File:Gilbert tessellation.svg
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Summary
DescriptionGilbert tessellation.svg |
English: Example of Gilbert tessellation with free angles. |
Date | |
Source | Own work |
Author | Claudio Rocchini |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
Source Code
/* (C) 2012 Claudio Rocchini - CC BY 3.0 */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <vector>
#include <algorithm>
const double PI = 3.1415926535897932384626433832795;
inline double drand() { return double(rand())/RAND_MAX; }
class point2 {
public:
double x,y;
point2() {}
point2( double nx, double ny ): x(nx),y(ny) {}
};
class seed {
public:
point2 p; // seed position
double a; // main angle
double l[2]; // extents
};
class inter { // intersection
public:
int i,j;
double ti; double tj;
inline inter();
inline inter( int ni, int nj, double nti, double ntj ) : i(ni),j(nj),ti(nti),tj(ntj) {}
inline bool operator< ( const inter & ii ) const { return fabs(ti)<fabs(ii.ti); }
};
bool intersects( const seed & s1, const seed & s2, double & t1, double & t2 ) {
double dx1 = cos(s1.a); double dy1 = sin(s1.a);
double dx2 = cos(s2.a); double dy2 = sin(s2.a);
const double de = dx1*dy2-dy1*dx2;
if(fabs(de)<1e-8) return false;
double ox1 = s1.p.x; double oy1 = s1.p.y;
double ox2 = s2.p.x; double oy2 = s2.p.y;
t1 = (-ox1*dy2+ox2*dy2+dx2*oy1-dx2*oy2)/de;
t2 = ( dx1*oy1-dx1*oy2-dy1*ox1+dy1*ox2)/de;
return t1<s1.l[0] && t1>-s1.l[1] && t2<s2.l[0] && t2>-s2.l[1];
}
int main() {
const double SX = 800; const double SY = 800; const int N = 256;
int i,j;
static seed seeds[N];
std::vector<inter> inters; std::vector<inter>::iterator ii;
for(i=0;i<N;++i) {
seeds[i].p.x = drand()*SX; seeds[i].p.y = drand()*SY;
seeds[i].a = PI*drand(); // ortho version: drand()>= 0.5 ? 0 : PI/2;
seeds[i].l[0] = SX*10; seeds[i].l[1] = SX*10;
}
for(i=0;i<N-1;++i) for(j=i+1;j<N;++j) {
double t1,t2;
if(intersects(seeds[i],seeds[j],t1,t2)) {
inters.push_back( inter(i,j,t1,t2) );
inters.push_back( inter(j,i,t2,t1) );
} }
std::sort(inters.begin(),inters.end());
for(ii=inters.begin();ii!=inters.end();++ii) { // compute intersection on time
if(ii->ti < seeds[ii->i].l[0] && ii->ti > -seeds[ii->i].l[1] &&
ii->tj < seeds[ii->j].l[0] && ii->tj > -seeds[ii->j].l[1]) {
if( fabs(ii->ti) > fabs(ii->tj) ) {
if(ii->ti>0) seeds[ii->i].l[0] = ii->ti;
else seeds[ii->i].l[1] = -ii->ti;
} } }
for(i=0;i<N;++i) { // page clipping
seed s;
s.p.x = 0; s.p.y = 0; s.a = 0; s.l[0] = SX; s.l[1] = 0;
double t1,t2;
if(intersects(seeds[i],s,t1,t2)) { if(t1>0) seeds[i].l[0] = t1; else seeds[i].l[1] = -t1; }
s.p.y = SY;
if(intersects(seeds[i],s,t1,t2)) { if(t1>0) seeds[i].l[0] = t1; else seeds[i].l[1] = -t1; }
s.p.x = 0; s.p.y = 0; s.l[0] = SY; s.l[1] = 0; s.a = PI/2;
if(intersects(seeds[i],s,t1,t2)) { if(t1>0) seeds[i].l[0] = t1; else seeds[i].l[1] = -t1; }
s.p.x = SX;
if(intersects(seeds[i],s,t1,t2)) { if(t1>0) seeds[i].l[0] = t1; else seeds[i].l[1] = -t1; }
}
FILE * fo = fopen("gilbert.svg","w"); // output the results
fprintf(fo,
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
"<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.0\" width=\"%g\" height=\"%g\" id=\"%s\">\n"
,SX,SY,"girlbert"
);
fprintf(fo,"<g style=\"stroke:#000000;stroke-width:2;stroke-linecap:round;fill:none\">\n");
for(i=0;i<N;++i){
fprintf(fo,"<line x1=\"%6.2f\" y1=\"%6.2f\" x2=\"%6.2f\" y2=\"%6.2f\"/>\n"
,seeds[i].p.x+seeds[i].l[0]*cos(seeds[i].a)
,seeds[i].p.y+seeds[i].l[0]*sin(seeds[i].a)
,seeds[i].p.x+seeds[i].l[1]*cos(seeds[i].a+PI)
,seeds[i].p.y+seeds[i].l[1]*sin(seeds[i].a+PI)
);
}
fprintf(fo,"</g>\n");
fprintf(fo,"</svg>\n");
fclose(fo);
return 0;
}
Items portrayed in this file
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8 August 2012
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 11:36, 8 August 2012 | 800 × 800 (14 KB) | wikimediacommons>Rocchini |
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