This paper is concerned with "open kernel" geometric modelling systems. It uses industrial needs to identify requirements for the geometric objects of a proposed interface. The necessary mixed-dimension cellular objects are formally defined as the fundamental data abstractions for that interface. Such definitions are imperative for the construction of robust functions and the integrity of data transfer. As an example, formal specifications are provided for "set-like" object combination functions.

Djinn is an API for solid modelling which is defined in the language of point-sets and is thus independent of any particular modelling data-structure (e.g. boundary representations or CSG trees). In designing this API, several significant and interesting questions have arisen, including: the basic feasibility of the approach; deciding how to support cellular models; providing facilities for navigation without traditional data-structures; addressing the problems of 'tweaks' and blends; ensuring that labels are preserved under geometric operations; permitting regions in which changes to a model have taken place to be identified; coping with approximate models; deciding whether to support variational models; keeping sweeps and transforms within a reasonable domain; and providing facilities to handle the many types of parametric surface. These questions are not all fully answered, but progress continues towards a published interface and C++ language binding.

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 preconditions for reliable results and requirements on the resolution of computer arithmetic. The algorithms thus provide a basis for the wide range of geometric constructions required by computer-aided drafting and design systems.

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 profile control. A discussion of blend conics is used to develop analogous surfaces for use in typical volume modelling systems. These surfaces are then used to set theoretically define bounded volumes for fillets and chamfers. Empirical results show that the method described suits many engineering applications.

Abstract This paper gives the rationale for the design of a nucleus to support real time control applications. In particular, mechanisms for communication between concurrent tasks are reviewed and analysed in the context of this application area. Finally, although no implementation is discussed in detail, techniques which have proved useful in implementing this nucleus on three different machines are described.

An algorithm is described for the decomposition of a bounded concave region of E2 space into a settheoretic 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 complexity for regions whose difference with their convex hull consists of only convex inner regions, a quadratic worst-case complexity, and an average complexity a little worse than linear.