Surface Construction with Fewer Patches

We present an algorithm to generate an interpolation or approximation model consisting of many patches from a triangle mesh, and each patch is a weighted combination of the three surfaces associated with the vertices of a triangle. Moreover, to make the whole surface include fewer patches, mesh simplification is introduced into the process of surface construction. The algorithm takes a triangle mesh and a given error as input, and iteratively deletes vertex whose distance to the surface model constructed from the simplified mesh is less than or equal to the given error until convergence. Since the method is based on surface approximation and vertex deletion, it allows us to control the error between the generated model and the original mesh precisely. Furthermore, many experimental results show that the generated models approximate the original models well.

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