Variational surface modeling

Abstract

We present a new approach to interactive modeling of free- form surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely mal- leable surface, with no fixed controls. The user is free to apply control points and curves which are then avail- able as handles for direct manipulation. The complexity of the surface's shape may be increased by adding more control points and curves, without apparent limit. Within the constraints imposed by the controls, the shape of the surface is fully determined by one or more simple criteria, such as smoothness. Our method for solving the resulting constrained variational optimization problems rests on a surface representation scheme allowing nonuniform sub- division of B-spline surfaces. Automatic subdivision is used to ensure that constraints are met, and to enforce er- ror bounds. Efficient numerical solutions are obtained by exploiting linearities in the problem formulation and the representation.