A Class of Cubic Trigonometric Automatic Interpolation Curves and Surfaces with Parameters

[摘要] This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin2t, sin3t, cos3t}. The new curves can not only automatically interpolate the given data points without solving equation systems, but are also C2 and adjust their shape by altering values of the two parameters. The optimal interpolation curves can be determined by an energy optimization model. The corresponding interpolation surfaces have characteristics similar to the new curves.

[学科分类] 计算数学

[关键词] trigonometric polynomial;interpolation curves;surfaces