/** Draw a 2d function
*/ 

import javax.media.opengl.*;

public class Function2D{

    private static float sqr(float x){
	return x*x;
    }

    //function that looks like a hat
    public static float f (float x, float y){
	float twopi = 2.0f*(float)Math.PI;
	float a = sqr(twopi*(x-0.5f)) + sqr(twopi*(y-0.5f));
	return (float) (0.8f*(- (0.2f)*Math.sin(twopi*x)*Math.cos(twopi*y) +
		     (1.5f)*Math.cos(7.0f*a/4.0f)*Math.exp(-a)));

    }

    //normal to a triangle
    public static Vector3D normal (Vector3D a, Vector3D b, Vector3D c){
	return b.subtract(a).cross(c.subtract(a));
    }


    public static void surface(GL gl, int level){
	Vector3D a,b,c,n;

        float h = 1.0f/level;
        float hh = h/10.0f;
	for (int i = 0; i < level; i++){
            float x = i*h;
	    gl.glBegin(GL.GL_TRIANGLE_STRIP);
	    for (int j = 0; j <= level; j++){
		float y = j*h;
		a = new Vector3D(x+h, f(x+h,y), y);
		b = new Vector3D(x+h+hh, f(x+h+hh,y), y);
		c = new Vector3D(x+h, f(x+h,y+hh), y+hh);
		n = normal(a,c,b);
		gl.glTexCoord2d(x+h,y);
		gl.glNormal3d(n.x,n.y,n.z);
		gl.glVertex3d(a.x,a.y,a.z);

		a = new Vector3D(x, f(x,y), y);
		b = new Vector3D(x+hh, f(x+hh,y), y);
		c = new Vector3D(x, f(x,y+hh), y+hh);
		n = normal(a,c,b);
		gl.glTexCoord2d(x,y);
		gl.glNormal3d(n.x,n.y,n.z);
		gl.glVertex3d(a.x,a.y,a.z);

	    }
	    gl.glEnd();
	}
    }

}