Splines on spherical triangulations with hanging vertices

Spline spaces defined on spherical triangulations with hanging vertices are studied. In addition to dimension formulae, explicit basis functions are constructed, and their supports and stability are discussed. The approximation power of the spaces is also treated.

► The theory of splines on H-triangulations is carried over to the sphere.
► These splines are useful in interpolation, data fitting, and solution of PDEʼs on the sphere.
► Spherical H-triangulations allow hanging vertices, and are much more flexible.
► There are results on dimension, local stable bases, and approximation power.
► Spherical Bernstein–Bézier methods are used.