On using planar developments to perform texture mapping on arbitrarily curved surfaces

Abstract This paper introduces a method for applying texture from a two-dimensional domain to a three-dimensional surface which is divided into two stages: the pre-processing stage, where a proper planar development of the three-dimensional surface is generated and the stage of mapping texture from the plane to the given surface. Several techniques for generating planar developments are studied and a new technique for surface flattening is proposed. Using this technique it is possible to control the local mapping accuracy. A new mapping method and a set of indices for evaluating the mapping accuracy are proposed. The accuracy indices are derived through the numerical method of singular-value decomposition. To reduce aliasing a space-variant filter, which can be incorporated within the two stages of the introduced texture mapping technique is developed. Finally, various applications are worked out to illustrate the effectiveness of the techniques proposed in this paper.

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