Journal ArticleDOI
Geometric spline curves
TLDR
The v-splines are generalized to geometric spline curves and the computational equations of quintic splines curves with curvature and torsion continuity are given.About:
This article is published in Computer Aided Geometric Design.The article was published on 1985-09-01. It has received 58 citations till now. The article focuses on the topics: Thin plate spline & Spline interpolation.read more
Citations
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Journal ArticleDOI
Surfaces in computer aided geometric design: a survey with new results
TL;DR: 'Surfaces in Computer Aided Geometric Design' focuses on the representation and design of surfaces in a computer graphics environment and can be traced from its inception in rectangular Coons patches and Bezier patches to triangular patches which are current research topics.
Journal ArticleDOI
Geometric continuity of parametric curves: three equivalent characterizations
Brian A. Barsky,Tony DeRose +1 more
TL;DR: The paper covers parametric representation and smoothness, parametric continuity, reparameterization and equivalent parameterization, beta-constraints, and arc-length parameterization.
Journal ArticleDOI
Spline approximation of offset curves
TL;DR: The approximating spline curves are determined by geometric continuity conditions and by parameter optimization for minimizing the range of the approximation error.
Journal ArticleDOI
Multidimensional curve fitting to unorganized data points by nonlinear minimization
Lian Fang,David C. Gossard +1 more
TL;DR: A method for generating a piecewise continuous parametric curve from a set of unordered and error-filled data points is presented, excluding the endpoints of the curve, thus eliminating the necessity of an initial parameterization.
Book ChapterDOI
Chapter 1 – A History of Curves and Surfaces in CAGD
TL;DR: The chapter reveals that curves were employed by draftsmen for centuries; the majority of these curves were circles, but some were free-form, and the generalization of the concept of splines to surfaces is discussed.
References
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Journal ArticleDOI
An Interpolation Curve Using a Spline in Tension
TL;DR: In this article, a spline in tension is considered and the value of tension which is sufficient to remove all extraneous inflection points is determined, and the slopes of the interpolating curve at each of the given stations are considered as the unknowns.
Journal ArticleDOI
Scalar- and planar-valued curve fitting using splines under tension
TL;DR: The spline under tension was introduced by Schweikert in an attempt to imitate cubic splines but avoid the spurious critical points they induce.
Book ChapterDOI
Some piecewise polynomial alternatives to splines under tension
TL;DR: In this paper, the authors discuss the characterization of splines under tension and present some piecewise polynomial alternatives to spline under tension. But they do not discuss the effect of the tension on splines in tension.
On splines and their minimum properties
TL;DR: A generalization of the notion of spline functions is given in this paper, where it is shown that spline interpolation is a process of best approximation, i.e., of orthogonal projection in this Hilbert space.
Related Papers (5)
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
Geometric continuity of parametric curves: three equivalent characterizations
Brian A. Barsky,Tony DeRose +1 more