Terrain and Model Queries Using Scalar Representations with Wavelet Compression

In this paper, we present efficient height/distance field data structures for line-of-sight (LOS) queries on terrains and collision queries on arbitrary 3-D models. The data structure uses a pyramid of quad-shaped regions with the original height/distance field at the highest level and an overall minimum/maximum value at the lower levels. The pyramid can compactly be stored in a wavelet-like decomposition but using max and plus operations. Additionally, we show how to get minimum/maximum values for regions in a wavelet decomposition using real algebra. For LOS calculations, we compare with a kd-tree representation containing the maximum height values. Furthermore, we show that the LOS calculation is a special case of a collision detection query. Using our wavelet-like approach, even general and arbitrary collision detection queries can efficiently be answered.