Abstract

A new parametric modelling approach focusing on trimmed free-form surfaces is introduced. The surface deformation process required is controlled through geometric constraints such as deforming the surface until it becomes tangent to a pre-defined plane.

Surfaces are bounded by trimming lines and use a multi-patch representation (i.e.: a B-Spline based model). The G1 continuity across the various surface patches is preserved during the deformation process. Therefore, the C0 and G1 continuities across trimmed surfaces boundaries can be correctly approximated by parametric constraints.

The surface deformation process uses an analogy between the mechanical equilibrium of a rigid bar network and the control polyhedron of free-form surfaces. The bar network parameters may be set up to achieve either isotropic or anisotropic surface deformations. The surface deformation may be located into an arbitrary shaped area to produce either a local or a global deformation.

Parametric modelling of trimmed free-form surfaces is subjected to non-linear geometric constraints. This problem resolution uses an optimization process which minimizes the shape changes of the surface area subjected to the parameters of the deformation process.

An example illustrates the behavior of the parametric modelling process applied to two trimmed surfaces under various sets of continuity and boundary conditions.

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