Hermitian B-Splines

Abstract

This paper proposes to study a spline model, called HB-splines, that is in fact a B-spline representation of Hermite splines, combined with some restriction on the differential values at segment boundaries. Although this model does not appear able to offer something new to the computer graphics community, we think that HB-splines deserve to be considered for themselves because they embed many interesting features. First, they include all the classical properties required in a geometric modeling environment (convex hull, local control, arbitrary orders of parametric or geometric continuity). Second, they have a nice aptitude for direct manipulation (i.e. manipulation without using control points). For this purpose, we propose a new graphic widget, called control sails, that offers the user an intuitive way to specify local properties (position, tangent, curvature) of a curve or a surface. Finally, they provide an elegant formulation of a biorthogonal wavelet family, that permits multiresolution manipulations of the resulting curves or surfaces, in a very efficient way.