OFFSETS of curves and surfaces are required in many geometric modelling applications, such as NC machining, geometric tolerancing, and the construction of blends and fillets.
SWEEPS are an essential tool for designing tensor-product surfaces and modelling tube-like shapes. Sweeps of polygons, polyhedra, and free-form curved objects are also needed for collision detection in robotics and CAD/CAM.
MINKOWSKI SUMS, on solids or in the plane, form the basis of a range of modelling operations, including interference checking, shape transformation and font design.
Offsets, sweeps, and Minkowski sums are geometrically well-defined; but their practical computation is an elusive and challenging task. In particular, they can easily generate non-rational curves and surfaces; and representing the result of such operations requires the global elimination of self-intersections, which is extremely difficult to implement robustly.
The guest editors of this special issue invite papers reporting interesting new results, pointing the way to resolution of these computational difficulties. Suggested topics include (but are not limited to):