Specifications The purpose of Abstract Specifications1 is to create and document a conceptual model sufficient enough to allow for the creation of Implementation Specifications. One OGC abstract specification, the Spatial Schema, gives a standard for geographic information by specifying geometry and topology separately as a UML (Unified Modeling Language)2 package dependency tree. The geometry ...

We present a surface generation method which produces B-spline-like surfaces (or curves) in any dimension. We focus on the 2D quadratic case.

Shape preservation behavior of a spline consists of criterial conditions for preserving convexity, inflection, collinearity, torsion and coplanarity shapes of data polgonal arc. We present our results which acts as an improvement in the definitions of and provide geometrical insight into each of the above shape preservation criteria. We also investigate the effect of various results from the li...

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show t...

A new method for manipulation of curves in several degrees is presented. When a point of curve is moved, it a ects a relative local segment, which size could depends of the propagation of the point through their lower resolution curves. So, for the same displacement of the point, could be generated relative local segments of di erent sizes, only varying a local parameter such sti ness constant....

This paper reports the work on a novel wavelet-based multi-scale filtering application used to generate very smooth subset of profiles known as Class-A curves. The multi-scale representation, based on B-spline wavelets, allows to split a spline curves in terms of a coarser least-square approximation and details coefficients. It raises that non-Class-A curves are determined by geometric imperfec...

For a planar curve C with positive affine curvature, we derive an asymptotic formula for the area approximation by quadratic spline curves with n knots lying on C. The order of approximation is 1/n4 and the formula depends on an integral over the affine curvature. 1991 AMS subject classification: 52A10, 53A04, 53A15, 41A15, 41A50

The unresolved subtleties of floating point computations in geometric modeling become considerably more difficult in animations and scientific visualizations. Some emerging solutions based upon topological considerations will be presented. A novel geometric seeding algorithm for Newton’s method was used in experiments to determine feasible support for these visualization applications. 1 Computi...

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 ...