+++ /dev/null
-/* spline.cc
- Routine to convert cubic splines into quadratic ones.
-
- Part of the swftools package.
-
- Copyright (c) 2001,2002,2003 Matthias Kramm <kramm@quiss.org>
-
- 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
-
-#include <stdlib.h>
-#include <stdio.h>
-#include <math.h>
-#include "spline.h"
-
-static int solve(double a,double b,double c, double*dd)
-{
- double det=b*b-4*a*c;
- int pos = 0;
- if(det<0) return 0; // we don't do imaginary. not today.
- if(det==0) { // unlikely, but we have to deal with it.
- dd[0]=-b/2*a;
- return (dd[0]>0 && dd[0]<1);
- }
-
- dd[pos]=(-b+sqrt(det))/(2*a);
- if(dd[pos]>0 && dd[pos]<1)
- pos++;
- dd[pos]=(-b-sqrt(det))/(2*a);
- if(dd[pos]>0 && dd[pos]<1)
- pos++;
- return pos;
-}
-
-struct plotxy splinepos(struct plotxy p0, struct plotxy p1, struct plotxy p2, struct plotxy p3, double d) {
- struct plotxy p;
- p.x = (p0.x * d*d*d + p1.x * 3*(1-d)*d*d + p2.x * 3*(1-d)*(1-d)*d + p3.x * (1-d)*(1-d)*(1-d));
- p.y = (p0.y * d*d*d + p1.y * 3*(1-d)*d*d + p2.y * 3*(1-d)*(1-d)*d + p3.y * (1-d)*(1-d)*(1-d));
- return p;
-}
-
-inline double plotxy_dist(struct plotxy a, struct plotxy b)
-{
- double dx = a.x - b.x;
- double dy = a.y - b.y;
- return sqrt(dx*dx+dy*dy);
-}
-
-
-int wp(double p0,double p1,double p2,double p3,double*dd)
-{
- double div= (6*p0-18*p1+18*p2-6*p3);
- if(!div) return 0;
- dd[0] = -(6*p1-12*p2+6*p3)/div;
- return (dd[0]>0 && dd[0]<1);
-}
-
-int approximate(struct plotxy p0, struct plotxy p1, struct plotxy p2, struct plotxy p3, struct qspline*q)
-{
- double roots[12];
- int pos = 0;
- int s,t;
- struct plotxy myxy[12];
- struct plotxy last;
- // the parameters for the solve function are the 1st deviation of a cubic spline
- roots[pos] = 0;pos++;
- pos += solve(3*p0.x-9*p1.x+9*p2.x-3*p3.x, 6*p1.x-12*p2.x+6*p3.x,3*p2.x-3*p3.x, &roots[pos]);
- pos += solve(3*p0.y-9*p1.y+9*p2.y-3*p3.y, 6*p1.y-12*p2.y+6*p3.y,3*p2.y-3*p3.y, &roots[pos]);
- pos += wp(p0.x,p1.x,p2.x,p3.x,&roots[pos]);
- pos += wp(p0.x,p1.x,p2.x,p3.x,&roots[pos]);
- roots[pos] = 1;pos++;
-
- // bubblesort - fast enough for 4-6 parameters
- for(s=0;s<pos;s++)
- for(t=s+1;t<pos;t++)
- if(roots[s]>roots[t])
- {
- double tmp=roots[s];
- roots[s]=roots[t];
- roots[t]=tmp;
- }
- for(t=0;t<pos;t++)
- myxy[t] = splinepos(p0,p1,p2,p3,roots[t]);
-
- s=1;
- last = myxy[0];
- for(t=1;t<pos;t++)
- {
- double dist=plotxy_dist(myxy[t],last);
- myxy[s]=myxy[t];
- roots[s]=roots[t];
- if(dist>0.01 || t==pos-1)
- {
- s++;
- last=myxy[t];
- }
- }
- pos = s;
-
- // try 1:curve through 3 points, using the middle of the cubic spline.
