Volume 23, Issue 1
Closed Smooth Surface Defined from Cubic Triangular Splines

Ren-Zhong Feng & Ren-Hong Wang

J. Comp. Math., 23 (2005), pp. 67-74.

Published online: 2005-02

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  • Abstract

In order to construct closed surfaces with continuous unit normal, we introduce a new spline space on an arbitrary closed mesh of three-sided faces. Our approach generalizes an idea of Goodman and is based on the concept of 'Geometric continuity' for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.

  • Keywords

Closed triangular mesh, Triangular Bernstein polynomial, Smooth spline, Geometric continuity.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-67, author = {}, title = {Closed Smooth Surface Defined from Cubic Triangular Splines}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {1}, pages = {67--74}, abstract = {

In order to construct closed surfaces with continuous unit normal, we introduce a new spline space on an arbitrary closed mesh of three-sided faces. Our approach generalizes an idea of Goodman and is based on the concept of 'Geometric continuity' for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8796.html} }
TY - JOUR T1 - Closed Smooth Surface Defined from Cubic Triangular Splines JO - Journal of Computational Mathematics VL - 1 SP - 67 EP - 74 PY - 2005 DA - 2005/02 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8796.html KW - Closed triangular mesh, Triangular Bernstein polynomial, Smooth spline, Geometric continuity. AB -

In order to construct closed surfaces with continuous unit normal, we introduce a new spline space on an arbitrary closed mesh of three-sided faces. Our approach generalizes an idea of Goodman and is based on the concept of 'Geometric continuity' for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.

Ren-Zhong Feng & Ren-Hong Wang. (1970). Closed Smooth Surface Defined from Cubic Triangular Splines. Journal of Computational Mathematics. 23 (1). 67-74. doi:
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