Developable surfaces have wide applications in free form surface mod-eling. In the three dimensional space, there is not always a regular developable surface that interpolates a given boundary which is an arbitrary piecewise closed curve. In this paper, we discuss how to construct an approximate developable surfaces interpolating a closed curve. We construct a surface, in tensor-product polynomial surface space, which minimizes the Ganssian curvature of the surface in some sense, where the nonlinear optimization problem is solved by trust region algorithm and quasi Newton method in optimization theory. The result is applied, as an application, into texture mapping in computer graphics, and a method is proposed to decrease the distortion.
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