Article Dans Une Revue Computer Graphics Forum Année : 2025

Lipschitz Pruning: Hierarchical Simplification of Primitive‐Based SDFs

Mathieu Sanchez
Axel Paris
Élie Michel
Thibaud Lambert
Tamy Boubekeur
Theo Thonat

Résumé

Rendering tree‐based analytical Signed Distance Fields (SDFs) through sphere tracing often requires to evaluate many primitives per tracing step, for many steps per pixel of the end image. This cost quickly becomes prohibitive as the number of primitives that constitute the SDF grows. In this paper, we alleviate this cost by computing local pruned trees that are equivalent to the full tree within their region of space while being much faster to evaluate. We introduce an efficient hierarchical tree pruning method based on the Lipschitz property of SDFs, which is compatible with hard and smooth CSG operators. We propose a GPU implementation that enables real‐time sphere tracing of complex SDFs composed of thousands of primitives with dynamic animation. Our pruning technique provides significant speedups for SDF evaluation in general, which we demonstrate on sphere tracing tasks but could also lead to significant improvement for SDF discretization or polygonization.

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hal-05050831 , version 1 (29-04-2025)

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Wilhem Barbier, Mathieu Sanchez, Axel Paris, Élie Michel, Thibaud Lambert, et al.. Lipschitz Pruning: Hierarchical Simplification of Primitive‐Based SDFs. Computer Graphics Forum, 2025, ⟨10.1111/cgf.70057⟩. ⟨hal-05050831⟩
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