Strip Approximation Using Developable Bézier Patches: A Local Optimization Approach

Abstract

This paper proposes a geometric design method for approximation of a strip defined by two space curves with freeform developable surfaces. Given a ruling defined by two sample points taken from each curve, it calculates the feasible patches starting with the ruling. A local optimal solution is selected among them in terms of surface assessment criteria based on a heuristic algorithm. An aggregate of Bézier patches in the conical form, either triangular or quadrilateral, is thus created. Each patch is then degree elevated to gain extra degrees of freedom. They produce G 1 across the patch boundaries by modifying the control points while preserving the surface developability. Test examples with different design parameters are illustrated to validate the feasibility of the proposed method. In comparison with previous studies using the BBT (Bridge Boundary Triangulations) method, this work allows surface design with freeform developable patches, generates better results in the surface assessment, and provides more flexible control on the approximation shape. It serves as a simple but effective approach for geometric design of developable surfaces.

Optimal Quadrangulation of a Strip for Flank Milling

“…The solution based on triangulation works fine with some applications (e.g., the developable surface approximation [13,14]). Nevertheless, it has several deficiencies when using the triangulation to simulate a ruled surface for flank milling.…”