Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Computer Aided Geometric Design; Proceedings of a Conference Held at the University of Utah, Salt Lake City, Utah, March 18-21, 1974
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Hermite interpolation of rational space curves using real algebraic surfaces
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Interpolation over Arbitrary Topology Meshes Using a Two-Phase Subdivision Scheme
IEEE Transactions on Visualization and Computer Graphics
Computer-Aided Design
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This paper is divided in two parts of which the first describes a method to obtain solid models with free-form geometry from polyhedral models. This is achieved by replacing the edges of the original model with curved faces, i.e. sharp edges are replaced by rounds or fillets. The “radii” of these rounds and fillets are controlled by weight values assigned to the original edges. The value of each weight can vary in the interval from 0 to 1, which gives increased possibilities for the user to control the radius of a round or fillet without changing the topology or shape of the polyhedral model.Several of the curved faces will be non-rectangular and in the second part of the paper a method to determine surfaces to these faces is described. To do this we can either split these faces into rectangular subfaces and fit rectangular surfaces to the subfaces or use non-rectangular surfaces. I have tried the second alternative and used a scheme that is inspired by the methods presented by Gregory & Charrot, (1980), (1983) and (1984). However, my method differs from theirs in some respects:Their methods are based on a convex combination of Boolean sum surfaces which interpolate position and slope along to adjacent boundaries. The Boolean sum surfaces are based on linear Taylor interpolants. Instead of Boolean sum surfaces I use convex combinations of Taylor interpolants.I have also found that linear Taylor interpolants may not always give a satisfactory shape of the interior of the surface. A considerable improvement can be obtained by using higher degree interpolants.