Research and Advances
Artificial Intelligence and Machine Learning

A null-object detection algorithm for constructive solid geometry


Constructive solid geometry (CSG) is the primary scheme used for representing solid objects in many contemporary solid modeling systems. A CSG representation is a binary tree whose nonterminal nodes represent Boolean operations and whose terminal nodes represent primitive solids. This paper deals with algorithms that operate directly on CSG representations to solve two computationally difficult geometric problems—null-object detection (NOD) and same-object detection (SOD). The paper also shows that CSG trees representing null objects may be reduced to null trees through the use of a new concept called primitive redundancy, and that, on average, tree reduction can be done efficiently by a new technique called spatial localization. Primitive redundancy and spatial localization enable a single complex instance of NOD to be converted into a number of simpler subproblems and lead to more efficient algorithms than those previously known.

View this article in the ACM Digital Library.

Join the Discussion (0)

Become a Member or Sign In to Post a Comment

The Latest from CACM

Shape the Future of Computing

ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.

Get Involved

Communications of the ACM (CACM) is now a fully Open Access publication.

By opening CACM to the world, we hope to increase engagement among the broader computer science community and encourage non-members to discover the rich resources ACM has to offer.

Learn More