The generic dimension of the space of C 1 splines of degree d ≥8 on tetrahedral decompositions

This paper considers the linear space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain which has been partitioned into tetrahedra. Combining Bernstein–Bezier methods and combinatorial and geometric techniques from rigidity theory, this paper gives an explicit expression for the generic dimension of this space for sufficiently large polynomial degrees $(d \geq 8)$. This is the first general dimension statement of its kind.