File:Poincare halfplane heptagonal hb.svg

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Summary

DescriptionPoincare halfplane heptagonal hb.svg	Stellated Eptagonal honeycomb (tiling) of the Poincare Half-Plane Model
Date	15 November 2007
Source	Own work
Author	Claudio Rocchini
Permission (Reusing this file)	CC-BY 3.0

Source Code

The complete and dirty C++ generating source code:

/* Poincare Half-plane model (C)2007 Claudio Rocchini, the SHQN man */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <vector>

const double PI = 3.1415926535897932384626433832795;
const double EPS  = 1e-12; const double EPS2 = 1e-4;
const int dimx = 800; const int dimy = 400;
const int OX = dimx/2; const int OY = dimy;

namespace hp {

class point {
public:
	double x,y;
	point(){}
	point( double nx, double ny ) : x(nx),y(ny) {}
};

class line {
protected:
	void at_param( double t, point & q ) const;
	double param( const point & q ) const;
public:
	bool   di;		// direzione: diretta o rovesciata
	double ra;		// raggio: 0 = linea verticale
	double cx;		// centro vertice
	void from_points( const point & p, const point & q );
	void from_point_angle( const point & p, double a );
	void at_dist( const point & p, double d, bool dir, point & q ) const;
	double angle( const point & p ) const;
};

double dist(  const point & p, const point & q );

void line::from_points( const point & p, const point & q ) {
	if( fabs(p.x-q.x)<EPS ) {
		ra = 0; cx = 0.5*(p.x+q.x);
	} else {
		cx = 0.5*(q.x*q.x+q.y*q.y-p.x*p.x-p.y*p.y)/(q.x-p.x);
		ra = sqrt( (p.x-cx)*(p.x-cx)+p.y*p.y );
	}
	double ip = param(p); double iq = param(q);
	di = ip<iq;
}

void line::from_point_angle( const point & p, double a ){
	if( fabs(a-PI/2)<EPS || fabs(a-PI*3/2)<EPS ) { ra = 0; cx = p.x; }
	else {
		double b = a+PI/2;
		double co = cos(b); double si = sin(b);
		ra = fabs(p.y/si); cx = -(p.y*co-p.x*si)/si;
	}
	di = cos(a)>=0;
}

void line::at_param( double t, point & q ) const {
	if(ra==0) { q.x = cx; q.y = t; }
	else { q.x = ra*cos(t) + cx; q.y = ra*sin(t); }
}

double line::param( const point & q ) const {
	if(ra==0) return q.y;
	else return atan2(q.y,q.x-cx);
}

void line::at_dist( const point & p, double d, bool dir, point & q ) const {
	if(ra==0) {
		double tmi,tma,tmm;		
		if(dir!=di) {
			tmi = 0 + EPS; tma = param(p);
			for(;;) {
				tmm = (tmi+tma)/2; at_param(tmm,q);
				double ld = dist(p,q); if(ld>d) tmi = tmm; else tma = tmm;
				if(tma-tmi<EPS) break;
		}	}
		else {
			tmi = param(p); tma = tmi*100;
			for(;;) {
				tmm = (tmi+tma)/2; at_param(tmm,q);
				double ld = dist(p,q); if(ld<d) tmi = tmm; else tma = tmm;
				if(tma-tmi<EPS) break;
	}	}	}
	else {
		double tmi,tma,tmm;	
		if(dir!=di) {
			tmi = 0 + EPS; tma = param(p);
			for(;;) {
				tmm = (tmi+tma)/2; at_param(tmm,q);
				double ld = dist(p,q); if(ld>d) tmi = tmm; else tma = tmm;
				if(tma-tmi<EPS) break;
		}	}
		else {
			tmi = param(p); tma = PI-EPS;
			for(;;) {
				tmm = (tmi+tma)/2; at_param(tmm,q);
				double ld = dist(p,q); if(ld<d) tmi = tmm; else tma = tmm;
				if(tma-tmi<EPS) break;
	}	}	}
}

double line::angle( const point & p ) const {
	double a = 0;
	if(ra==0) a = PI/2;
	else a = atan2(p.y,p.x-cx) - PI/2;
	if(di) a += PI; return a;
}

double dist(  const point & p, const point & q ) {
	line l; l.from_points(p,q);
	if(l.ra!=0) 	{
		double A = l.cx - l.ra;
		double B = l.cx + l.ra;
		double PA = sqrt( (p.x-A)*(p.x-A)+p.y*p.y );
		double PB = sqrt( (p.x-B)*(p.x-B)+p.y*p.y );
		double QA = sqrt( (q.x-A)*(q.x-A)+q.y*q.y );
		double QB = sqrt( (q.x-B)*(q.x-B)+q.y*q.y );
		return fabs(log( (PA/PB) / (QA/QB) ));
	} else {
		double A = l.cx;
		double PA = sqrt( (p.x-A)*(p.x-A)+p.y*p.y );
		double QA = sqrt( (q.x-A)*(q.x-A)+q.y*q.y );
		return fabs(log( (PA/QA) ));
	}
}

