A class of blending functions with \(C^{\infty}\) smoothness. (English) Zbl 1489.65035
Summary: In this work, by combining a class of local support and infinitely differentiable functions together with the sinc function, we construct a new class of univariate blending functions with three local shape parameters \(\alpha_i\), \(\beta_i\), and \(\lambda_i\). The new blending functions have the properties of \(C^{\infty}\) smoothness, compact support, and partition of unity. The shape parameter \(\alpha_i\) has tension property, and \(\beta_i\) can adjust the support of the blending functions. With \(\lambda_i\), the given blending functions can be used to interpolate sets of points partly or entirely without solving a linear system of equations. Some simple conditions for the blending functions possessing nonnegativity and/or linear independence are developed. Based on the new univariate blending functions, tensor product blending functions and local tensor product blending functions are also developed.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
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