On approximating contours of the piecewise trilinear interpolant using triangular rational quadratic Bezier patches

Given a three dimensional (3D) array of function values F/sub i,j,k/ on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x, y, z)=T. We describe the construction of a C/sup 0/ continuou...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 1997-07, Vol.3 (3), p.215-227
Main Authors: Hamann, B., Trotts, I.J., Farin, G.E.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer graphics
Computer science
Computer science
control theory
systems
Data visualization
Exact sciences and technology
Grid computing
Indexing
Interpolation
Isosurfaces
Legged locomotion
Pattern recognition. Digital image processing. Computational geometry
Piecewise linear approximation
Surface cracks
Theoretical computing
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Summary:Given a three dimensional (3D) array of function values F/sub i,j,k/ on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x, y, z)=T. We describe the construction of a C/sup 0/ continuous surface consisting of rational quadratic surface patches interpolating the triangles in T. We determine the Bezier control points of a single rational quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.
ISSN:1077-2626
1941-0506
DOI:10.1109/2945.620489