DIMENSION AND LOCAL BASES OF HOMOGENEOUS SPLINE SPACES

Recently, we have introduced spaces of splines defined on triangulatio ns lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-Bezier theory on such surfaces. The pur pose of this paper is to contribute to the development of a constructi ve theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangulations. Rather than working with splines on sphere-like surfaces directly, we instead investigate more general spaces of homogeneous splines in R(3). In particular, we pres ent formulas for the dimensions of such spline spaces, and construct l ocally supported bases for them.