Most volume modelling systems are very limited in the complexity of the surfaces which they support. This is satisfactory for basic models of most mechanical components, since the functional surfaces are not usually complex. However, there are often blends between simple base surfaces. This paper presents a technique appropriate for blend definition and… (More)
An algorithm is described for the decomposition of a bounded concave region of E2 space into a set-theoretic combination of convex regions. This algorithm finds the convex hull of the region and then recurses to find the convex hulls of the difference between the original region and its convex hull, until such regions are convex. It exhibits a linear-time… (More)
This paper provides a rationale for its abstract data definitions of geometric features. These definitions are used as the basis of a suite of functions to support feature modelling. It assumes that implementations of the proposed functions will make use of a solid modelling kernel that supports objects with a disjoint cellular structure and persistent cell… (More)
This paper is concerned with the mathematics and formal specification of " set-like " operations for the mixed dimension cellular objects of the Djinn Application Programming Interface. The relationships between these operations and stratifications of dimensionally heterogeneous semi-analytic point-sets are uncovered and formalised. Semianalytic geometry is… (More)
The class of scan-line processing algorithms introduced here can be used for efficient image generation and volume integral calculations and is shown to outperform previous methods.
The major purpose of this paper is to introduce a general theory within which previous boundary representations (B-reps) are a special case. Basically, this theory combines sub-analyt,ic geometry and theory of stratifications. The sub-analyt,ic geometry covers almost, all geometric engineering artefacts, and it is a generalisation of the semi-analytic… (More)
This paper presents a unified representation scheme for the implicit equations of points, lines, and circles. An associated set of geometric algorithms operates successfully on degenerate and nearly degenerate geometry, and when necessary produces degenerate geometric results. Computation errors are interpreted geometrically in order to establish… (More)