Every curve or surface can be defined by a set of parametric functions. For instance, (x,y,z) coordinates of the points of the curve can be given by:) (), (), (t Z z t Y y t X x = = = t being the parameter and X, Y, Z being polynomial functions in t. If X, Y and Z are 1 st degree polynomials, a line segment will be defined. In that case, two knowns only (i.e. two points or a point and a slope) ...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.

This paper presents a C Pythagorean-Hodograph (PH) spline curve interpolator for contourfollowing tasks. To generate the C PH quintic spline curve, a uniform knot sequence is employed. The Scurve motion planning architecture with variable feedrate for a planar C PH quintic spline curve is also developed. In particular, C cubic feed acceleration/deceleration is imposed on the first and last PH q...

Diffusion Tensor MRI (DT-MRI) measurements are a discrete noisy sample of an underlying macroscopic effective diffusion tensor field, D(x), of water. This field is presumed to be piecewise continuous/smooth at a gross anatomical length scale. Here we describe a mathematical framework for obtaining an estimate of this tensor field from the measured DT-MRI data using a spline-based continuous app...

Elliptic and hyperbolic partial differential equation methods for generating both surface and volume structured grids have been implemented in the Gridgen software system. Their implementation provides the means by which very high quality quad and hex grids can be generated for computational fluid dynamics (CFD). The grids, in turn, provide the basis for highly accurate CFD simulations of visco...

Interrogative visualization refers to the process of interactive computer graphics display and accurate quantitative querying of physical data. Quantitative querying includes search for metric, combinato-rial and topological information. To support this paradigm, we build uniform, compact, co-registered representations (spline models) of multiple physical data elds over the same domain. Dense, ...

In this paper we present a NURBS version of the rational interpolating spline with tension introduced in [2], and we extend our proposal to the rectangular topology case. In particular we present some rational interpolating techniques that enable us to reconstruct shape-preserving bivariate NURBS and allow us to interactively modify the resulting surface by a set of tension parameters.

A new formulation of energy minimising splines, based on Non-Uniform Rational B-Spline (NURBS) curves, is presented. The existing snake models do not facilitate the local control of their shapes without increasing the number of control points. The introduction of NURBS renders more flexibility into the snake model due to the weighting parameters that are made to adapt according to the curvature...