Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Triangulation of scattered data in 3D space
Computer-Aided Design
Smooth piecewise quadric surfaces
Mathematical methods in computer aided geometric design
Boundary curves with quadric precision for a tangent continuous scattered data interpolant
Boundary curves with quadric precision for a tangent continuous scattered data interpolant
Computing optimal triangulations using simulated annealing
Selected papers of the international symposium on Free-form curves and free-form surfaces
Geometric concepts for geometric design
Geometric concepts for geometric design
A data reduction scheme for triangulated surfaces
Computer Aided Geometric Design
Curves with quadric boundary precision
Computer Aided Geometric Design
The NURBS book
ACM Transactions on Graphics (TOG)
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
Exploring scalar fields using critical isovalues
Proceedings of the conference on Visualization '02
Improving the Robustness and Accuracy of the Marching Cubes Algorithm for Isosurfacing
IEEE Transactions on Visualization and Computer Graphics
Tricubic Interpolation of Discrete Surfaces for Binary Volumes
IEEE Transactions on Visualization and Computer Graphics
Simple local interpolation of surfaces using normal vectors
Computer Aided Geometric Design
Simple local interpolation of surfaces using normal vectors
Computer Aided Geometric Design
On accuracy of marching isosurfacing methods
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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Given a three-dimensional (3D) array of function values Fi,驴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.