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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define PI 3.14159265358979

bool intersection(
				  double mp0_x, double mp0_y, double mp1_x, double mp1_y,//mirror segment
				  double ip0_x, double ip0_y, double ip1_x, double ip1_y, //iteration segment
				  double *i_x, double *i_y //intersection point
				  )
{
	const double s1_x = mp1_x - mp0_x;     
	const double s1_y = mp1_y - mp0_y;
	const double s2_x = ip1_x - ip0_x;     
	const double s2_y = ip1_y - ip0_y;
	const double denom= (-s2_x * s1_y + s1_x * s2_y);
	const double s = (-s1_y * (mp0_x - ip0_x) + s1_x * (mp0_y - ip0_y)) / denom;
	const double t = ( s2_x * (mp0_y - ip0_y) - s2_y * (mp0_x - ip0_x)) / denom;
	if (s >= 0 && s < 1 && t >= 0 && t < 1)
	{
		//intersection        
		*i_x = mp0_x + (t * s1_x);
		*i_y = mp0_y + (t * s1_y);
		return true;
	}
	return false; // no intersection
}


//Intructions:
//Put the mirror in any point of the mandelbrot set and set the angle and the diameter.
//It will reflect the iteration values if the iteration line segment intersects the mirror.
//When the calculation is complete,the program will save the result in a graphics file 
//called "Mirror.ppm"
int main(int argc, char* argv[])
{
	//Simple PPM file output, use your favorite graphics program for visualizing it.
	FILE *outputfile;
	printf("Mirror in the Mandebrot Set\n");
	printf("Intructions:\n");
	printf("Position the mirror in any point of the Mandelbrot set and set both the\n");
	printf("rotation angle and the mirror length. It will reflect the current iteration\n");
	printf("value if the line segment between two consecutive iterations intersects\n");
	printf("the mirror.\n");
	printf("When the calculation is complete,the program will save the result in a\n"); 
	printf("graphics file called \"Mirror.ppm\"\n");

	outputfile=fopen("Mirror.ppm","wb");

	//Very simple ppm file header
	fprintf(outputfile,"P6 1024 1024 255 ");
	printf("Calculating..\n");
	unsigned char color;

	//Mirror Parameters

	double mposx=-1.0; //Mirror Position X
	double mposy=0.0; //Mirror Position Y
	double mangle=90; //Mirror Angle in degrees 
	double mlength=50000; //length of the mirror, use very large values for an infinite reflecting line

	double x,y;
	double mx[2],my[2]; //starting and ending segments of the mirror
	double tx[2],ty[2]; //starting and ending points of the iteration
	double ipointx,ipointy; //intersection point
	
	//mirror normal
	double nx,ny;

	//iteration normal
	double anglex;
	double angley;
	
	mangle*=(PI/180.0);//convert from degrees to radians
	mlength*=0.5;//calculate the mirror radius
	const float rightangle=(PI/180.0)*90; 
	//calculate the mirror starting and ending point 
	mx[0]=mposx+sin(mangle+rightangle)*mlength;
	my[0]=mposy+cos(mangle+rightangle)*mlength;
	mx[1]=mposx+sin(mangle-rightangle)*mlength;
	my[1]=mposy+cos(mangle-rightangle)*mlength;

	//mirror normal
	nx=sin(mangle);
	ny=cos(mangle);

	int Counter;
	for(int jc=0;jc<1024;jc++)
		for(int ic=0;ic<1024;ic++)
		{
			const double ik=(float(ic-512)/512.0)*2-0.75;
			const double jk=(float(jc-512)/512.0)*2;	
			x=0;
			y=0;

			//iteration loop
			for(Counter=0;Counter<100;Counter++){
				//get the first iteration segment
				tx[0]=x;
				ty[0]=y;
				//calculate the mandelbrot set
				const float xp=x*x-y*y+ik;
				const float yp=2*x*y+jk;
				//get the second iteration segment
				tx[1]=xp;
				ty[1]=yp;

				//check if the resulting iteration segment intersects the mirror and stores the result if it intersect
				if(intersection(mx[0],my[0],mx[1],my[1],tx[0],ty[0],tx[1],ty[1],&ipointx,&ipointy)){

					//calculate the distance between the intersection point and the mandelbrot iteration
					const double ndistance=sqrt((ipointx-tx[1])*(ipointx-tx[1])+(ipointy-ty[1])*(ipointy-ty[1]));

					//calculates the dot product between the intersection point and the the first iteration segment
					anglex=ipointx-tx[0];
					angley=ipointy-ty[0];
					const double langle=1.0/sqrt(anglex*anglex+angley*angley);
					anglex*=langle;
					angley*=langle;
					const double dot = anglex*nx+angley*ny;

					//calculates the actual reflected point
					const double resx=anglex-2*nx*dot;
					const double resy=angley-2*ny*dot;

					//use the resulting angle and the distance between the intersection point and the last iteration value to
					//calculate the reflected iteration point
					x=ipointx+resx*ndistance;
					y=ipointy+resy*ndistance;
				

				} else {
					//if there's no intersection, the iteration continues with the mandelbrot values
					x=xp;
					y=yp;
				}
				if(sqrt(x*x+y*y)>10)break;
			}
			//use the iteration count as a grayscale gradient
			if(Counter<100) color=(unsigned char)Counter; else color=0;
			//write to the output file
			fputc (color,outputfile);
			fputc (color,outputfile);
			fputc (color,outputfile);

		}
		fclose(outputfile);
		printf("Calculation finished..\n\n");
		return 0;
}

% gcc -o mirrorbrot mirrorbrot.c 
mirrorbrot.c:7:1: error: unknown type name 'bool'
mirrorbrot.c: In function 'intersection':
mirrorbrot.c:25:10: error: 'true' undeclared (first use in this function)
mirrorbrot.c:25:10: note: each undeclared identifier is reported only once for each function it appears in
mirrorbrot.c:27:9: error: 'false' undeclared (first use in this function)
mirrorbrot.c: In function 'main':
mirrorbrot.c:89:2: error: 'for' loop initial declarations are only allowed in C99 mode
mirrorbrot.c:89:2: note: use option -std=c99 or -std=gnu99 to compile your code
mirrorbrot.c:90:3: error: 'for' loop initial declarations are only allowed in C99 mode
mirrorbrot.c:92:27: error: expected ')' before 'ic'
mirrorbrot.c:92:34: error: expected ')' before '/' token
mirrorbrot.c:93:27: error: expected ')' before 'jc'
mirrorbrot.c:93:34: error: expected ')' before '/' token

% gcc -std=c99 -o mirrorbrot mirrorbrot.c 
mirrorbrot.c:7:1: error: unknown type name 'bool'
mirrorbrot.c: In function 'intersection':
mirrorbrot.c:25:10: error: 'true' undeclared (first use in this function)
mirrorbrot.c:25:10: note: each undeclared identifier is reported only once for each function it appears in
mirrorbrot.c:27:9: error: 'false' undeclared (first use in this function)
mirrorbrot.c: In function 'main':
mirrorbrot.c:92:27: error: expected ')' before 'ic'
mirrorbrot.c:92:34: error: expected ')' before '/' token
mirrorbrot.c:93:27: error: expected ')' before 'jc'
mirrorbrot.c:93:34: error: expected ')' before '/' token