Introduction

Parallax occlusion mapping is a technique that reduces model geometry by encoding surface information in a texture. The surface information that is typically used is a height-map representation of the replaced geometry. When the model is rendered, the surface details are reconstructed from the texture information in the pixel shader.

I recently read through the GDC06 presentation on parallax occlusion mapping titled Practical Parallax Occlusion Mapping for Highly Detailed Surface Rendering by Natalya Tatarchuk of ATI Research Inc. In the presentation, an improved version of Parallax Occlusion Mapping is discussed along with possible optimizations that can be used to accelerate the technique on current and next generation hardware.

Of course, after reading the presentation I had to try to implement the technique for myself to evaluate its performance and better understand its inner workings. This article attempts to present an easy to understand guide to the theory behind the algorithm as well as my reference implementation of basic parallax occlusion mapping.

My investigation is focused on the surface reconstruction calculations and what parameters come into play when using this technique. I have decided not to discuss any particular lighting model explicitly since, as you will see, the algorithm is very flexible and can easily be adapted to just about any lighting model that you would like. Natalya Tatarchuk has provided a sample in the DirectX SDK called "ParallaxOcclusionMapping". This is an excellent resource that can be used to further explore a very full-featured lighting model if you are interested.

The reference implementation is written in DirectX 9 HLSL. The effect file that is developed in this exercise is provided with the article and may be used in whatever manner you desire.

Algorithm Overview

So what exactly is parallax occlusion mapping? First let's look at an image of a polygonal surface that we would like to apply our technique to. Let's assume that this polygonal surface is square, and has texture coordinates set to include an entire texture. Figure 1 shows this polygonal surface.

Figure 1:  Flat polygonal surface

The basic idea behind parallax occlusion mapping is relatively simple. For each polygonal surface, we would like to simulate a complex volumetric shape. This shape will be represented by a height-map encoded into a texture that is applied to the polygonal surface. Figure 2 shows this idea.

Figure 2:  Flat polygonal surface approximating a volumetric shape

We will assume that the height-map values range in value from 0.0 – 1.0, with 1.0 being at the polygonal surface and 0.0 being at the deepest possible position of the volumetric shape. To be able to correctly reconstruct the volumetric shape represented by the height map, the viewing direction must be used in conjunction with the height map data to calculate which parts of the surface would be visible at each screen pixel of the polygonal surface, for the given viewing direction.

This is accomplished by using a simple ray-tracer in the pixel shader. The ray that we will be tracing is formed from the vector from the eye (or camera) location to the current pixel. Imagine this vector piercing the polygonal surface, and travelling until it hits the bottom of the virtual volume. Figure 3 shows a side profile of these intersections.

Figure 3:  View vector intersecting the virtual volume

The line segment from the polygonal surface to the bottom of the virtual volume represents the 'line of sight' for our surface. The task at hand is to figure out the first point on this segment that intersects with our height-map. That point is what would be visible to the viewer if we were to render a full geometric model of our surface.

Since the point of intersection between our line segment and the height-map surface represents the visible point at that pixel, it also describes the corrected offset texture coordinates that should be used to look up a color map, normal map, or whatever other textures you use to illuminate the surface. If this correction is carried out on all of the pixels that the polygonal surface is rendered to, then the overall effect is to reconstruct the volumetric surface – which is what we originally set out to do.

Implementing Parallax Occlusion Mapping