/* coutour2.c                              */

/* E. Angel, Interactive Computer Graphics */
/* A Top-Down Approach with OpenGL, Third Edition */
/* Addison-Wesley Longman, 2003 */

/* Genarates contours using marching squares */

/* region size */

#define X_MAX 1.0
#define Y_MAX 1.0
#define X_MIN -1.0
#define Y_MIN -1.0

/* number of cells */

#define N_X 50
#define N_Y 50

/* contour value */

#define THRESHOLD 0.0

#include <GL/glut.h>

void display()
{
double f(double,double);
int cell(double, double, double, double);
void lines(int, int, int, double, double, double, double);

double data[N_X][N_Y];
int i,j;
int c;

glClear(GL_COLOR_BUFFER_BIT);

/* form data array from function */

for(i=0;i<N_X;i++) for (j=0;j<N_Y;j++) 
	data[i][j]=f(X_MIN+i*(X_MAX-(X_MIN))/(N_X-1.0),Y_MIN+j*(Y_MAX-(Y_MIN))/(N_Y-1.0));

/* process each cell */

for(i=0;i<N_X;i++) for (j=0;j<N_Y;j++) 
    {
	c=cell(data[i][j], data[i+1][j], data[i+1][j+1], data[i][j+1]);
	lines(c,i,j,data[i][j], data[i+1][j], data[i+1][j+1], data[i][j+1]);
	}
glFlush();
}

/* define function f(x,y)      */

double f(double x, double y)
{
/* return x*x+y*y-0.1; */
double a=0.49, b=0.5;

/* Ovals of Cassini  */
return (x*x+y*y+a*a)*(x*x+y*y+a*a)-4*a*a*x*x-b*b*b*b;
}


/* define cell vertices */

int cell(double a, double b, double c , double d)
{
    int n=0;
	if(a>THRESHOLD) n+=1;
	if(b>THRESHOLD) n+=8;
	if(c>THRESHOLD) n+=4;
	if(d>THRESHOLD) n+=2;
	return n;
}


/* draw line segments for each case */

void lines(int num, int i, int j, double a, double b, double c, double d)
{
void draw_one(int, int, int, double, double, double, double);
void draw_adjacent(int, int, int, double, double, double, double);
void draw_opposite(int, int, int, double, double, double, double);
     switch(num)
	 {
	 case 1: case 2: case 4: case 7: case 8: case 11: case 13: case 14: 
		draw_one(num, i,j,a,b,c,d); 
		break;
	 case 3: case 6: case 9: case 12: 
	    draw_adjacent(num,i,j,a,b,c,d); 
		break;
	 case 5: case 10: 
		draw_opposite(num, i,j,a,b,c,d); 
		break;
	 case 0: case 15: break;
	 }
}

