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

Author

Hamann, Bernd ; Trotts, Issac J. ; Farin, Gerald E.

Author_Institution

Dept. of Comput. Sci., California Univ., Davis, CA, USA

Volume

3

Issue

3

fYear

1997

Firstpage

215

Lastpage

227

Abstract

Given a three dimensional (3D) array of function values F_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 C⁰ 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

Keywords

computational geometry; data visualisation; interpolation; piecewise polynomial techniques; surface fitting; Bezier control points; C⁰ continuous surface; Hessians; contour approximation; function values; marching cubes method; piecewise trilinear interpolant; rational quadratic surface patches; rectilinear grid; single rational quadratic surface patch; surface triangulation; three dimensional array; triangular rational quadratic Bezier patches; vertices; Computer graphics; Computer science; Data visualization; Grid computing; Indexing; Interpolation; Isosurfaces; Legged locomotion; Piecewise linear approximation; Surface cracks;

fLanguage

English

Journal_Title

Visualization and Computer Graphics, IEEE Transactions on

Publisher

ieee

ISSN

1077-2626

Type

jour

DOI

10.1109/2945.620489

Filename

620489