HB - splines : a Blend of Hermite splines and B - splinesLaurent Grisoni

HB-splines: a Blend of Hermite splines and B-splines Laurent Grisoni Carole Blanc Christophe Schlick LaBRI [grisonijblancjschlick]@labri.u-bordeaux.fr 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 di erential values at segment boundaries. Although this model does not appear able to o er 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 o ers 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 e cient way.