void draw_point( FILE * fp, const point & p, double R ) {
	fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%g\"/>\n",p.x+OX,OY-p.y,R);
}

void draw_line( FILE * fp, const line & l ) {
	if(l.ra==0)
		fprintf(fp,"<line x1=\"%5.1lf\" y1=\"0\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>"
			,OX+l.cx ,OX+l.cx ,double(dimy) );
	else
		fprintf(fp,"<path d=\"M %5.1lf,%5.1lf A %g,%g 0 0,1 %5.1lf,%5.1lf\"/>\n"
			,OX+l.cx-l.ra,double(dimy),l.ra,l.ra,OX+l.cx+l.ra,double(dimy) );
}

void draw_arc( FILE * fp, const line & l, const point & p, const point & q )
{
	if(l.ra==0)
		fprintf(fp,"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
			,OX+l.cx,OY-p.y,OX+l.cx,OY-q.y);
	else
		fprintf(fp,"<path d=\"M %5.1lf,%5.1lf A %g,%g 0 0,%d %5.1lf,%5.1lf\"/>\n"
			,OX+p.x,OY-p.y,l.ra,l.ra,p.x<q.x ? 1 : 0,OX+q.x,OY-q.y);
}

double e_dist( const point & p1, const point & p2 ){
	const double dx = p1.x - p2.x; const double dy = p1.y - p2.y;
	return sqrt(dx*dx+dy*dy);
}

}	// End namespace hp

class edge
{
public:
	int i[2];
	edge(){}
	edge( int i0, int i1 ) { i[0]=i0; i[1]=i1; }
	inline operator== ( const edge & e ) const {
		return (i[0]==e.i[0] && i[1]==e.i[1]) ||
			   (i[0]==e.i[1] && i[1]==e.i[0]) ;
	}
};

int main(){
	const double R = 2;
	const int L = 7;
	const double qangle = 2*PI/3;	// Angolo di tassellazione

	std::vector<hp::point> nodes;
	std::vector< edge >    edges; std::vector< edge >    edges2;
	int i;
		// Ricerca lato
	hp::point q[L];
	hp::point c(dimx/2-502.5,dimy/2);
	const double sangle = 0;
	
	double lato = 0; double milato = 1e-4; double malato = 5; const int D = 2;
	for(;;) {
		lato = (milato+malato)/2;
		q[0] = c;
		hp::line k; k.from_point_angle(c,sangle);
		k.at_dist(c,lato,false,q[1]);
		for(i=1;i<L-1;++i) {
			hp::line l; l.from_points(q[i-1],q[i]);
			double a0 = l.angle(q[i]); a0 -= PI-qangle;
			hp::line l1; l1.from_point_angle(q[i],a0);
			l1.at_dist(q[i],lato,false,q[i+1]);
		}
		double d = hp::dist(q[0],q[L-1]);
		if(d<lato) milato = lato; else malato = lato;
		if( malato-milato<EPS) {
			lato = (milato+malato)/2; break;
		}
	}
	std::vector< int > openedges;	
	q[0] = c;
	hp::line k; k.from_point_angle(c,sangle);
	k.at_dist(c,lato,false,q[1]);
	for(i=1;i<L-1;++i) {
		hp::line l; l.from_points(q[i-1],q[i]);
		double a0 = l.angle(q[i]); a0 -= PI-qangle;
		hp::line l1; l1.from_point_angle(q[i],a0);
		l1.at_dist(q[i],lato,false,q[i+1]);
	}
	for(i=0;i<L;++i) {
		nodes.push_back(q[i]);
		edges.push_back( edge(i,(i+1)%L) );
		openedges.push_back( edges.size()-1 );
	}
	for(i=0;i<L;++i)
		edges2.push_back( edge(i,(i+D)%L) );
		// Ciclo di espansione
	int nn = 0; int maxn = 3000;
	while( !openedges.empty() ) {
		int e = openedges.front(); //openedges.erase( openedges.begin() );
		int ip1 = edges[e].i[0]; int ip0 = edges[e].i[1];
		hp::point p0 = nodes[ ip0 ]; hp::point p1 = nodes[ ip1 ];
		int eee[L];
		for(i=0;i<L;++i) {
			eee[i] = ip0;
			hp::line l; l.from_points(p0,p1);
			double a0 = l.angle(p1); a0 -= PI-qangle;
			hp::line l1;  l1.from_point_angle(p1,a0);
			hp::point p2; l1.at_dist(p1,lato,false,p2);

			int ip2 = -1;
			for(ip2=0;ip2<nodes.size();++ip2)
				if( hp::e_dist(nodes[ip2],p2)<EPS2 )
					break;
			if(ip2==nodes.size()) nodes.push_back(p2);

			edge e(ip1,ip2);
			std::vector< int >::iterator jj;
			for(jj=openedges.begin();jj!=openedges.end();++jj)
				if(edges[*jj]==e)
					break;
			if(jj==openedges.end()) {
				openedges.push_back(edges.size());
				edges.push_back(e);
			}
			else openedges.erase(jj);
			p0 = p1; ip0 = ip1;
			p1 = p2; ip1 = ip2;
		}
		for(i=0;i<L;++i)
			edges2.push_back( edge(eee[i],eee[(i+D)%L]) );
		if(++nn>=maxn) break;
	}

