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

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

typedef void(*function_t)(float*,int, int, int);

void mobius(float *d_surface, int i, int j, int grid_size)
{
	const float width = 0.5;
	float u = (2*M_PI) * ((float)i/grid_size );
	float v = (2*width) * ((float)j/grid_size ) - width;

	d_surface[0] = cos(u) + v * cos(u / 2) * cos(u);
	d_surface[1] = sin(u) + v * cos(u / 2) * sin(u);
	d_surface[2] = v * sin(u / 2);
}

void toro(float *d_surface, int i, int j, int grid_size)
{
	float u = (2*M_PI) * ((float)i/grid_size );
	float v = (2*M_PI) * ((float)j/grid_size );

	d_surface[0] = (1 + 0.5*cos(v))*cos(u);
	d_surface[1] = (1 + 0.5*cos(v))*sin(u);
	d_surface[2] = 0.5*sin(v);
}

void klein(float *d_surface, int i, int j, int grid_size)
{
	float u = (2*M_PI) * ((float)i/grid_size );
	float v = (2*M_PI) * ((float)j/grid_size );

	d_surface[0] = (0.5*cos(v) + 0.5) * cos(u);
	d_surface[1] = (0.5*cos(v) + 0.5) * sin(u);
	d_surface[2] = sin(v) * cos(u/2);
    //d_surface[2] = sin(v)*sin(u/2);
}

float * generate_surface(int grid_size)
{
	long size = grid_size*grid_size*2*3*3*2;
	function_t f = klein;
	float * d_surface;
	int k=0;

	d_surface = malloc((size+1)*sizeof(float));
	d_surface[0] = size;

	for (int i = 0; i < grid_size; i++)
	{ 
		for (int j = 0; j < grid_size; j++)
		{
			// triangle 1, front
			f(&d_surface[k + 1], i, j, grid_size);
			k+=3;
			f(&d_surface[k + 1], i + 1, j, grid_size);
			k+=3;
			f(&d_surface[k + 1], i + 1, j + 1, grid_size);
			k+=3;

			// triangle 1, back
			f(&d_surface[k + 1], i + 1, j + 1, grid_size);
			k+=3;
			f(&d_surface[k + 1], i + 1, j, grid_size);
			k+=3;
			f(&d_surface[k + 1], i, j, grid_size);
			k+=3;

			// triangle 2, font
			f(&d_surface[k + 1], i, j, grid_size);
			k+=3;
			f(&d_surface[k + 1], i, j + 1, grid_size);
			k+=3;
			f(&d_surface[k + 1], i + 1, j + 1, grid_size);
			k+=3;

			// triangle 2, back
			f(&d_surface[k + 1], i + 1, j + 1, grid_size);
			k+=3;
			f(&d_surface[k + 1], i, j + 1, grid_size);
			k+=3;
			f(&d_surface[k + 1], i, j, grid_size);
			k+=3;
		}
	}

	return d_surface;
}