Journal ArticleDOI
A locally controllable spline with tension for interactive curve design
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A new type of parametrically defined space curve is described, which allows for the convenient control over local shape attributes while maintaining global second order geometric continuity.About:
This article is published in Computer Aided Geometric Design.The article was published on 1984-12-01. It has received 31 citations till now. The article focuses on the topics: Parallel curve & Curve fitting.read more
Citations
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Journal ArticleDOI
Rectangular v-Splines
TL;DR: This article describes and presents examples of some techniques for the representation and interactive design of surfaces based on a parametric surface representation that user v-spline curves and extends their application to a rectangular grid of control points.
Journal ArticleDOI
A rational cubic spline with tension
John A. Gregory,Muhammad Sarfraz +1 more
TL;DR: A rational cubic spline curve is described which has tension control parameters for manipulating the shape of the curve and the behaviour of the resulting representations is analysed with respect to variation of the control parameters.
Minimum curvature variation curves, networks, and surfaces for fair free-form shape design
TL;DR: This work presents a new technique for curve and surface design that combines a geometrically based specification with constrained optimization (minimization) of a fairness functional, and demonstrates the superiority of curvature variation as a fairness metric and efficacy of optimization as a tool in shape design, albeit at significant computational cost.
Journal ArticleDOI
Convexity-preserving piecewise rational cubic interpolation
TL;DR: In this article, a twice continuously differentiable, piecewise rational, cubic interpolant f is proposed to preserve the local convexity/concavity properties of a data set S. A fast, simple, and robust procedure for generating f is described.
References
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Book
Computational Geometry for Design and Manufacture
I. D. Faux,M. J. Pratt +1 more
TL;DR: In this paper, the mathematical techniques for the representation, analysis and synthesis of shape information by computers are discussed, and splines and related means for defining composite curves and "patched" surfaces are discussed.
Book ChapterDOI
B-spline curves and surfaces
TL;DR: This chapter presents the use of this algorithm for various computations and also describes the procedure for evaluating B-spline functions.
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.