The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

Abstract We present a new method to compress triangle meshes in a lossless manner. Triangle compression requires compression of the geometry (vertices) as well as the topology (connectivity). The method is loosely based on the Edgebreaker algorithm by Rossignac et al. in the sense that the traversal of the mesh is done the same way during compression. We use B-Spline curves to store, compute an...

In the present paper the problem of removing one inner knot from the knot sequence of a B-spline curve is discussed. Doing so, a local (geometric) construction of the new control points from the given ones is rst introduced. Then the degrees of freedom appearing in this general construction are determined by minimizing three diierent norms between the old curve and the new curve. Here the best ...

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...

In this paper, we present a non-uniform subdivision scheme of arbitrary degree with a variable parameter sequence. By this scheme, blending curves which are composing of different types of generalized B-spline curves including many analytic curves can be successfully reproduced. Generalized subdivision and the classical B-spline subdivision are all special cases of the proposed variable paramet...

Splines are part of the standard toolbox for the approximation of functions and curves in Rd . Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a “spline” with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be ...

This article describes a F0 curve estimation scheme based on a B-spline model1. We compare this model with more classical spline representation. The free parameters of both models are the number of knots and their location. An optimal location is proposed using a simulated annealing strategy. Experiments on real F0 curves confirm the adequacy and good performance of the B-spline approach, estim...

Cranial implants, especially custom made are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of manual design implant is time consuming complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline radial basis functions have been used for crania...