A Topological Approach to Voxelization

Abstract

We present a novel approach to voxelization, based on intersecting the input primitives against intersection targets in the voxel grid. Instead of relying on geometric proximity measures, our approach is topological in nature, i.e., it builds on the connectivity and separability properties of the input and the intersection targets. We discuss voxelization of curves and surfaces in both 2D and 3D, and derive intersection targets that produce voxelizations with various connectivity, separability and thinness properties. The simplicity of our method allows for easy proofs of these properties. Our approach is directly applicable to curved primitives, and it is independent of input tessellation.

ICVG : Practical Constructive Volume Geometry for Indirect Visualization

“…Based on these definitions, they define notions of N-separating and covering and then propose that an effective voxelization should provide a minimal cover of the object. A more recent approach, called topological voxelization, is based on the topological properties of the objects [18]. Every voxel is given an associated geometric intersection target and the voxel is marked as solid if any input primitive intersects this target.…”

Collaborating with an Artist in Digital Geometry

“…The ake digitization allows to dene digital surfaces with a controlled topology (control on tunnels of the digital surface). The paper [16] can be seen as an extension to all tunnel connectivities and dimensions of the paper of S. Laine [14].…”

Influence of voxelization on finite difference time domain simulations of head-related transfer functions

“…11, the two voxelization algorithms seem to induce opposite bias in the high-frequency spectral features of the HRTFs. The 6-separating voxelization induced volume bias is somewhere in between since the intersection volume is inscribed in each voxel (see work by Laine 46 ) leaving parts of the polyhedron mesh close to the vertices of the Cartesian grid outside the voxelized mesh. The amount of bias depends on the voxel size: for example, the shifts in frequency for the first peak and first notch of the d.f.…”