Technique enables geometric queries on displacement mapped surfaces without tessellation
Geometric Queries on Tessellation-Free Displaced Surfaces
Graphics
Summary
Displacement maps add tiny details to surfaces but usually require turning those surfaces into many triangles, using lots of memory. The authors found a way to answer questions about these surfaces, like finding exact points or sampling, without converting them into triangles first. They created a method using simple planar patches with bounds that keep the surface’s shape information precise. This method helps in tasks like realistic rendering of light effects and solving equations on surfaces, all while saving memory and running efficiently.
What this means in practice
- •For graphics engineers: Perform accurate geometric queries on displacement-mapped surfaces at lower memory cost, improving realistic rendering and simulation workflows without tessellation.
- •For computational physicists: Use displacement map surfaces for solving partial differential equations directly without costly triangle meshes, speeding up simulation set-up and memory usage.
Authors
Bing Xu, Yang Zhou, Brian Budge
Abstract
Displacement maps encode fine geometric detail in compact textures and simplify surface authoring, but using them typically requires pre-tessellating surfaces into dense triangle meshes, incurring a heavy memory cost. Recent tessellation-free methods enable direct ray tracing. However, broader geometric queries such as surface sampling, specular manifold search, and closest-point queries remain less explored. Supporting these operations requires surface enclosures, area estimates, and normal bounds, which scalar height intervals alone do not fully provide. We present a first-order texture-space hierarchy that unlocks these queries directly without pre-tessellation. Each node stores a local affine height plane and a conservative residual bound, retaining spatial height variation that scalar minimum--maximum bounds discard. The plane and residual provide surface enclosures for intersection and distance searches, while the plane's height and slopes supply area estimates for sampling. Additional slope bounds support specular light-path search. Building on this representation, we develop query-specific traversal, pruning, and sampling algorithms, and demonstrate them in caustics rendering, sampling displaced emitters, and surface partial differential equation (PDE) solvers. We demonstrate memory savings over pre-tessellation and performance improvements over query-specific baselines, while retaining efficient ray tracing.