Optimization of geometrically trimmed b-spline surfaces

Unlike the visual trimming of B-spline surfaces, which hides unwanted portions in rendering, the geometric trimming approach provides a mathematically clean representation without redundancy. However, the process may lead to significant deviation from the corresponding portion on the original surface. Optimization is required to minimize approximation errors and obtain higher accuracy. In this paper, we describe the application of a novel global optimization method, so-called hybrid Parallel Tempering (PT) and Simulated Annealing (SA) method, for the minimization of B-spline surface representation errors. The high degree of freedom within the configuration of B-spline surfaces as well as the "rugged" landscapes of objective functions complicate the error minimization process. The hybrid PT/SA method, which is an effective algorithm to overcome the slow convergence, waiting dilemma, and initial value sensitivity, is a good candidate for optimizing geometrically trimmed B-spline surfaces. Examples of application to geometrically trimmed wing components are presented and discussed. Our preliminary results confirm our expectation. Copyright © 2005 by ASME.