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In this paper, we present a novel workflow consisting of algebraic algorithmsand data structures for fast and topologically accurate conversion of vectordata models such as Boundary Representations into voxels (topologicalvoxelization); spatially indexing them; constructing connectivity graphs fromvoxels; and constructing a coherent set of multivariate differential andintegral operators from these graphs. Topological Voxelization is revisited andpresented in the paper as a reversible mapping of geometric models from$\mathbb{R}^3$ to $\mathbb{Z}^3$ to $\mathbb{N}^3$ and eventually to an indexspace created by Morton Codes in $\mathbb{N}$ while ensuring the topologicalvalidity of the voxel models; namely their topological thinness and theirgeometrical consistency. In addition, we present algorithms for constructinggraphs and hyper-graph connectivity models on voxel data for graph traversaland field interpolations and utilize them algebraically in elegantlydiscretizing differential and integral operators for geometric, graphical, orspatial analyses and digital simulations. The multi-variate differential andintegral operators presented in this paper can be used particularly in theformulation of Partial Differential Equations for physics simulations.

Voxel Graph Operators: Topological Voxelization, Graph Generation, and Derivation of Discrete Differential Operators from Voxel Complexes