Journal Article10.1007/BF01901946
Cutting cubes—visualizing implicit surfaces by adaptive polygonization
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TL;DR: A method for visualizing implicit surfaces that makes as few assumptions as possible concerning the surface and representation of its defining function and some examples obtained are presented.
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Abstract: A method for visualizing implicit surfaces is discussed. This method makes as few assumptions as possible concerning the surface and representation of its defining function. The surface may contain singularities, for instance, because it has self-intersections or it is reducible. A userdefined part of space is filled by a set of cubes, cutting pieces (called facets) off the surface. The set of cubes is controlled by an octree converging to the surface. The set of resulting facets can be taken as a piecewise linear approximation, which is sufficiently close to the given surface with respect to criteria specified by the user. Finally, some examples obtained with this method are presented.
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Citations
Function representation in geometric modeling : concepts, implementation and applications
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A marching method for the triangulation of surfaces
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A unified approach for hierarchical adaptive tesselation of surfaces
TL;DR: A unified and general tesselation algorithm for parametric and implicit surfaces that produces a hierarchial mesh that is adapted to the surface geometry and has a multiresolution and progressive structure.
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Robust adaptive meshes for implicit surfaces
Afonso Paiva,Hélio Lopes,Thomas Lewiner,Luiz Henrique de Figueiredo +3 more
- 11 Dec 2006
TL;DR: This work introduces a robust algorithm for computing good polygonal approximations of implicit surfaces, where robustness entails recovering the exact topology of the implicit surface.
Interactive Visualization of Implicit Surfaces with Singularities
TL;DR: This paper presents work on two methods for interactive visualization of implicit surfaces: physically‐based sampling using particle systems and polygonization followed by physically-based mesh improvement which explicitly makes use of the surface‐defining equation.
References
Marching cubes: A high resolution 3D surface construction algorithm
William E. Lorensen,Harvey E. Cline +1 more
- 01 Aug 1987
TL;DR: In this paper, a divide-and-conquer approach is used to generate inter-slice connectivity, and then a case table is created to define triangle topology using linear interpolation.
The Quadtree and Related Hierarchical Data Structures
TL;DR: L'accentuation est mise sur la representation de donnees dans les applications de traitement d'images, d'infographie, les systemes d'informations geographiques and the robotique.
Geometric modeling using octree encoding
TL;DR: Efficient (linear time) algorithms have been developed for the Boolean operations, geometric operations,translation, scaling and rotation, N-dimensional interference detection, and display from any point in space with hidden surfaces removed.
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Data Structure for Soft Objects
TL;DR: A method to represent asoft object, or collection of objects, as a surface of constant value in a scalar field over three dimensions, and its uses in animation are discussed.
Polygonization of implicit surfaces
TL;DR: A numerical technique that approximates an implicit surface with a polygonal representation, so that the roots to the function need not be solved each time the surface is rendered.
567
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