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On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bézier Patches
July-September 1997 (vol. 3 no. 3)
pp. 215-227
ASCII Text
x 
 
Bernd Hamann, Issac J. Trotts, Gerald E. Farin, "On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bézier Patches," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 3, pp. 215-227, July-September, 1997.
 
 
BibTex
x
 
@article{ 10.1109/2945.620489,
author = {Bernd Hamann and Issac J. Trotts and Gerald E. Farin},
title = {On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bézier Patches},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {3},
number = {3},
issn = {1077-2626},
year = {1997},
pages = {215-227},
doi = {http://doi.ieeecomputersociety.org/10.1109/2945.620489},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bézier Patches
IS - 3
SN - 1077-2626
SP215
EP227
EPD - 215-227
A1 - Bernd Hamann,
A1 - Issac J. Trotts,
A1 - Gerald E. Farin,
PY - 1997
KW - Approximation
KW - contour
KW - isosurface
KW - marching cubes
KW - rational Bézier curve
KW - rational Bézier surface
KW - triangular patch
KW - triangulation
KW - trilinear interpolation
KW - visualization.
VL - 3
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 

Abstract—Given a three-dimensional (3D) array of function values Fi, j,k on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation ${\cal T}$ approximating a contour (isosurface) F(x, y, z) = T. We describe the construction of a C0-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in ${\cal T}.$ We determine the Bézier 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.

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Index Terms:
Approximation, contour, isosurface, marching cubes, rational Bézier curve, rational Bézier surface, triangular patch, triangulation, trilinear interpolation, visualization.
Citation:
Bernd Hamann, Issac J. Trotts, Gerald E. Farin, "On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bézier Patches," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 3, pp. 215-227, July-Sept. 1997, doi:10.1109/2945.620489
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