Abstract

Developable surfaces and minimal surfaces have been employed in many areas such as sheet-metal and plate-metal based industries, architecture, aviation and ship manufacture. However, nonplanar minimal surfaces cannot be developable surfaces. In this paper, we firstly introduce the new concept of weighted approximate developable minimal surface. It contains approximate developable surface and approximate minimal surface as special cases. For the case of tensor product B́zier surface, given the boundary control points, the interior control points can be constructed using nonlinear optimization algorithm. We mainly adopt the trust-region method in this paper. We also present several examples and the corresponding numeric results on Gaussian curvature and mean curvature.

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