Solid and Physical Modeling

The detection of the number of disjoint components is a well-known procedure for surface objects. However, this problem has not been solved for solid models defined with scalar fields in the so-called implicit form. In this paper, we present a technique which allows for detection of the number of disjoint components with a predefined tolerance for an object defined with a single scalar function. The core of the technique is a reliable continuation of the spatial enumeration based on the interval methods. We also present several methods for separation of components using set-theoretic operations for further handling these components individually in a solid modelling system dealing with objects defined with scalar fields.

Section: Related Workmentioning

confidence: 99%

Reliable detection and separation of components for solid objects defined with scalar fields

Fryazinov

Pasko

2015

“…Rossignac gives a good overview of current solid modeling techniques and applications [3]. For this paper, we briefly summarize two general approaches to evaluating boolean operations: Boundary Representations (BREPs) and Constructive Solid Geometry (CSG).…”

Section: Previous Workmentioning

confidence: 99%

Improved Binary Space Partition merging

Lysenko

D’Souza

Shene

2008

This paper presents a new method for evaluating boolean set operations between Binary Space Partition (BSP) trees. Our algorithm has many desirable features including both numerical robustness and O(n) output sensitive time complexity, while simultaneously admitting a straightforward implementation. To achieve these properties, we present two key algorithmic improvements. The first is a method for eliminating null regions within a BSP tree using linear programming. This replaces previous techniques based on polygon cutting and tree splitting. The second is an improved method for compressing BSP trees based on a similar approach within binary decision diagrams. The performance of the new method is analyzed both theoretically and experimentally. Given the importance of boolean set operations, our algorithms can be directly applied to many problems in graphics, CAD and computational geometry.

Fast global and partial reflective symmetry analyses using boundary surfaces of mechanical components

Foucault

Léon

et al. 2014