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SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Surface design with minimum energy networks
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
A Note on Quadrilateral Interpolation
Journal of the ACM (JACM)
IEEE Annals of the History of Computing
A Tension-Compatible Patch for Shape-Preserving Surface Interpolation
IEEE Computer Graphics and Applications
Applications of a numerical geometry system in engineering
DAC '76 Proceedings of the 13th Design Automation Conference
Tabular representation of multivariate functions—with applications to topographic modeling
ACM '67 Proceedings of the 1967 22nd national conference
A partial solution to fitting large parametric surfaces in computer-aided design systems
DAC '79 Proceedings of the 16th Design Automation Conference
A solution to surface connectivity problems in computer-aided design
ACM SIGGRAPH Computer Graphics
Constructing spherical curves by interpolation
Advances in Engineering Software
Image vectorization using optimized gradient meshes
ACM SIGGRAPH 2007 papers
Algorithms in Numerical Geometry System
IEEE Transactions on Computers
Automatic and topology-preserving gradient mesh generation for image vectorization
ACM SIGGRAPH 2009 papers
NC machining of free form surfaces
Computer-Aided Design
Procedural representation of three-dimensional objects
IBM Journal of Research and Development
Bicubic patch surfaces for high-speed numerical control processing
IBM Journal of Research and Development
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
On a new approach to obtain spline Bézier curves
ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume II
Design techniques for the definition of solid objects with free-form geometry
Computer Aided Geometric Design
Efficient solid texture synthesis using gradient solids
CVM'12 Proceedings of the First international conference on Computational Visual Media
Efficient synthesis of gradient solid textures
Graphical Models
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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The problem of defining a smooth surface through an array of points in space is well known. Several methods of solution have been proposed. Generally, these restrict the set of points to be one-to-one defined over a planar rectangular grid (X, Y-plane). Then a set of functions Z = F(X, Y) is determined, each of which represents a surface segment of the composite smooth surface. In this paper, these ideas are generalized to include a much broader class of permissible point array distributions: namely (1) the point arrangement (ordering) is topologically equivalent to a planar rectangular grid, (2) the resulting solution is a smooth composite of parametric surface segments, i.e. each surface piece is represented by a vector (point)-valued function. The solution here presented is readily applicable to a variety of problems, such as closed surface body definitions and pressure envelope surface definitions. The technique has been used successfully in these areas and others, such as numerical control milling, Newtonian impact and boundary layer.