Sparse, Opaque Three-Dimensional Texture: 2a. Visibility

Abstract This paper considers three-dimensional textures composed of opaque planar texels uniformly distributed over a volume of space. When such a texture is viewed from a distance (orthographic projection), the probability of seeing through a given-thickness volume of the texture depends only on the spatial density of the texels and on their distribution of areas and slants (of their normals away from the viewing direction); it does not depend on texel shape or on the distribution of tilt directions. We evaluate the probability for various texel orientation models including uniformly distributed orientations, parallel texels (e.g., phototropic leaves), “drooping” texels, and texels composed of “leaves” whose stems conform to a standard tree branching model. In real scenes containing falling disks (“snowflakes”) we find that the disks have about the same average slant as texels whose distribution of orientations is uniform; thus the uniform orientation model should be the appropriate one for predicting visibility through a snowstorm.