P. Alfeld et al., THE GENERIC DIMENSION OF THE SPACE OF C1 SPLINES OF DEGREE D-GREATER-THAN-OR-EQUAL-TO-8 ON TETRAHEDRAL DECOMPOSITIONS, SIAM journal on numerical analysis, 30(3), 1993, pp. 889-920
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.