Strip approximation with Bezier patches in conical form for design and manufacturing of developable materials

This article proposes a novel geometric modelling method for strip approximation using developable Bezier patches in the conical form. Given two space curves, a greedy algorithm is applied to generate an aggregate of quadrilateral and triangular patches based on local optimisation of normal variation across the patch boundaries. These patches, only with positional continuity, are degree elevated to produce additional control points for further shape adjustment. G1 continuity is thus created by the extra degrees of freedom obtained from the degree elevation while the surface developability is preserved. An adaptive refinement algorithm is introduced to minimise the deviation between the boundaries of the approximation patches and the given curves. The experimental results of test examples demonstrate the advantages of the proposed method, which provides flexible modelling capability with quadrilateral and triangular patches, approximates with high-order patches and allows error control in the approximation. This work offers an effective approach for design and manufacturing of developable materials.