own implementation of phong illumination with ray casting

Question

I am trying to write a program in java from scratch that renders a sphere with ray casting technique and phong illumination, but I am a bit lost.

I understand the concept behind the phong equation coefficients, but I don't understand how to get to the vector values, and what is the relation of all this with ray casting

so let's say I want to renders the sphere in the middle of my screen, and I have it's position and radius, so (cx,cy,r). Where exactly do I start now? how exactly do I get to the vector values? my idea is as follows (pseudocode)

int cx = window width/2
int cy = window height/2
int r = 30;
for(i = 0 -> window height) {
    for(j = 0 -> window width) {
        if( (j-cx)^2 + (i-cy)^2 < r^2) {
            //point inside
            Color c = phong(arguments..)
            draw pixel j,i with color c
        }

    }
}

but I have no idea if this is correct or not, and if it is, how do I get the vector values, for starters, the Normal?

could you point me in the right way? I have tried googling a lot with no success, thank you in advance

Answer 1

The vectors for calculating the normal usually come from a tessellation (approximation) of the real geometrical object. So you break the sphere up into, say, triangles. Then each triangle (p1,p2,p3) has its own normal vector ((p2-p1)×(p3-p1).

The phong shading method is an interpolation which then (ideally) blurs over the lines that give away the fact that you're drawing triangles instead of a true sphere. It's doesn't help with corners around the sides, though. :(

For the tessellation, one way is to approximate the sphere with Bezier surface patches which can then be subdivided to a suitably small sizes and simplified to triangles. My question over here explores doing this work to draw a teapot (mostly surfaces of revolution, not unlike spheres).