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An algorithm is presented that generates developable Bézier surfaces through a Bézier curve of arbitrary degree and shape. The algorithm has two important advantages. No (nonlinear) characterizing equations have to be solved and the control of singular points is guaranteed. Further interpolation conditions can be met.
The most important properties of Bézier and B-spline curves are the convex hull property, the affine invariance, the possibility to subdivide and the variation diminishing property. Therefore it would be of great interest to have a larger class of point controlled curves with the same properties. It is known that all corner cutting curves have the first two… (More)