Stripification of Free-Form Surfaces With Global Error Bounds for Developable Approximation

Abstract

Developable surfaces have many desired properties in the manufacturing process. Since most existing CAD systems utilize tensor-product parametric surfaces including B-splines as design primitives, there is a great demand in industry to convert a general free-form parametric surface within a prescribed global error bound into developable patches. In this paper, we propose a practical and efficient solution to approximate a rectangular parametric surface with a small set of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> -joint developable strips. The key contribution of the proposed algorithm is that, several optimization problems are elegantly solved in a sequence that offers a controllable global error bound on the developable surface approximation. Experimental results are presented to demonstrate the effectiveness and stability of the proposed algorithm.