Spherical Essentially Non-Oscillatory (SENO) Interpolation

12/05/2022

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by   Ki Wai Fong, et al.

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We develop two new ideas for interpolation on 𝕊^2. In this first part, we will introduce a simple interpolation method named Spherical Interpolation of orDER n (SIDER-n) that gives a C^n interpolant given n ≥ 2. The idea generalizes the construction of the Bézier curves developed for ℝ. The second part incorporates the ENO philosophy and develops a new Spherical Essentially Non-Oscillatory (SENO) interpolation method. When the underlying curve on 𝕊^2 has kinks or sharp discontinuity in the higher derivatives, our proposed approach can reduce spurious oscillations in the high-order reconstruction. We will give multiple examples to demonstrate the accuracy and effectiveness of the proposed approaches.