THE GENERIC DIMENSION OF THE SPACE OF C1 SPLINES OF DEGREE D-GREATER-THAN-OR-EQUAL-TO-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 greater-than-or-equal-to 8). This is the first general dimension statement of its kind.