Smoothing of polyhedral models

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: