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.

this paper, all these models will be grouped under the generic name: iso-surfaces. In the iso-surface model, an object is defined by a set of primitives that can be considered as potential fields. The boundary surface of the object is then represented by the set of points for which the sum of the potential values equates a given isovalue. Two competitive approaches can be taken to create complex shapes with the iso-surface model. Either the object may be described by a very large number of simple primitives (e.g. spheres or ellipsoids) or by a small number of complex ones (e.g. distance or convolution surfaces). The first approach is well adapted to the automatic matching of 3D experimental data [11] while the second one is merely used in a design process which allows the user to define interactively each primitive

This paper presents a new model of spline curves and surfaces. The main characteristic of this model is that it has been created from scratch by using a kind of mathematical engineering process. In a first step, a list of specifications was established. This list groups all the properties that a spline model should contain in order to appear intuitive to a non-mathematician end-user. In a second step, a new family of blending functions was derived, trying to fulfill as many items as possible of the previous list. Finally, the degrees of freedom offered by the model have been reduced to provide only shape parameters that have a visual interpretation on the screen. The resulting model includes many classical properties such as affine and perspective invariance, convex hull, variation diminution, local controlandC2=G2 orC2=G0 continuity. But it also includesoriginal features such as a continuum between B-splines and Catmull-Rom splines, or the ability to define approximation zones and interpolation zones in the same curve or surface.