Output details

Feature based volumes for implicit intersections

Originality - The paper addresses the problem of obtaining bounding volumes for the purposes of Computer-Aided design with geometric objects defined in implicit form. Bounding volumes are important for many different applications as they can be used as a primitive in the solid modelling systems as well as the basis for various geometric operations such as feature-based deformations. Traditionally the construction of the bounding volumes in the solid modelling with real functions was considered as a ‘heavy weighted’ operation that usually requires high numerical computation power. This paper presents a novel formulation that allows building bounding volumes based on the intersection curve in a simple yet very efficient way. Solid mathematical foundations presented in the paper allow user to choose different variations in implementation of the proposed technique and therefore user can control the resulting shape by choosing the variation and its parameters. The originality of the proposed technique is based on the way the intersection curve is treated in the context of the geometric objects defined in the implicit form.

Significance - The simple mathematical formulation allows using bounding volumes for novel applications in various areas of computer-aided geometric design. These applications include generative design for digital fabrication, automatisation of the operations in the solid volumetric modelling systems based on the geometric objects represented in the implicit form and also feature curves visualisation.

Rigour - The formulation used in the paper is based on the principles of function-based modelling. The paper presents various mathematical techniques to the problem of implicit offsetting which is a core of the presented method.