三角形上的一种C^2插值

A TRIANGULAR C 2 INTERPOLANT

对平面多边形区域的三角剖分，我们提出一种Ｃ２插值格式，基于任意三角形上的插值由５次多项式配以有理权函数组合而成，它满足给定于三角形项点的直到２阶的偏导数。

For a triangulation of a planar polygonal region, we develop a C 2 interpolation scheme. The interpolant on any triangle is a combination of quintics with rational weights and interpolates arbitrarily given values and derivatives of orders up to 2 at the vertices, while the normal derivatives of orders 1 and 2 of the interpolant on the edges of the triangle are polynomials of degrees 3 and 1 respectively.