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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 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)

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)

Results from the study of O-minimal structures are used to formalise fundamental objects and operations for geometric modelling kernels. O-minimal structures provide a more general setting than the traditional semialgebraic sets; they allow semianalytic sets such as screw-threads to be modelled accurately. O-minimality constrains the class of sets to ensure… (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)