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File:Lemoine Hexagon.svg

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Original file (SVG file, nominally 800 × 800 pixels, file size: 2 KB)

Summary

Description
English: Lemoine Hexagon and its construction
Date
Source Own work
Author Claudio Rocchini

Source Code

#include <stdio.h>
#include <math.h>

class point
{
public:
	double x,y;
	point() {}
	point( double nx, double ny ) : x(nx),y(ny) {}
	point  operator+ ( const point & p ) const { return point(x+p.x,y+p.y); }
	point  operator- ( const point & p ) const { return point(x-p.x,y-p.y); }
	point  operator* ( const double s  ) const { return point(x*s,y*s); }
	double operator* ( const point & p ) const { return x*p.x+p.y*y; }	// dot   product
	double operator^ ( const point & p ) const { return x*p.y-p.x*y; }	// cross product
	double angle() const { return atan2(y,x); }
	point& at_angle( double a ) { x = cos(a); y = sin(a); return *this; }
	point  perp() const { return point(y,-x); }
	double norm () const { return sqrt(x*x+y*y); }
	point& normalize() { double n = norm(); if(n!=0) { x/=n; y/=n; } return *this; }
};

class line
{
public:
	point orig;
	point dire;
	line() {}
	line( const point & no, const point & nd ) : orig(no),dire(nd) {}
	point param( double t ) const { return orig+dire*t; }
	point intersect( const line & l ) { return param( (l.dire^(orig-l.orig))/(dire^l.dire) ); }
};

void main()
{
	const double SX = 800; const double SY = 800;
	const double S  = 700; const double Q = 75;
	const int N = 3;
	int i;

	point tri[N] = { point(80,50) ,point(680,750), point(165,715) };
	line  median   [N];
	line  bisector [N];
	line  symmedian[N];
	point inter[N][2];

	for(i=0;i<N;++i) {
		median[i].orig = tri[i];
		median[i].dire = ((tri[(i+1)%N]+tri[(i+2)%N])*0.5 - tri[i]).normalize();

		bisector[i].orig = tri[i];
		bisector[i].dire = (tri[(i+1)%N]-tri[i]).normalize() + (tri[(i+2)%N]-tri[i]).normalize();
		bisector[i].dire.normalize();

		symmedian[i].orig = tri[i];
		symmedian[i].dire.at_angle( bisector[i].dire.angle()*2 - median[i].dire.angle() );
	}

	point symmedian_p = symmedian[0].intersect(symmedian[1]);

	for(i=0;i<N;++i) {
		line pa(symmedian_p, (tri[(i+2)%N]-tri[(i+1)%N]).normalize() );
		for(int j=0;j<2;++j) {
			line la(tri[i], (tri[(i+1+j)%N]-tri[i]).normalize() );
			inter[i][j] = pa.intersect(la);
		}
	}

	line l1( (inter[0][0]+inter[0][1])*0.5, (inter[0][0]-inter[0][1]).perp().normalize() );
	line l2( (inter[1][0]+inter[1][1])*0.5, (inter[1][0]-inter[1][1]).perp().normalize() );
	point  first_lem_c = l1.intersect(l2);
	double first_lem_r = (first_lem_c-inter[0][0]).norm();

	FILE * fp = fopen("c:\\temp\\Lemoine_Hexagon.svg","w");
	fprintf(fp,
		"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
		"<svg\n"
		"xmlns:svg=\"http://www.w3.org/2000/svg\"\n"
		"xmlns=\"http://www.w3.org/2000/svg\"\n"
		"version=\"1.0\"\n"
		"width=\"%g\"\n"
		"height=\"%g\"\n"
		"id=\"Lemoine_Hexagon\">\n"
		,SX,SY
	);

	fprintf(fp,"<g style=\"stroke:#0000C0;stroke-width:1;stroke-opacity:1;stroke-dasharray:6,4;fill:none\">\n");
	for(i=0;i<N;++i)
		fprintf(fp,
			"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
			,median[i].orig.x,median[i].orig.y
			,(median[i].orig+median[i].dire*S).x,(median[i].orig+median[i].dire*S).y
		);
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:#00C000;stroke-width:1;stroke-opacity:1;stroke-dasharray:6,4;fill:none\">\n");
	for(i=0;i<N;++i)
		fprintf(fp,
			"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
			,bisector[i].orig.x,bisector[i].orig.y
			,(bisector[i].orig+bisector[i].dire*S).x,(bisector[i].orig+bisector[i].dire*S).y
		);
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:#C00000;stroke-width:1;stroke-opacity:1;stroke-dasharray:6,4;fill:none\">\n");
	for(i=0;i<N;++i)
		fprintf(fp,
			"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
			,symmedian[i].orig.x,symmedian[i].orig.y
			,(symmedian[i].orig+symmedian[i].dire*S).x,(symmedian[i].orig+symmedian[i].dire*S).y
		);
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:#C0C0C0;stroke-width:1;stroke-opacity:1;stroke-dasharray:6,4;fill:none\">\n");
	for(i=0;i<N;++i) {
		point d = (inter[i][1] - inter[i][0]).normalize();
		point p1 = inter[i][0] - d*Q; point p2 = inter[i][1] + d*Q;
		fprintf(fp,
			"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
			,p1.x, p1.y, p2.x, p2.y
		);
	}
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:#00C0C0;stroke-width:1;stroke-opacity:1;fill:none\">\n");
	fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n"
		,first_lem_c.x, first_lem_c.y
		,first_lem_r
	);
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:#C000C0;stroke-width:2;stroke-opacity:1;fill:none\">\n");
	fprintf(fp,"<path d=\"");
	for(i=0;i<3;++i){
		if(i==0) fprintf(fp,"M ");
		else     fprintf(fp,"L ");
		fprintf(fp,"%5.1lf,%5.1lf ",tri[i].x,tri[i].y);
	}
	fprintf(fp,"z\"/>\n");
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:#000000;stroke-width:2;stroke-opacity:1;fill:#C0C000;fill-opacity:0.5\">\n");
	fprintf(fp,"<path d=\"");
	for(i=0;i<3;++i) {
		for(int j=0;j<2;++j) {
			if(i==0 && j==0) fprintf(fp,"M ");
			else             fprintf(fp,"L ");
			fprintf(fp,"%5.1lf,%5.1lf ",inter[i][j]);
		}
	}
	fprintf(fp,"z\"/>\n");
	fprintf(fp,"</g>\n");

	fprintf(fp,"<g style=\"stroke:none;fill:#000000\">\n");
	fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n"
		,symmedian_p.x, symmedian_p.y
		,6.0
	);
	for(i=0;i<N;++i) for(int j=0;j<2;++j)
			fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n"
				,inter[i][j].x, inter[i][j].y
				,6.0
			);
	fprintf(fp,"</g>\n");

	fprintf(fp,"</svg>\n");
	fclose(fp);
}

Licensing

Claudio Rocchini, the copyright holder of this work, hereby publishes it under the following licenses:
GNU head 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.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
Attribution: Claudio Rocchini
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.
You may select the license of your choice.

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9 July 2008

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Date/TimeThumbnailDimensionsUserComment
current08:32, 9 July 2008Thumbnail for version as of 08:32, 9 July 2008800 × 800 (2 KB)Rocchini{{Information |Description={{en|1=Lemoine Hexagon and its construction}} |Source=Opera creata dall'uploader (own work by uploader) |Author=Claudio Rocchini |Date=2008-07-09 |Permission= |other_versions= }} {{ImageUpload|full}}

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