Computer Aided Geometric Design
Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
An intuitive approach to geometric continuity for parametric curves and surfaces
Proceedings of Graphics Interface '85 on Computer-generated images: the state of the art
Local control of interval tension using weighted splines
Computer Aided Geometric Design
ACM Transactions on Mathematical Software (TOMS)
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
Elementary Numerical Analysis: An Algorithmic Approach
Elementary Numerical Analysis: An Algorithmic Approach
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Interpolating splines with local tension, continuity, and bias control
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Weighted bicubic spline interpolation to rapidly varying data
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Journal of Computational and Applied Mathematics
Robust B-spline Snakes For Ultrasound Image Segmentation
Journal of Signal Processing Systems
A curve design method with shape control
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
C-B-spline singular blending interpolating
ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
Fairing of parametric cubic splines
Mathematical and Computer Modelling: An International Journal
A shape-preserving approximation by weighted cubic splines
Journal of Computational and Applied Mathematics
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Various methods have been developed to control the shape of an interpolating curve for computer-aided design applications. Some methods are better suited for controlling the tension of the curve on an interval, while others are better suited for controlling the tension at the individual interpolation points. The weighted v-spline is a C1 piecewise cubic polynomial interpolant that generalizes C2 cubic splines, weighted splines, and v-splines. Shape controls are available to “tighten” the weighted v-spline on intervals and/or at the interpolation points. The mathematical theory is presented together with short algorithms for parametric interpolation.