Polygonization of non-manifold implicit surfaces

Bloomenthal, Jules; Ferguson, Keith

doi:10.1145/218380.218462

Cited by 57 publications

(32 citation statements)

References 10 publications

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“…In some cases, see e.g. [9][10][11], they are created through a series of heuristic decisions that decide a plausible topology, making it unclear if the resulting meshes are guaranteed to be free of artefacts. In another approach, in [12] a subdivision algorithm is used together with trilinear interpolation that leads to a mesh guaranteed to be topologically consistent; however the subdivision comes at the price of generating very large lookup tables or a large number of tiny mesh elements.…”

Section: Related Workmentioning

confidence: 99%

An algorithm to mesh interconnected surfaces via the Voronoi interface

Saye

2013

Engineering with Computers

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Many scientific and engineering problems involve interconnected surfaces meeting at junctions. For example, understanding the dynamics of a soap bubble foam can require modelling the fluid mechanics of liquid inside an intricate network of thin-film membranes. If a mesh of these surfaces is needed, the use of standard meshing algorithms often leads to voids, overlapping elements, or other artefacts near the junctions. Here, we present an algorithm to generate high-quality triangulated meshes of a set of interconnected surfaces with high surface accuracy. By capitalising on mathematical aspects of a geometric construction known as the ''Voronoi interface'', the algorithm first creates a topologically consistent mesh automatically, without making heuristic or complex decisions about surface topology. In particular, elements that meet at a junction do so by sharing a common edge, leading to simplifications in finite element calculations. In the second stage of the algorithm, mesh quality is improved by applying a short sequence of force-based smoothing, projection, and edge-flipping steps. Efficiency is further enhanced by using a locally adaptive time stepping scheme that prevents inversion of mesh elements, and we also comment on how the algorithm can be parallelised. Results are shown using a variety of examples arising from multiphase curvature flow, geometrically defined objects, surface reconstruction from volumetric point clouds, and a simulation of the multiscale dynamics of a cluster of soap bubbles. In this last example, generating high-quality meshes of evolving interconnected surfaces is crucial in determining thin-film liquid dynamics via finite element methods.

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Section: Related Workmentioning

confidence: 99%

An algorithm to mesh interconnected surfaces via the Voronoi interface

Saye

2013

Engineering with Computers

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“…Our new representation can further encode loops and singular connections inside a cell. Bloomenthal and Ferguson [1] have addressed the non-manifold polygonization problem. Their method can't handle loops in cells.…”

Section: Definition Of Enhanced Cellsmentioning

confidence: 99%

“…The simplified isosurfaces preserve the topology of the isosurface in the finest resolution. Due to the space limitation, we omit the discussion here 1 .…”

Section: Introductionmentioning

confidence: 99%

Dual contouring with topology-preserving simplification using enhanced cell representation

Zhang

Hong

Kaufman

IEEE Visualization 2004

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Figure 1: Simplifying the zero-isosurface of a directed distance volume of 256 3 using our topology-preserving isosurface simplification algorithm. Although the cylinders and the box are very close to each other, they don't touch, and thus there are several disconnected surface components in this volume. Note that disconnected surface components are assigned different materials and are clustered independently. ABSTRACTWe present a fast, topology-preserving approach for isosurface simplification. The underlying concept behind our approach is to preserve the disconnected surface components in cells during isosurface simplification. We represent isosurface components in a novel representation, called enhanced cell, where each surface component in a cell is represented by a vertex and its connectivity information. A topology-preserving vertex clustering algorithm is applied to build a vertex octree. An enhanced dual contouring algorithm is applied to extract error-bounded multiresolution isosurfaces from the vertex octree while preserving the finest resolution isosurface topology. Cells containing multiple vertices are properly handled during contouring. Our approach demonstrates better results than existing octree-based simplification techniques.

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“…Based on the discussion, Bloomenthal et al [2] proposed a concrete method of polygonizing non-manifold implicit surfaces using multiple regionalization. Hege et al [?…”

Section: Representation Of Implicit Surfacesmentioning

confidence: 99%

“…Although many works [2,14,7, ?] have been done on generating a nonmanifold polygonal mesh from a volume, they are not suitable for real-time visualization since extracting parametric surfaces before rendering is required as a preprocessing step.…”

Section: Visualization Of Implicit Surfacesmentioning

confidence: 99%

Hardware-accelerated visualization of volume-sampled distance fields

Yamazaki¹,

Kase²,

Ikeuchi

2003 Shape Modeling International.

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We present a method of visualizing volume-sampled distance fields, taking advantage of hardware-acceleration of modern graphics hardware. Although conventional distance fields can represent only 2-manifold surfaces in a stable way, we have developed a technique of representing both manifold and non-manifold surfaces in a volume created by sampling a segmented distance field. The volumesampled distance fields can be visualized effectively with pre-integrated volume rendering by embedding the interpolating function as a lookup table called vertex generation diagram into graphics hardware. We developed a simple system for smoothly blending two surface models in the distance function domain, and confirmed that our proposed representation of surface models is applicable to existing methods of geometric processing using implicit representations. We also confirmed that proposed methods of deformation and visualization can be executed at sufficient quality and speed using commodity graphics hardware on a standard PC.

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Polygonization of non-manifold implicit surfaces

Cited by 57 publications

References 10 publications

An algorithm to mesh interconnected surfaces via the Voronoi interface

An algorithm to mesh interconnected surfaces via the Voronoi interface

Dual contouring with topology-preserving simplification using enhanced cell representation

Hardware-accelerated visualization of volume-sampled distance fields

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