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Volume 18, Issue 4
On Triangular C1 Schemes: A Novel Construction

Yin-Wei Zhan

J. Comp. Math., 18 (2000), pp. 403-412.

Published online: 2000-08

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  • Abstract

In this paper we present a $C^1$ interpolation scheme on a triangle. The interpolant assumes given values and one order derivatives at the vertices of the triangle. It is made up of partial interpolants blended with corresponding weight functions. Any partial interpolant is a piecewise cubics defined on a split of the triangle, while the weight function is just the respective barycentric coordinate. Hence the interpolant can be regarded as a piecewise quartic. We device a simple algorithm for the evaluation of the interpolant. It's easy to represent the interpolant with B-net method. We also depict the Franke's function and its interpolant, the illustration of which shows good visual effect of the scheme.  

  • Keywords

Spline, interpolation scheme, partial interpolants, barycentric coordinates, splits, B-net.

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COPYRIGHT: © Global Science Press

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@Article{JCM-18-403, author = {Zhan , Yin-Wei}, title = {On Triangular C1 Schemes: A Novel Construction}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {4}, pages = {403--412}, abstract = {

In this paper we present a $C^1$ interpolation scheme on a triangle. The interpolant assumes given values and one order derivatives at the vertices of the triangle. It is made up of partial interpolants blended with corresponding weight functions. Any partial interpolant is a piecewise cubics defined on a split of the triangle, while the weight function is just the respective barycentric coordinate. Hence the interpolant can be regarded as a piecewise quartic. We device a simple algorithm for the evaluation of the interpolant. It's easy to represent the interpolant with B-net method. We also depict the Franke's function and its interpolant, the illustration of which shows good visual effect of the scheme.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9052.html} }
TY - JOUR T1 - On Triangular C1 Schemes: A Novel Construction AU - Zhan , Yin-Wei JO - Journal of Computational Mathematics VL - 4 SP - 403 EP - 412 PY - 2000 DA - 2000/08 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9052.html KW - Spline, interpolation scheme, partial interpolants, barycentric coordinates, splits, B-net. AB -

In this paper we present a $C^1$ interpolation scheme on a triangle. The interpolant assumes given values and one order derivatives at the vertices of the triangle. It is made up of partial interpolants blended with corresponding weight functions. Any partial interpolant is a piecewise cubics defined on a split of the triangle, while the weight function is just the respective barycentric coordinate. Hence the interpolant can be regarded as a piecewise quartic. We device a simple algorithm for the evaluation of the interpolant. It's easy to represent the interpolant with B-net method. We also depict the Franke's function and its interpolant, the illustration of which shows good visual effect of the scheme.  

Zhan , Yin-Wei. (2000). On Triangular C1 Schemes: A Novel Construction. Journal of Computational Mathematics. 18 (4). 403-412. doi:
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