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File:Gilbert tessellation.svg

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Original file(SVG file, nominally 800 × 800 pixels, file size: 14 KB)

Summary

Description
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:
w:en:Creative Commons
attribution
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;
}

File history

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Date/TimeThumbnailDimensionsUserComment
current09:36, 8 August 2012Thumbnail for version as of 09:36, 8 August 2012800 × 800 (14 KB)Rocchini
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