Journal Article10.1111/1467-8659.00196
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.
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Abstract: 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 While most previous work applied to bounded manifolds without singularities and without boundary (topological spheres) we broaden the scope of the methods to include surfaces with such features, in particular cusp points and surface self-intersections These aspects are not (yet) essential for computer graphics modelling with implicit surfaces but they naturally occur in simulations of interest in mathematical visualization In this paper we use the Kummer family of algebraic surfaces as an example
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Citations
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Barton T. Stander,John Hart +1 more
- 03 Aug 1997
TL;DR: The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
A Survey on Implicit Surface Polygonization
TL;DR: This article presents a survey of different techniques for fast visualization of implicit surfaces, focusing closely on polygonization methods, as they are the most suited to fast visualization.
77
Topology and arrangement computation of semi-algebraic planar curves
TL;DR: It is shown on examples that this algorithm is able to handle curves defined by high degree polynomials with large coefficients, to identify regions of interest and use the resulting structure for either efficient rendering of implicit curves, point localization or boolean operation computation.
71
Particle Systems for Efficient and Accurate High-Order Finite Element Visualization
TL;DR: This work presents a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions.
A programmable particle system framework for shape modeling
Wen Y. Su,John Hart +1 more
- 31 Jul 2005
TL;DR: A particle system programming framework consisting of behaviors, attributes and shaders that allows users to rapidly create, debug, and deploy particle systems for sensing and extracting specific surface information and displaying this information in an visually effective manner is designed.
30
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Hugues Hoppe,Tony DeRose,Tom Duchamp,John W. McDonald,Werner Stuetzle +4 more
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TL;DR: In this article, the authors present a method for solving the following problem: given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0 that fits the data well and has a small number of vertices.
Marching cubes: a high resolution 3D surface construction algorithm
William E. Lorensen,Harvey E. Cline +1 more
- 01 Jul 1998
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.
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Greg Turk
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TL;DR: This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a re-tiling of a surface that is faithful to both the geometry and the topology of the original surface.
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