Practical Shading of Height Fields and Meshes using Spherical Harmonic Exponentiation

Abstract

Interactively computing smooth shading effects from environmental lighting, such as soft shadows and glossy reflections, is a challenge in scenes with dynamic objects. We present a method to efficiently approximate these effects in scenes comprising animating objects and dynamic height fields, additionally allowing interactive manipulation of view and lighting. Our method extends spherical harmonic (SH) exponentiation approaches to support environmental shadowing from both dynamic blockers and dynamic height field geometry. We also derive analytic expressions for the view-evaluated BRDF, directly in the log-SH space, in order to support diffuse-to-glossy shadowed reflections while avoiding expensive basis-space product operations. We illustrate interactive rendering results using a hybrid, multi-resolution screen- and object-space visibility-marching algorithm that decouples geometric complexity from shading complexity.