	FILE * fp = fopen("hp.svg","w");
	fprintf(fp,
		"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
		"<!-- Created with svg-rocco-library v1.0 -->\n"
		"<svg\n"
		"xmlns:svg=\"http://www.w3.org/2000/svg\"\n"
		"xmlns=\"http://www.w3.org/2000/svg\"\n"
		"xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n"
		"version=\"1.0\"\n"
		"width=\"%d\"\n"
		"height=\"%d\"\n"
		"id=\"rocco\"\n"
		">\n"
		,dimx,dimy
	);

	const double MINDIST = 1; const double MINDIST2 = 4;
	fprintf(fp,"<g id=\"arc_s\" style=\"fill:none;stroke:#0000E0;stroke-width:1;stroke-opacity:0.95;stroke-dasharray:none\">\n");
	std::vector< edge >::iterator jj;
	for(jj=edges2.begin();jj!=edges2.end();++jj){
		if( (nodes[ jj->i[0]].x<-dimx/2 || nodes[ jj->i[0]].x>dimx/2 ||
			 nodes[ jj->i[0]].y<0       || nodes[ jj->i[0]].y>dimy   ) &&
			(nodes[ jj->i[1]].x<-dimx/2 || nodes[ jj->i[1]].x>dimx/2 ||
			 nodes[ jj->i[1]].y<0       || nodes[ jj->i[1]].y>dimy   ) )
			continue;
		double dd = hp::e_dist( nodes[ jj->i[0]], nodes[ jj->i[1]] );
		if(dd<MINDIST2) continue;
		hp::line l; l.from_points( nodes[ jj->i[0]], nodes[ jj->i[1]] );
		hp::draw_arc(fp,l,nodes[ jj->i[0]], nodes[ jj->i[1]] );
	}
	fprintf(fp,"</g>\n");
	fprintf(fp,"<g id=\"arc_s\" style=\"fill:none;stroke:#000000;stroke-width:2;stroke-opacity:0.95;stroke-dasharray:none\">\n");
	for(jj=edges.begin();jj!=edges.end();++jj){
		if( (nodes[ jj->i[0]].x<-dimx/2 || nodes[ jj->i[0]].x>dimx/2 ||
			 nodes[ jj->i[0]].y<0       || nodes[ jj->i[0]].y>dimy   ) &&
			(nodes[ jj->i[1]].x<-dimx/2 || nodes[ jj->i[1]].x>dimx/2 ||
			 nodes[ jj->i[1]].y<0       || nodes[ jj->i[1]].y>dimy   ) )
			continue;
		double dd = hp::e_dist( nodes[ jj->i[0]], nodes[ jj->i[1]] );
		if(dd<MINDIST) continue;
		hp::line l;l.from_points( nodes[ jj->i[0]], nodes[ jj->i[1]] );
		hp::draw_arc(fp,l,nodes[ jj->i[0]], nodes[ jj->i[1]] );
	}
	fprintf(fp,"</g>\n");
	fprintf(fp,"</svg>\n");
	fclose(fp);
	return 0;
}

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

This file is licensed under the Creative Commons Attribution 3.0 Unported license.

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to share – to copy, distribute and transmit the work
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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.

You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	09:27, 15 November 2007		800 × 400 (173 KB)	Rocchini	{{Information \|Description=Stellated Eptagonal Tiling (Honeycomb) of Poincare Half-plane model \|Source=self-made \|Date=2007-11-15 \|Author= Claudio Rocchini \|Permission=CC-BY 3.0 }}
	09:23, 15 November 2007		800 × 400 (726 KB)	Rocchini	{{Information \|Description=Stellated Eptagonal honeycomb (tiling) of the Poincare Half-Plane Model \|Source=self-made \|Date=2007-11-15 \|Author= Claudio Rocchini \|Permission=CC-BY 3.0 }}

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Usage on de.wikipedia.org
- Hyperbolischer Raum
Usage on it.wikipedia.org
- Semispazio di Poincaré
Usage on ja.wikipedia.org
- ポワンカレの上半平面モデル
Usage on ru.wikipedia.org
- Замощение (геометрия)
- Модель Пуанкаре в верхней полуплоскости
Usage on uk.wikipedia.org
- Теселяція
- Модель Пуанкаре у верхній півплощині
Usage on zh.wikipedia.org

File:Poincare halfplane heptagonal hb.svg

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GNU Free Documentation License, version 1.2 or later

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