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 cor...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.展开更多
重心坐标为多边形域上的数据插值提供了一种简便而有效的方法,可以把域内的任意点表示为一组控制顶点的线性组合。已有重心坐标大都需要预先对多边形区域进行三角剖分。提出一种最小二乘正则化模型广义重心坐标,用交替方向乘子法(Altern...重心坐标为多边形域上的数据插值提供了一种简便而有效的方法,可以把域内的任意点表示为一组控制顶点的线性组合。已有重心坐标大都需要预先对多边形区域进行三角剖分。提出一种最小二乘正则化模型广义重心坐标,用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)进行求解,且不需要对区域预先进行三角剖分,可用于任意简单多边形。理论分析和算法实例表明,此坐标是非负的、光滑的。展开更多
文摘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.
文摘重心坐标为多边形域上的数据插值提供了一种简便而有效的方法,可以把域内的任意点表示为一组控制顶点的线性组合。已有重心坐标大都需要预先对多边形区域进行三角剖分。提出一种最小二乘正则化模型广义重心坐标,用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)进行求解,且不需要对区域预先进行三角剖分,可用于任意简单多边形。理论分析和算法实例表明,此坐标是非负的、光滑的。
