15,466 research outputs found
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
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.Comment: revised version submitted to Computer-Aided Geometric Desig
Isogeometric Analysis on V-reps: first results
Inspired by the introduction of Volumetric Modeling via volumetric
representations (V-reps) by Massarwi and Elber in 2016, in this paper we
present a novel approach for the construction of isogeometric numerical methods
for elliptic PDEs on trimmed geometries, seen as a special class of more
general V-reps. We develop tools for approximation and local re-parametrization
of trimmed elements for three dimensional problems, and we provide a
theoretical framework that fully justify our algorithmic choices. We validate
our approach both on two and three dimensional problems, for diffusion and
linear elasticity.Comment: 36 pages, 44 figures. Reviewed versio
CSGNet: Neural Shape Parser for Constructive Solid Geometry
We present a neural architecture that takes as input a 2D or 3D shape and
outputs a program that generates the shape. The instructions in our program are
based on constructive solid geometry principles, i.e., a set of boolean
operations on shape primitives defined recursively. Bottom-up techniques for
this shape parsing task rely on primitive detection and are inherently slow
since the search space over possible primitive combinations is large. In
contrast, our model uses a recurrent neural network that parses the input shape
in a top-down manner, which is significantly faster and yields a compact and
easy-to-interpret sequence of modeling instructions. Our model is also more
effective as a shape detector compared to existing state-of-the-art detection
techniques. We finally demonstrate that our network can be trained on novel
datasets without ground-truth program annotations through policy gradient
techniques.Comment: Accepted at CVPR-201
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