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 piece wise polynomial functions defined on a three-dimensional polyhedral do main which has been partitioned into tetrahedra. Combining Bernstein-B ezier methods and combinatorial and geometric techniques from rigidity theory, this paper gives an explicit expression for the generic dimen sion of this space for sufficiently large polynomial degrees (d greate r-than-or-equal-to 8). This is the first general dimension statement o f its kind.