Hierarchical surface fairing with constraints

Abstract

The surfaces of complex free-form objects can typically be modeled by a hierarchy of primary surfaces, connecting surfaces and corner patches. Within the context of digital shape reconstruction, these surfaces simultaneously approximate measured data points, satisfy fairness criteria and adhere to continuity constraints according to their dependencies. A new framework algorithm is introduced to perfect existing B-spline surfaces; the algorithm alternates --- in a stepwise manner --- between continuity constraint satisfaction and fairing by the remaining degrees of freedom. Some well-known fairing methods are adapted to this framework. Constrained fairing for n-sided corner patches, composed of quadrilaterals, is also briefly discussed. A few examples illustrate the results.