void draw_one(int num, int i, int j, double a, double b, double c, double d)
{
  double x1, y1, x2, y2;
  double ox, oy;
  double dx, dy;
  dx=(X_MAX-(X_MIN))/(N_X-1.0);
  dy=(Y_MAX-(Y_MIN))/(N_Y-1.0);
  ox=X_MIN+i*(X_MAX-(X_MIN))/(N_X-1.0);
  oy=Y_MIN+j*(Y_MAX-(Y_MIN))/(N_Y-1.0);
    switch(num)
	{
	case 1: case 14:
	  x1=ox;
	  y1=oy+dy*(THRESHOLD-a)/(d-a);
	  x2=ox+dx*(THRESHOLD-a)/(b-a);
	  y2=oy;
	  break;
	case 2: case 13:
	  x1=ox;
	  y1=oy+dy*(THRESHOLD-a)/(d-a);
	  x2=ox+dx*(THRESHOLD-d)/(c-d);
	  y2=oy+dy;
	  break;
	case 4: case 11:
	  x1=ox+dx*(THRESHOLD-d)/(c-d);
	  y1=oy+dy;
	  x2=ox+dx;
	  y2=oy+dy*(THRESHOLD-b)/(c-b);
	  break;
	case 7: case 8:
	  x1=ox+dx*(THRESHOLD-a)/(b-a);
	  y1=oy;
	  x2=ox+dx;
	  y2=oy+dy*(THRESHOLD-b)/(c-b);
	  break;
	}
  glBegin(GL_LINES);
	glVertex2d(x1, y1);
	glVertex2d(x2, y2);
  glEnd();
}
void draw_adjacent(int num, int i, int j, double a, double b, double c, double d)
{
  double x1, y1, x2, y2;
  double ox, oy;
  double dx, dy;
  dx=(X_MAX-(X_MIN))/(N_X-1.0);
  dy=(Y_MAX-(Y_MIN))/(N_Y-1.0);
  ox=X_MIN+i*(X_MAX-(X_MIN))/(N_X-1.0);
  oy=Y_MIN+j*(Y_MAX-(Y_MIN))/(N_Y-1.0);
  switch(num)
  {
	case 3: case 12:
	  x1=ox+dx*(THRESHOLD-a)/(b-a);
	  y1=oy;
	  x2=ox+dx*(THRESHOLD-d)/(c-d);
	  y2=oy+dy;
	  break;
	case 6: case 9:
	  x1=ox;
	  y1=oy+dy*(THRESHOLD-a)/(d-a);
	  x2=ox+dx;
	  y2=oy+dy*(THRESHOLD-b)/(c-b);
	  break;
  }
  glBegin(GL_LINES);
    glVertex2d(x1, y1);
    glVertex2d(x2, y2);
  glEnd();

}
void draw_opposite(int num, int i, int j, double a, double b, double c, double d)
{
  double x1,y1,x2,y2,x3,y3,x4,y4;
  double ox, oy;
  double dx, dy;
  dx=(X_MAX-(X_MIN))/(N_X-1.0);
  dy=(Y_MAX-(Y_MIN))/(N_Y-1.0);
  ox=X_MIN+i*(X_MAX-(X_MIN))/(N_X-1.0);
  oy=Y_MIN+j*(Y_MAX-(Y_MIN))/(N_Y-1.0);
  switch(num)
  {
    case5: 
	  x1=ox;
	  y1=oy+dy*(THRESHOLD-a)/(d-a);
	  x2=ox+dx*(THRESHOLD-a)/(b-a);
	  y2=oy;
	  x3=ox+dx*(THRESHOLD-d)/(c-d);
	  y3=oy+dy;
	  x4=ox+dx;
	  y4=oy+dy*(THRESHOLD-b)/(c-b);
	  break;
	case 10:
	  x1=ox;
	  y1=oy+dy*(THRESHOLD-a)/(d-a);
	  x2=ox+dx*(THRESHOLD-d)/(c-d);
	  y2=oy+dy;
	  x3=ox+dy*(THRESHOLD-a)/(b-a);
	  y3=oy;
	  x4=ox+dx;
	  y4=oy+dy*(THRESHOLD-b)/(c-b);
	  break;
  }
  glBegin(GL_LINES);
    glVertex2d(x1, y1);
    glVertex2d(x2, y2);
    glVertex2d(x3, y3);
    glVertex2d(x4, y4);
  glEnd();
}

void myReshape(int w, int h)
{
glViewport(0, 0, w, h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
if (w <= h)
gluOrtho2D(X_MIN, X_MAX, Y_MIN * (GLfloat) h / (GLfloat) w,
Y_MAX * (GLfloat) h / (GLfloat) w);
else
gluOrtho2D(X_MIN * (GLfloat) w / (GLfloat) h,
X_MAX * (GLfloat) w / (GLfloat) h, Y_MIN, Y_MAX);
glMatrixMode(GL_MODELVIEW);
}

void
main(int argc, char **argv)
{
glutInit(&argc, argv);

glutInitWindowSize(500, 500);
glutCreateWindow("contour plot");
glutReshapeFunc(myReshape);
glutDisplayFunc(display);
glClearColor(0.0,0.0,0.0,1.0);
glColor3f(1.0,1.0,1.0);

glutMainLoop();
}