Efficient Wavelet Rotation for Environment Map Rendering

These images show a 120,000 vertex dragon model rendered using our environment map rendering algorithm. The view-dependent rendering speed is maintained at 5 fps, and we can dynamically change the lighting at 1.8 fps. From left to right, the model is rendered with a plastic, skin, and measured blue metallic BRDF illuminated by dynamically changing environment lighting. The renderings have been attenuated by precomputed ambient occlusion to produce shadowing effects. Our algorithm is based on efficient rotation of wavelets using precomputed matrices. The model, viewpoint, lighting environment, and surface BRDFs can all be modified interactively at run-time.

Rui Wang¹ Ren Ng² David Luebke¹ Greg Humphreys¹

¹ University of Virginia
² Stanford University

Eurographics Symposium on Rendering (EGSR) 2006

Abstract

Real-time shading with environment maps requires the ability to rotate the global lighting to each surface point's local coordinate frame. Although extensive previous work has studied rotation of functions represented by spherical harmonics, little work has investigated efficient rotation of wavelets. Wavelets are superior at approximating high frequency signals such as detailed high dynamic range lighting and very shiny BRDFs, but present difficulties for interactive rendering due to the lack of an analytic solution for rotation. In this paper we present an efficient computational solution for wavelet rotation using precomputed matrices. Each matrix represents the linear transformation of source wavelet bases defined in the global coordinate frame to target wavelet bases defined in sampled local frames. Since wavelets have compact support, these matrices are very sparse, enabling efficient storage and fast computation at run-time. In this paper, we focus on the application of our technique to interactive environment map rendering. We show that using these matrices allows us to evaluate the integral of dynamic lighting with dynamic BRDFs at interactive rates, incorporating efficient non-linear approximation of both illumination and reflection. Our technique improves on previous work by eliminating the need for prefiltering environment maps, and is thus significantly faster for accurate rendering of dynamic environment lighting with high frequency reflection effects.

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