Spherical Essentially Non-oscillatory (SENO) Interpolation

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