
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* r+d circle. Right now, it's just the opposite.
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*/
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}
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u = tan(p)*(r-d);
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v = tan(q)*(r-d);
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f = (u+v)/aa;
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for (i = 0; i <= n; i++) {
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x += f*ax*cos(ang-q)-dir*f*ay*sin(ang-q);
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y += dir*f*ax*sin(ang-q)+f*ay*cos(ang-q);
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if (debug)
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fprintf(stderr, " %d/%d: %g %g @ %g\n", i, n,
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x, y, deg(ang));
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add_vertex(path, x, y, 0, 0, NULL);
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ang += 2*q;
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f = (2*v)/aa;
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}
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}
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/*
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* Step 6: emit the finishing point of the arc
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*/
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fb = s/bb;
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v1 = add_vertex(path, b->x+fb*bx, b->y+fb*by, 0, 0, NULL);
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v1->len = b->len*(1-fb);
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/*
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* Step 7: adjust the nominal length of the segments
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*/
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adjust_length(v0, v1, a->len*fa+b->len*fb);
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return v1;
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}
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struct path *round_path(const struct path *path, double r, double d)
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{
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struct path *new;
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struct vertex *prev;
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const struct vertex *v;
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new = alloc_path();
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if (!path->vertices)
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return new;
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prev = clone_vertex(path->vertices);
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append_vertex(new, prev);
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if (!path->vertices->next)
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return new;
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if (prev->r)
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r = prev->r;
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if (prev->d)
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d = prev->d;
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for (v = path->vertices->next; v->next; v = v->next) {
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if (v->r)
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r = v->r;
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if (v->d)
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d = v->d;
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prev = corner(new, prev, v, v->next, r, d);
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}
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append_vertex(new, clone_vertex(v));
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return new;
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}
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static void move_vertex(struct path *path, const struct vertex *v,
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double nx, double ny, double dist, double r)
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{
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struct vertex *new;
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new = clone_vertex(v);
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new->x += nx*dist;
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new->y += ny*dist;
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new->r = r;
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append_vertex(path, new);
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}
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struct path *stretch_path(const struct path *path, double dist, double r)
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{
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struct path *new; /* new path */
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const struct vertex *v; /* current vertex (for iteration) */
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const struct vertex *a, *b, *c; /* previous, current, next vertex */
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double nx, ny; /* 2D normals */
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double f; /* factor for normalization */
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double tx, ty; /* temporary 2D normals */
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new = alloc_path();
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a = path->vertices;
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b = a->next;
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nx = b->y-a->y;
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ny = a->x-b->x;
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f = hypot(nx, ny);
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if (a->r)
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r = a->r;
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move_vertex(new, a, nx/f, ny/f, dist, r);
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for (v = path->vertices->next; v->next; v = v->next) {
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double tmp;
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b = v;
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c = v->next;
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tx = b->y-a->y;
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ty = a->x-b->x;
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f = hypot(tx, ty);
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nx = tx/f;
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ny = ty/f;
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tmp = f;
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tx = c->y-b->y;
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ty = b->x-c->x;
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f = hypot(tx, ty);
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nx += tx/f;
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ny += ty/f;
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if (b->r)
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r = b->r;
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f = hypot(nx, ny);
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nx /= f;
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ny /= f;
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/*
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* We have this far:
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* nx, ny = normal on corner, normalized
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* tmp = |a|, length of vector "a" (A -> B)
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* dist = the distance by which we stretch
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*
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* As shown in stretch.fig, we the length we need is
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* d' = d/cos(90-t)
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*
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* With
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* http://en.wikipedia.org/wiki/Trigonometric_identities#Symmetry
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* cos(90-t) = sin t = (n x a)/(|n|*|a|)
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*
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* Thus
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* d' = d/sin(t) - d*(|n|*|a|)/(n x a)
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* = d/sin(t) - d*|a|/(n x a)
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*/
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tmp = dist*tmp/(nx*(b->y-a->y)-ny*(b->x-a->x));
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move_vertex(new, b, nx, ny, tmp, r+dist);
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a = v;
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}
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nx = v->y-a->y;
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ny = a->x-v->x;
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f = hypot(nx, ny);
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if (v->r)
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r = v->r;
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move_vertex(new, v, nx/f, ny/f, dist, r);
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return new;
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}
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struct path *load_path(FILE *file)
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{
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struct path *path;
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char buf[1100]; /* plenty :) */
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char buf2[sizeof(buf)];
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char *s;
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float x, y, tmp;
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float r = 0, d = 0;
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const char *tag = NULL;
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path = alloc_path();
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while (fgets(buf, sizeof(buf),file)) {
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s = strchr(buf, '\n');
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if (s)
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*s = 0;
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if (sscanf(buf, "#r=%f", &tmp) == 1) {
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r = tmp;
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continue;
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}
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if (sscanf(buf, "#delta=%f", &tmp) == 1) {
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d = tmp;
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continue;
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}
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if (sscanf(buf, "#tag=%s", buf2) == 1) {
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tag = stralloc(buf2);
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continue;
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}
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if (*buf == '#')
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continue;
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if (sscanf(buf, "%f %f", &x, &y) != 2) {
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fprintf(stderr, "can't parse \"%s\"\n", buf);
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exit(1);
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}
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add_vertex(path, x, y, r, d, tag);
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r = 0;
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d = 0;
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tag = NULL;
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}
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path_set_length(path);
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return path;
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}
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void save_path(FILE *file, const struct path *path)
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{
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const struct vertex *v;
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for (v = path->vertices; v; v = v->next) {
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if (v->r)
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fprintf(file, "#r=%f\n", v->r);
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if (v->d)
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fprintf(file, "#delta=%f\n", v->d);
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if (v->tag)
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fprintf(file, "#delta=%f\n", v->d);
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fprintf(file, "%f %f\n", v->x, v->y);
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}
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}
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