- for(t=0;t<pos-1;t++) {
-// circle(myxy[t].x,myxy[t].y,5);
- struct plotxy control;
- struct plotxy midpoint = splinepos(p0,p1,p2,p3,(roots[t]+roots[t+1])/2);
- control.x = midpoint.x + (midpoint.x-(myxy[t].x+myxy[t+1].x)/2);
- control.y = midpoint.y + (midpoint.y-(myxy[t].y+myxy[t+1].y)/2);
- //qspline(myxy[t],control,myxy[t+1]);
- q[t].start=myxy[t];
- q[t].control=control;
- q[t].end=myxy[t+1];
- }
-
- /*
- for(t=0;t<pos-1;t++) {
- plotxy control;
- vga.setcolor(0xffffff);
- circle(myxy[t].x,myxy[t].y,5);
- if(t==0) {
- //double lenmain = distance(p3,p0);
- //double lenq = distance(myxy[0],myxy[1]);
- //control.x = myxy[0].x + (p2.x-p3.x);// /lenmain*lenq;
- //control.y = myxy[0].y + (p2.y-p3.y);// /lenmain*lenq;
- plotxy midpoint = splinepos(p0,p1,p2,p3,(roots[t]+roots[t+1])/2);
- control.x = midpoint.x + (midpoint.x-(myxy[t].x+myxy[t+1].x)/2);
- control.y = midpoint.y + (midpoint.y-(myxy[t].y+myxy[t+1].y)/2);
- qspline(myxy[0], control, myxy[1]);
- } else {
- control.x = 2*myxy[t].x - last.x;
- control.y = 2*myxy[t].y - last.y;
- qspline(myxy[t], control, myxy[t+1]);
- }
- last = control;
- }*/
- return pos-1;
-}
-
-/* move the control point so that the spline runs through the original
- control point */
-void fixcp(qspline*s)
-{
- plotxy mid,dir;
- mid.x = (s->end.x + s->start.x)/2;
- mid.y = (s->end.y + s->start.y)/2;
- dir.x = s->control.x - mid.x;
- dir.y = s->control.y - mid.y;
- s->control.x = mid.x + 2*dir.x;
- s->control.y = mid.y + 2*dir.y;
-}
-
-int approximate2(struct cspline*s, struct qspline*q, double quality, double start, double end);
-
-void check(struct cspline*s, struct qspline*q, int num)
-{
- int t;
- plotxy p = s->start;
- for(t=0;t<num;t++) {
- plotxy p2 = q[t].start;
- if(plotxy_dist(p,p2) > 0.005) {
- printf("--\n");
- exit(1);
- }
- p = q[t].end;
- }
- if(plotxy_dist(p, s->end) > 0.005) {
- printf("--\n");
- exit(1);
- }
-}
-
-int cspline_approximate(struct cspline*s, struct qspline*q, double quality, approximate_method method)
-{
- if(method==0) {
- return approximate(s->start, s->control1, s->control2, s->end, q);
- } else {
- return approximate2(s, q, quality, 0.0, 1.0);
- }
-}
-inline plotxy cspline_getpoint(cspline*s, double t)
-{
- plotxy p;
- p.x= s->end.x*t*t*t + 3*s->control2.x*t*t*(1-t)
- + 3*s->control1.x*t*(1-t)*(1-t) + s->start.x*(1-t)*(1-t)*(1-t);
- p.y= s->end.y*t*t*t + 3*s->control2.y*t*t*(1-t)
- + 3*s->control1.y*t*(1-t)*(1-t) + s->start.y*(1-t)*(1-t)*(1-t);
- return p;
-}
-plotxy cspline_getderivative(cspline*s, double t)
-{
- plotxy d;
- d.x = s->end.x*(3*t*t) + 3*s->control2.x*(2*t-3*t*t) +
- 3*s->control1.x*(1-4*t+3*t*t) + s->start.x*(-3+6*t-3*t*t);
- d.y = s->end.y*(3*t*t) + 3*s->control2.y*(2*t-3*t*t) +
- 3*s->control1.y*(1-4*t+3*t*t) + s->start.y*(-3+6*t-3*t*t);
- return d;
-}
-plotxy cspline_getderivative2(cspline*s, double t)
-{
- plotxy d;
- d.x = s->end.x*(6*t) + 3*s->control2.x*(2-6*t) +
- 3*s->control1.x*(-4+6*t) + s->start.x*(6-6*t);
- d.y = s->end.y*(6*t) + 3*s->control2.y*(2-6*t) +
- 3*s->control1.y*(-4+6*t) + s->start.y*(6-6*t);
- return d;
-}
-plotxy cspline_getderivative3(cspline*s, double t)
-{
- plotxy d;
- d.x = 6*s->end.x - 18*s->control2.x + 18*s->control1.x - 6*s->start.x;
- d.y = 6*s->end.y - 18*s->control2.y + 18*s->control1.y - 6*s->start.y;
- return d;
-}
-void cspline_getequalspacedpoints(cspline*s, float**p, int*num, double dist)
-{
- plotxy d,next;
- double t = 0;
- int end = 0;
- int pos = 0;
- float*positions = (float*)malloc(1048576);
- do
- {
- if(t>=1.0) {
- t = 1.0;
- end = 1;
- }
-
- plotxy d = cspline_getderivative(s, t);
- plotxy d2 = cspline_getderivative2(s, t);
-
- double dl = sqrt(d.x*d.x+d.y*d.y);
- double dl2 = sqrt(d2.x*d2.x+d2.y*d2.y);
-
- double rdl = dist/dl;
-
- if(rdl>1.0-t)
- rdl = 1.0-t;
-
- plotxy p = cspline_getpoint(s, t);
- while(plotxy_dist(cspline_getpoint(s, t+rdl), p) > dist) {
- /* we were ask to divide the spline into dist long fragments,
- but for the value we estimated even the geometric distance
- is bigger than 'dist'. Approximate a better value.
