various methods for parametric interpolation of nurbs curves have been proposed in the past. however, the errors caused by the approximate nature of the nurbs interpolator were rarely taken into account. this paper proposes an integrated look-ahead algorithm for parametric interpolation along nurbs curves. the algorithm interpolates the sharp corners on the curve with the pythagorean-hodograph ...

The goal of this master thesis is to study, compare, and improve existing approaches for direct ray tracing trimmed NURBS surfaces. In order to be able to study the topic efficiently, a library for NURBS evaluation has been implemented. The library is supposed to be easily integrated in any ray tracing application to make it support direct ray tracing trimmed NURBS surfaces.

A new class of spline curves in polar coordinates has been presented in (SS anchez-Reyes, 1992) and independently considered in (de Casteljau, 1994). These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling sp...

This paper presents dynamic NURBS or D NURBS a physics based generalization of non uniform ra tional B splines NURBS have become a de facto standard in commercial modeling systems because of their power to represent both free form and common analytic shapes Traditionally however NURBS have been viewed as purely geometric primitives which require the designer to interactively adjust many degrees...

NURBS curve is widely used in Computer Aided Design and Computer Aided Geometric Design. When a single weight approaches infinity, the limit of a NURBS curve tends to the corresponding control point. In this paper, a kind of control structure of a NURBS curve, called regular control curve, is defined. We prove that the limit of the NURBS curve is exactly its regular control curve when all of we...

Non-Uniform Rational B-Spline (NURBS) surfaces can be non-uniform and defined for any degree, but existing subdivision surfaces are either uniform or of fixed degree. The resulting incompatibility forms a barrier to the adoption of subdivision for ComputerAided Design. In this talk I will discuss our work towards a superset of NURBS which can handle irregularities in the control mesh. We call t...

We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial order, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates....

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

The representation, matching and analysis of objects of interest are of prime importance in shape-based retrieval systems. Considering that these systems involve analysis of various complex shapes, an accurate representation of free form shape is required. A simple and accurate shape representation procedure would ensure meaningful results from the shape-based retrieval systems. Motivated by th...

Constructing a CAD model from a physical model plays a key role in some rapid product development processes. Presented in the paper is a method of ®tting NURBS surfaces for rotational freeform shapes: (1) cloud-of-points data (COP-data) representing a rotational freeform shape are transformed into an orthogonal coordinate system, (2) a single-valued B-spline surface is ®tted to the transformed ...