Converting orthogonal polyhedra from extreme vertices model to B-Rep and to alternating sum of volumes

Abstract

In recent published papers we presented the Extreme Vertices Model (EVM), a concise and complete model for representing orthogonal polyhedra and pseudo-polyhedra (OPP). This model exploits the simplicity of its domain by allowing robust and simple algorithms for set-membership classification and Boolean operations that do not need to perform floating-point operations.

Several applications of this model have also been published, including the suitability of OPP as geometric bounds in Constructive Solid Geometry (CSG).

In this paper, we present an algorithm which converts from this model into a B-Rep model. We also develop the application of the Alternating Sum of Volumes decomposition to this particular type of polyhedra by taking advantage of the simplicity of the EVM. Finally we outline our future work, which deals with the suitability of the EVM in the field of digital images processing.