Dual Marching Tetrahedra: Contouring in the Tetrahedronal Environment

Nielson, Gregory M.

doi:10.1007/978-3-540-89639-5_18

Cited by 11 publications

(7 citation statements)

References 17 publications

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“…Given a consistent set of lookup tables defined on the vertex categories, our framework should work equally well for multiresolution non-manifold meshes [37], multi-material interface reconstruction [10], [38] or dual contouring on the tetrahedra or duets within each diamond [39]. We intend to explore these possibilities in our future work.…”

Section: Discussionmentioning

confidence: 99%

Isodiamond Hierarchies: An Efficient Multiresolution Representation for Isosurfaces and Interval Volumes

Weiss

Floriani

2010

IEEE Trans. Visual. Comput. Graphics

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Abstract-Efficient multiresolution representations for isosurfaces and interval volumes are becoming increasingly important as the gap between volume data sizes and processing speed continues to widen. Our multiresolution scalar field model is a hierarchy of tetrahedral clusters generated by longest edge bisection, that we call a hierarchy of diamonds. We propose two multiresolution models for representing isosurfaces, or interval volumes, extracted from a hierarchy of diamonds which exploit its regular structure. These models are defined by subsets of diamonds in the hierarchy, that we call isodiamonds, which are enhanced with geometric and topological information for encoding the relation between the isosurface, or interval volume, and the diamond itself. The first multiresolution model, called a relevant isodiamond hierarchy, encodes the isodiamonds intersected by the isosurface, or interval volume, as well as their non-intersected ancestors, while the second model, called a minimal isodiamond hierarchy, encodes only the intersected isodiamonds. Since both models operate directly on the extracted isosurface or interval volume, they require significantly less memory and support faster selective refinement queries than the original multiresolution scalar field, but do not support dynamic isovalue modifications. Moreover, since a minimal isodiamond hierarchy only encodes intersected isodiamonds, its extracted meshes require significantly less memory than those extracted from a relevant isodiamond hierarchy. We demonstrate the compactness of isodiamond hierarchies by comparing them to an indexed representation of the mesh at full resolution.

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Section: Discussionmentioning

confidence: 99%

Isodiamond Hierarchies: An Efficient Multiresolution Representation for Isosurfaces and Interval Volumes

Weiss

Floriani

2010

IEEE Trans. Visual. Comput. Graphics

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“…The level set geometries are obtained by contouring these discrete function representations, as done for computed tomography data reconstruction, by a classical contouring method ( e.g. the marching cube [ 56,57 ], the dual contouring [ 58,59 ] ). Φ i denotes a closed surface representing the boundary of an inclusion i, member of a set I gathering all inclusions of a packing ( represented by white dashed line on figure 1a ).…”

Section: Notations and Definitionsmentioning

confidence: 99%

An advanced approach for the generation of complex cellular material representative volume elements using distance fields and level sets

2015

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A general and widely tunable method for the generation of Representative Volume Elements ( RVEs ) for cellular materials based on distance and level set functions is presented. The approach is based on random tessellations constructed from random inclusion packings. A general methodology to obtain arbitraryshaped tessellations to produce disordered foams is presented and illustrated. These tessellations can degenerate either in classical Voronoï tessellations potentially additively weighted depending on properties of the initial inclusion packing used, or in Laguerre tessellations through a simple modification of the formulation. A versatile approach to control the particular morphology of the obtained foam is introduced. Specific local features such as concave triangular Plateau borders and non-constant thickness heterogeneous coatings can be built from the tessellation in a straightforward way and are tuned by a small set of parameters with a clear morphological interpretation.

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“…Marching Tetrahedra (MT) [DK91] also removes topological ambiguities by uniformly partitioning space with tetrahedra rather than cubes, which has the additional benefit of using a smaller table of sign configurations than MC. Semi‐regular grids of tetrahedra have also been used to find surfaces for data where each sample is either inside, outside, or unknown [Nie08, NL09].…”

Section: Related Workmentioning

confidence: 99%