How to render a textured polygon on top of another?

Question

Let's say i have 2 textured triangles. I want to draw one triangle over the other one, such that the top one is basically laying on top of the second one.

Now technically they are on the same plane, but they do not share the same "space" (they do not intersect), though visually it is tough to tell at a certain distance.

Basically when these triangles are very close together (in parallel) i see texture "artifacts". I should ONLY see the triangle that is on top. But what im seeing is that the triangle in the background tends to "bleed" through.

Is there a way to alleviate this side effect, like increasing the depth precision or something? Maybe even increase the tessellation of the triangles?

* Update *

I am using vertex and index buffers. This is using OpenGL ES on iPhone.

I dont know if this picture will help or make things worse. But here it is. Two triangles very close to each other along the Z-axis (but not touching). (NOTE: the normal vector for these triangles are going straight towards you).

Answer 1

You could try changing the Depth Buffer function to something more appropriate...

glDepthFunc(GL_ALWAYS) - Essentially disables depth testing

glDepthFunc(GL_GEQUAL) - Overwrites when greater OR equal