A locally controllable spline with tension for interactive ... - Science Direct

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Computer Aided Geometric Design 1 (1984) 199-205 North-HoUand

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A locally controllable spline with tension for interactive curve design G r e g o r y M. N I E L S O N

Computer Science Department, Arizona State University, Tempe, AZ 85287, USA Received 1 May 1984 Revised 15 November 1984 Abstract. We describe a new type of parametrically defined space curve. The parameters which define these curves allow for the convenient control over local shape attributes while maintaining global second order geometric continuity. The coordinate functions are defined by piecewise segments of rational functions, each segment being the ratio of cubic polynomials and a common quadratic polynomial. Each curve segment is a planar curve and where two segments meet the curvature is zero. This simple mathematical representation permits these curves to be efficiently manipulated and displayed. Keywords. Curve design, interactive graphics, geometric modelling, spline.

1. Introduction Interactive curve design requires a class of curves which have a simple mathematical representation yet flexible e n o u g h to allow a wide variety of curve shapes to be represented. Most m e t h o d s utilize parametrically defined curves,

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