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/2000-JCM-9052}, url = {https://global-sci.com/article/85563/on-triangular-csup1sup-schemes-a-novel-construction} }