Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

Stolte, Nilo; Kaufman, Arie

doi:10.1006/gmod.2001.0559

Cited by 18 publications

(12 citation statements)

References 32 publications

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“…One way around the problem is to locally refine the grid size. This is not new and is actually the way the digitization of implicit curves and surfaces have been done most of the time [1,2,[4][5][6][7][8][9]. Our aim is to explore such subdivision methods for surfaces in dimension n. …”

Section: Discussion Conclusion and Perspectivesmentioning

confidence: 99%

“…The question regarding implicit surfaces in the discrete space is a long standing problem that has been studied mainly because it allows the visualization of often (topologically) complicated surfaces [3,4]. Different rasterization algorithms for implicit curves and surfaces have been proposed [4][5][6][7][8][9]. Many of the rasterization methods dealing with implicit curves and surfaces are associated with some subdivision scheme in order to deal with all the singularities and topological inconsistencies that may appear at a given scale.…”

Section: Introductionmentioning

confidence: 99%

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Implicit Digital Surfaces in Arbitrary Dimensions

Toutant

Andrès

Largeteau-Skapin

et al. 2014

Advanced Information Systems Engineering

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Abstract. In this paper we introduce a notion of digital implicit surface in arbitrary dimensions. The digital implicit surface is the result of a morphology inspired digitization of an implicit surface {x ∈ R n : f (x) = 0} which is the boundary of a given closed subset ofUnder some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness, and can be analytically characterized.

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Section: Discussion Conclusion and Perspectivesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implicit Digital Surfaces in Arbitrary Dimensions

Toutant

Andrès

Largeteau-Skapin

et al. 2014

Advanced Information Systems Engineering

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show abstract

“…Interval methods were used in ray casting for parametric surfaces by Toth [2] and by Barth et al [3] and for implicit surfaces by Mitchell [4], by Duff [5], and by Stolte [6]. Affine arithmetic [7] was used to render implicit surfaces by Figueiredo and Stolfi [8] and by Cusatis Jr. et al [9].…”

Section: Related Workmentioning

confidence: 99%

Beam Casting Implicit Surfaces on the GPU with Interval Arithmetic

Ganacim

Figueiredo

Nehab

2011

2011 24th SIBGRAPI Conference on Graphics, Patterns and Images

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“…Even though voxelization plays a crucial role, methods that do not ensure robustness [19,20,21] cannot be used in our context. By chance, implicit surfaces can be voxelized robustly [22,14,13,23,24] and a huge variety of forms and shapes can be defined implicitly.…”

Section: Introductionmentioning

confidence: 99%

“…Robust voxelization of implicit surfaces is generally implemented using spatial recursive subdivision [22,14,23,24]. The methods are all conservative, though.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary 3D Resolution Discrete Ray Tracing of Implicit Surfaces

Stolte

2005

Discrete Geometry for Computer Imagery

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Abstract.A new approach to ray tracing implicit surfaces based on recursive space subdivision is presented in this paper. Interval arithmetic, already used to calculate intersections in ray tracing and ray casting (numerically or subdividing 1D or 2D spaces), is now used here to implement a ray tracing based on reliable rays traversals into a potentially infinite octree-like subdivided space, eliminating explicit intersections. Novel, robust and efficient algorithms for ray voxelization and BSP octant ordering are used to recursively traverse rays through the space. Implicit surfaces are robustly voxelized and hierarchically stored into an octree to a certain given level. During rendering, the subdivision based voxelization of surfaces and rays continues further down until a resolution near the discrete domain of the floating point numbers is acquired. To guarantee robustness of the ray voxelization, interval arithmetic with calculations performed under appropriate rounding modes in Pentium-4 x87 and SSE2 FPUs respectively is applied. The major advantage is that the traversal algorithm is guaranteed to find reliable intersections between the rays and the scene without any explicit intersection calculation, solving a known precision problem of the ray traversal in a previous approach, used here for comparison. The precision of the traversal can be arbitrarily increased within the limitation of the floating point representation.

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Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

Cited by 18 publications

References 32 publications

Implicit Digital Surfaces in Arbitrary Dimensions

Implicit Digital Surfaces in Arbitrary Dimensions

Beam Casting Implicit Surfaces on the GPU with Interval Arithmetic

Arbitrary 3D Resolution Discrete Ray Tracing of Implicit Surfaces

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