We proposed a recursive interpolation scheme that gives high order interpolants called Spherical Interpolation of DEgRee (SIDER in short) on the unit sphere S². The idea generalizes the construction of the Bézier curves in R. We also adopt the philosophy of Essentially Non-Oscillatory (ENO) schemes from R to S² to develop Spherical Essentially Non-Oscillatory (SENO in short) schemes using SIDER as the building pieces. Given n+1 data points that satisfy certain constraints, there must be one SIDERn that passes through all the data points with Cⁿ continuity (if n = 2 or 3). When the underlying curve on S² has kinks or sharp discontinuity in the higher derivatives, SENO can reduce spurious oscillations in high order reconstructions....[ Read more ]

We proposed a recursive interpolation scheme that gives high order interpolants called Spherical Interpolation of DEgRee (SIDER in short) on the unit sphere S². The idea generalizes the construction of the Bézier curves in R. We also adopt the philosophy of Essentially Non-Oscillatory (ENO) schemes from R to S² to develop Spherical Essentially Non-Oscillatory (SENO in short) schemes using SIDER as the building pieces. Given n+1 data points that satisfy certain constraints, there must be one SIDERn that passes through all the data points with Cⁿ continuity (if n = 2 or 3). When the underlying curve on S² has kinks or sharp discontinuity in the higher derivatives, SENO can reduce spurious oscillations in high order reconstructions.