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Local and singularity-free G 1 triangular spline surfaces using a minimum degree scheme

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Abstract

We develop a scheme for constructing G 1 triangular spline surfaces of arbitrary topological type. To assure that the scheme is local and singularity-free, we analyze the selection of scalar weight functions and the construction of the boundary curve network in detail. With the further requirements of interpolating positions, normals, and surface curvatures, we show that the minimum degree of such a triangular spline surface is 6. And we present a method for constructing boundary curves network, which consists of cubic Bézier curves. To deal with certain singular cases, the base mesh must be locally subdivided and we proposed an adaptive subdivision strategy for it. An application of our G 1 triangular spline surfaces to the approximation of implicit surfaces is described. The visual quality of this scheme is demonstrated by some examples.

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Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 151-744, Republic of Korea

    Wei-hua Tong

  2. Department of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University, Seoul, 151-744, Republic of Korea

    Tae-wan Kim

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  1. Wei-hua Tong
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  2. Tae-wan Kim
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Correspondence to Tae-wan Kim.

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Communicated by C.H. Cap.

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Tong, Wh., Kim, Tw. Local and singularity-free G 1 triangular spline surfaces using a minimum degree scheme. Computing 86, 235–255 (2009). https://doi.org/10.1007/s00607-009-0056-5

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  • DOI: https://doi.org/10.1007/s00607-009-0056-5

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