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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.

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 G1 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.