DeepAI AI Chat
Log In Sign Up

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

by   Alberto Paoluzzi, et al.

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.


page 6

page 8

page 9

page 11

page 14

page 15


UCSG-Net – Unsupervised Discovering of Constructive Solid Geometry Tree

Signed distance field (SDF) is a prominent implicit representation of 3D...

CSGNet: Neural Shape Parser for Constructive Solid Geometry

We present a neural architecture that takes as input a 2D or 3D shape an...

Topological computing of arrangements with (co)chains

In many areas of applied geometric/numeric computational mathematics, in...

On the Complexity of the CSG Tree Extraction Problem

In this short note, we discuss the complexity of the search space for th...

Solid Geometry Processing on Deconstructed Domains

Many tasks in geometry processing are modeled as variational problems so...

Incorporating Sharp Features in the General Solid Sweep Framework

This paper extends a recently proposed robust computational framework fo...