In this paper we derive an approximation property of four-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth ...

Trimming is an important primitive operation in geometric modeling. It is also the root of many numerical and topological problems in modern NURBS based CAGD systems. In this paper we introduce a new method for trimming subdivision surfaces. It is based on the use of combined subdivision schemes to guarantee exact interpolation of trim curves. The latter ensures, for example, that if two surfac...

The four-point curve subdivision scheme is one of the classic reference points of subdivision theory. It has effective C2 continuity, although the curvature at the data points actually diverges slowly to infinity as very large numbers of subdivision steps are taken. However, it has rather large longitudinal artifacts, so that points interpolated around a curve of almost constant curvature are f...

In this paper we present a novel subdivision scheme that can produce a nice-looking interpolation of the control points of the initial polyline, giving the possibility of adjusting the local shape of the limit curve by choosing a set of tension parameters associated with the polyline edges. If compared with the other existing methods, the proposed model is the only one that allows to exactly re...

Yesterday, we introduced barycentric coordinates and de Casteljau’s algorithm. Today, we want to go more in depth into the mechanics of de Casteljau’s algorithm, and understand some of the nuances of the algorithm. We also want to discuss the efficiency of this algorithm in creating the curve. The algorithm’s power is not necessarily in defining a polynomial curve, but in how the algorithm can ...

A quadratic Bézier spline with G-continuity is given to approximate a planar parametric curve. In its construction, the parametric curve is first divided into several segments. A rational quadratic Bézier curve is then applied to approximate each segment and recursive subdivision for the segment may be used if the approximation error is out of the given range. With this method, we not only keep...

Interactive implicit modelling with complex skeletons was recently improved with the introduction of primitives de ned at di erent LODs. These implicit primitives use a subdivision curve as a skeleton. In this paper an extension to this representation is presented, in order to make it suitable for the interactive modelling and animation of soft objects in contact situations. The rst contributio...

Boundary conditions are still an open question in the field of approximating subdivision since the problem of determining a general construction of the endpoint rules we need when subdividing a B-spline curve/surface with Bézier end conditions has not been solved yet. This consideration prompted us to present an efficient algorithm for the conversion between B-spline bases defined over differen...