This thesis presents the theory and several methods involved with multivariate polyhedral splines and spline spaces. B-splines are generalized from univariate spline theory to the multivariate setting where the definition of a polyhedral spline is introduced. Characteristics and properties of multivariate polyhedral splines are then explored via distribution theory, and the geometric interpretation (in terms of cross-sectional volumes of polyhedra) is presented. Properties of spline spaces (spaces spanned by B-splines) are examined, a subdivision algorithm is given, and finally, calculations and computer graphic displays demonstrate several of the algorithms available for surface fitting which involve multivariate polyhedral splines.

Bibliography: p. 111-114.