- */
- rdl = rdl*0.9;
- }
-
- positions[pos] = t;
- t+=rdl;
- pos++;
- }
- while(!end);
- *num = pos;
- *p = positions;
-}
-
-plotxy qspline_getpoint(qspline*s, double t)
-{
- plotxy p;
- p.x= s->end.x*t*t + 2*s->control.x*t*(1-t) + s->start.x*(1-t)*(1-t);
- p.y= s->end.y*t*t + 2*s->control.y*t*(1-t) + s->start.y*(1-t)*(1-t);
- return p;
-}
-plotxy qspline_getderivative(qspline*s, double t)
-{
- plotxy p;
- p.x= s->end.x*2*t + 2*s->control.x*(1-2*t) + s->start.x*(-2+2*t);
- p.y= s->end.y*2*t + 2*s->control.y*(1-2*t) + s->start.y*(-2+2*t);
- return p;
-}
-plotxy qspline_getderivative2(qspline*s, double t)
-{
- plotxy p;
- p.x= s->end.x*2 + 2*s->control.x*(-2) + s->start.x*(2);
- p.y= s->end.y*2 + 2*s->control.y*(-2) + s->start.y*(2);
- return p;
-}
-double qspline_getlength(qspline*s)
-{
- double t = 0;
- int end = 0;
- double len;
- plotxy last = qspline_getpoint(s, 0.0);
- do {
- if(t>=1.0) {
- t = 1.0;
- end = 1;
- }
- plotxy d2 = qspline_getderivative2(s, t);
- double dl2 = sqrt(d2.x*d2.x+d2.y*d2.y);
- double rdl = 1.0/dl2;
- if(rdl>0.01)
- rdl = 0.01;
- t+=rdl;
- plotxy here = qspline_getpoint(s, t);
- len += plotxy_dist(last, here);
- last = here;
- }
- while(!end);
- return len;
-}
-void qsplines_getequalspacedpoints(qspline**s, int num, float**p, int*pnum, double acc)
-{
-/* int t;
- float r[128];
- for(t=0;t<num;t++) {
- qspline_getlength();
- }*/
- return;
-}
-
-void qsplines_getdrawpoints(qspline*s, int num, float**p, int*pnum, double acc)
-{
- plotxy d,next;
- double t = 0;
- int end = 0;
- int pos = 0;
- float*positions = (float*)malloc(1048576);
- do
- {
- if(t>=1.0) {
- t = 1.0;
- end = 1;
- }
-
- plotxy d = qspline_getderivative(s, t);
- double dl = sqrt(d.x*d.x+d.y*d.y);
- double rdl = acc/dl;
-
- if(rdl>acc)
- rdl = acc;
-
- positions[pos] = t;
- t+=rdl;
- pos++;
- }
- while(!end);
- *pnum = pos;
- *p = positions;
-}
-
-
-#define TANGENTS
-
-int approximate2(struct cspline*s, struct qspline*q, double quality, double start, double end)
-{
- int num=0;
- plotxy qr1,qr2,cr1,cr2;
- double dist1,dist2;
- int t;
- int recurse = 0;
- int probes = 15;
- qspline test;
- test.start = cspline_getpoint(s, start);
- test.control = cspline_getpoint(s, (start+end)/2);
- test.end = cspline_getpoint(s, end);
- fixcp(&test);
-
-#ifdef TANGENTS
- if(start< 0.5) {
- test.control = cspline_getderivative(s, start);
- test.control.x *= (end-start)/2;
- test.control.y *= (end-start)/2;
- test.control.x += test.start.x;
- test.control.y += test.start.y;
- } else {
- test.control = cspline_getderivative(s, end);
- test.control.x *= -(end-start)/2;
- test.control.y *= -(end-start)/2;
- test.control.x += test.end.x;
- test.control.y += test.end.y;
- }
-#endif
-
- for(t=0;t<probes;t++) {
- double pos = 0.5/(probes*2)*(t*2+1);
- qr1 = qspline_getpoint(&test, pos);
- cr1 = cspline_getpoint(s, start+pos*(end-start));
- dist1 = plotxy_dist(qr1, cr1);
- if(dist1>quality) {
- recurse=1;break;
- }
- qr2 = qspline_getpoint(&test, (1-pos));
- cr2 = cspline_getpoint(s, start+(1-pos)*(end-start));
- dist2 = plotxy_dist(qr2, cr2);
- if(dist2>quality) {
- recurse=1;break;
- }
- }
-
- if(recurse && (end-start)>1.0/120) {
- /* quality is too bad, split it up recursively */
- num += approximate2(s, q, quality, start, (start+end)/2);
- q+=num;
- num += approximate2(s, q, quality, (start+end)/2, end);
- return num;
- } else {
- *q = test;
- return 1;
- }
-}
-
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