Differentiable Voxelization of Surface Representations

2026-08-16

AI Summary

This study addresses the inefficiency of gradient computation in voxel-attribute-based surface optimization by proposing a differentiable surface-to-voxel conversion method. By deriving analytical gradients of winding numbers with respect to surface geometry, we establish a differentiable mapping from volumetric attributes to mesh parameters, enabling direct surface optimization via gradient descent. The proposed approach effectively handles complex tasks, including mesh self-intersection resolution, bandsaw manufacturability constraints, and 3D tessellation shape generation. Consequently, this method significantly enhances both the efficiency and accuracy of geometric optimization driven by voxel attributes. Furthermore, it introduces a novel paradigm for differentiable interaction between implicit and explicit representations, bridging the gap between volumetric processing and surface-based modeling in computational geometry and graphics.

Abstract

Different shape representations facilitate different computations. Surface representations, in particular meshes, are often used for modeling, whereas volume representations are useful for spatial queries such as intersection or containment. Optimizing a surface representation based on a volumetric properties by gradient descent requires the derivatives of the volume relative to its bounding surface. We derive this gradient for winding numbers and show that it can be efficiently computed for volumetric values sampled on a regular grid (voxel representation) and surface parameters based on vertex sets (triangle meshes). This enables an efficient solution for a variety of optimization problems. We demonstrate the practical use of this approach at the examples of deforming meshes to resolve intersections, being manufacturable by cutting with a bandsaw from three directions, and creating shapes that are close to tiling 3D space.

Problem

• Differentiable Voxelization
• Surface Representation
• Volumetric Properties
• Gradient Descent
• Winding Numbers

Innovation

• Differentiable Voxelization
• Winding Number Gradient
• Surface Optimization
• Gradient Descent
• Geometric Modeling