Z-buffer algorithm implementation problem

Newbie & Debugging Questions
#1

Hi guys, now I’m making a 3d game engine in Java from scratch.

Now I’m working at the Z-buffer because I didn’t like the effect of the Painter’s Algorithm(Z-sorting).

My question is: what is the easiest way to determine the Z value of each pixel? Please include a source code if you can :wink:

P.S.: The renderer contains just triangles, something like that:

class Vector3d {
double x,y,z;
}
class Triangle {
Vector3d v1,v2,v3;
Color color;
}
class Renderer {
public Triangle[] triangles;
[ . . . ]
}

#2

When you transform the 3d points into 2d screen coordinares the z value of the transformed point is the z value you use.

#3
  1. So don’t I need the z value of the points inside the triangle?
    EDIT
  2. if so, what if the triangle’s vertices have different Z values?
#4

You need to do perspective-correct interpolation of the three vertices’ Z values for each fragment generated within the triangle.

#5

OK, I understand a bit.
Can someone give me a function like that:


public void getZ(point3d v1,point3d v2,point3d v3, // triangle vertices
                        point2d screen) // x y coordinates
{
    // [what I need] (calculate the Z value of the pixel located at screen.x X screen.y)
}

PLS answer as soon possible

#6

Are you familiar with linear interpolation?

Consider the function X1 = X1 + F(X2-X1)
Where X1 is the start value, X2 is the end value, and F is the fraction between 0 and 1.
This fraction represents how far along in between X1 and X2 you want to go. For example,
if F = 0 you’ll get X1, if F = 1, you’ll get X2, and if F = 0.5, you’ll get a value half way in between X1 and X2.

You use linear interpolation to find values along the triangle’s edges, and across the triangle’s surface. So for your Z problem, you interpolate between the Z values of vertex 1 (X1) and vertex 2 (X2). An F value of 0 will give you the Z value of vertex 1 and an F value of 1 will give you the Z value of vertex 2.

In order to find the F value, you need to find the change of Z over the change in Y. This dz/dy is the F value and is constant for the entire edge of the triangle.

Loop over each of the Y values between vertex 1 and vertex 2, incrementing a counter by F.



float F = (vertex2.z - vertex1.z) / (vertex2.y - vertex1.y);
float interpZ = vertex1.z;
while (vertex1.y < vertex2.y) {
     // interpolate across X using a similar method
     // interpZ is the Z value in between the edges.
     interpZ += F;
}
#7

I’VE FINALLY FOUND WHAT I NEED!
Thank you a lot, you made my day!

And your 3d renderer is very cool. It seems that you wanted to remake the OpenGL. Nice work!

#8

Haha yup, no problem. And thanks, you’re doing the same stuff I was doing when I started working on my renderer. So keep going! :stuck_out_tongue: