C1 interpolation splines over type-1 triangulations with shape parameters

Authors：Qin, Xiangbin; Zhu, Yuanpeng^*

Source：COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 40(8): 275.

DOI：10.1007/s40314-021-01664-7

• Interpolation spline
• Triangular partitions
• C-1 continuity
• Shape parameter

In this work, we construct a class of C-1 quintic interpolation basis functions over type-I triangulations with two shape parameters. The given interpolation basis functions have the properties of compact support, non-negativity and partition of unity. Based on the new interpolation basis functions, a kind of C-1 quintic triangular interpolation spline surfaces with two shape parameters is proposed. The resulting spline surfaces interpolate control points associated with barycentric parametric triples arranged in type-1 triangulations directly, without using any prescribed derivatives at any point of the domain. The local Bernstein-Bezier representation of the triangular interpolation spline surfaces is developed. In addition, the effects of the two shape parameters on generating the Bezier control points of the local surface patch are illustrated. Moreover, by blending the new C-1 quintic interpolation basis functions with linear parametrized basis surfaces, a kind of C-1 Overhauser-type interpolation spline surfaces with two shape parameters is also constructed.