Shaping geometric objects by cumulative translational sweeps

Abstract

Cumulative translational sweeps are used to shape geometric objects in a computer model, and they permit display of the resulting changes in shape in the object modelled, and control of processes involving the object modelled. If the geometric object is polyhedral, the cumulative translational sweeps, by creating additional facets, effect selective rounding along model edges and around model vertices. This permits computer modelling of the growth of layers, encompassing in addition to flat surface growth, growth with rounding around corners and over obstacles. Such growth occurs in the manufacture of semiconductors. Modelling a change in a solid structure in stages of growth (or shrinking) and of rounding, as might take place during processing of integrated circuits is achieved by controlled sweep sequences that sweep the structure a finite number of times in accordance with a rayset and stipulated parameters of shape, balance, convexity/concavity, degree of faceting, and memory limitation. The cumulative translational sweep (CTS) is applied in combination with Boolean operations to simulate growth and shrinking over the boundary regions of polyhedral models. By creating additional facets, it effects stipulated selective or global rounding effects along model edges and around model vertices. Such sweeps are examined in terms of Minkowski sums--of the geometric objects that are swept, with structuring geometric shapes that are convex polyhedron from the zonotope subclass of the mathematical family of objects known as polytopes.