1. Stochastic Microgeometry for Displacement Mapping
Craig Schroeder

2. Distributions on a Surface
Create the appearance of complex geometry
Don’t want to store all that information
Want to create multiple instances that are not identical but look similar
Don’t want the patterns, boundary artifacts, repeated appearance, or distortion of textures

3. The Algorithm
Convert the two distributions into a two-sided distribution. Use the number of triangles to make into a histogram.
Consider the histogram bins one by one, starting from the outermost, working towards the innermost and ending with bin 0.
When processing each bin, identify triangles that must have values from that bin
Empty bin by placing randomly throughout the mesh

4. Displacement Mapping
Takes the labels assigned to triangles in the previous slide
Converts these labels into changes in geometry
Calculate normal for each vertex by averaging normals from surrounding triangles
Give each vertex a label by averaging the labels of the surrounding triangles
Apply some function of that label (one function for negative labels, another for positive labels) to get an offset factor for each vertex
Multiply the offset factor by the vertex normal to obtain an offset vector
Add this vector to the original position to obtain the final position of that vertex.

5. Results