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
Interpolation with interval and point tension controls using cubic weighted v-splines
ACM Transactions on Mathematical Software (TOMS)
Local control of interval tension using weighted splines
Computer Aided Geometric Design
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Geometric Continuity of Parametric Curves
Geometric Continuity of Parametric Curves
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Scientific data visualization: a formal introduction to the rendering and geometric modeling aspects
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
A blending model for parametrically defined geometric objects
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
A Two-Stage Algorithm for Discontinuity-Preserving Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Interactive Editing and Contouring of Empirical Fields
IEEE Computer Graphics and Applications
A curve design method with shape control
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Fairing of parametric cubic splines
Mathematical and Computer Modelling: An International Journal
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The weighted bicubic spline that is a C1 piecewise bicubic interpolant to three-dimensional gridded data is introduced. This is a generalization of the univariate weighted spline, developed by Salkauskas, in that a weighted minimization problem is solved. The minimization problem solved is a weighted version of the problem that the natural bicubic spline and Gordon's spline-blended interpolants minimize. The surface is represented as a piecewise bicubic Hermite interpolant whose derivatives are the solution of a linear system of equations. For computer-aided-design applications, the shape of the surface is controlled by weighting the variation over the individual patches, whereas many other shape-control methods weight the discrete data points. A method for selecting the weights is presented so that the weighted bicubic spline effectively solves the important and often difficult problem of interpolating rapidly varying data.