Dual/Primal mesh optimization for polygonized implicit surfaces
17 Jun 2002-pp 171-178
TL;DR: A new method for improving polygonizations of implicit surfaces with sharp features is proposed, which outperforms approaches based on the mesh evolution paradigm in speed and accuracy.
Abstract: A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard marching cubes mesh Lorensen(in our experiments we use VTK marching cubes VTK). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that "double dual" mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.
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TL;DR: Variational version of self-organization algorithm based on Belyaev–Ohtake edge sharpener based on alignment of boundary cell normals becomes unstable when implicit function strongly deviates from the signed distance function is presented.
1 citations
Cites background or methods or result from "Dual/Primal mesh optimization for p..."
...Delaunay mesh for “cube minus ball” model from [15]: (a) initial guess, (b) intermediate mesh, (c) mesh after domain recovery, (d) mesh after optimization....
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...First results for model “cube with extracted ball” from [15] are presented....
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...Since precise model description was not available we created reconstruction which resembles model from [15]....
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...This sharpening force is not the same as in [15] due to the additional projection procedure....
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...Next model from [15] is the “twisted prism”....
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Book•
01 Jan 2004
TL;DR: This thesis focuses on the tightly-woven relationship between the simulation of a Lagrangian solid and its discretization, and introduces a mesh generation technique as well as a new method for simulating meshes and materials with changing topology.
Abstract: Numerical simulation complements both theory and experimentation as an important component of today's research. This thesis focuses on the tightly-woven relationship between the simulation of a Lagrangian solid and its discretization. We introduce a mesh generation technique as well as a new method for simulating meshes and materials with changing topology.
The tetrahedral mesh generation algorithm is designed for the Lagrangian simulation of deformable bodies. The algorithm's input is a level set. First a bounding box of the object is covered with a uniform lattice of subdivision-invariant tetrahedra. The level set is then used to guide a red green adaptive subdivision procedure that is based on both the local curvature and the proximity to the object boundary. The final topology is carefully chosen so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, this candidate mesh is compressed to match the object boundary. To maintain element quality during this compression phase we relax the positions of the nodes using finite elements, masses and springs, or an optimization procedure.
We also propose a virtual node algorithm that allows material to separate along arbitrary paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This results in elements that contain both some real material and empty regions. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material. This approach provides for the efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small time step restrictions since they are embedded in well shaped larger elements.
1 citations
Cites background from "Dual/Primal mesh optimization for p..."
...Ohtake and Belyaev advocated moving the triangle centroids to the zero isocontour instead of the nodes, and matching the triangle normals with the implicit surface normals [98]....
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01 Jan 2007
TL;DR: An overview of the state-of-the art in 3D emerging measurement technologies is provided and new approaches and methods for data fusion and digital processing of sampled 3D data are proposed.
Abstract: In recent years, globalization has begun to drive industries to operate in a highly competitive environment and to improve the time to market In order to deal with this challenge, rapid production methods have been developed and incorporated into many phases of the product life cycle Reverse Engineering (RE) technology enables fast design based on an existing physical object, and on-line 3D noncontact inspection significantly reduces manufacturing time This paper provides an overview of the state-of-the art in 3D emerging measurement technologies Moreover, it proposes new approaches and methods for data fusion and digital processing of sampled 3D data
1 citations
Patent•
02 Mar 2006
TL;DR: A boundary surface information creating method comprising an input step of inputting object boundary surfaces information (11) into a computer, a grid sampling step of determining cut points (13) at which a boundary surface cuts edges of a predetermined rectangular parallel piled grid (14) and a normal vector (15) of the boundary surface at the cut point and storing them as primary data (16) in a storage unit is presented in this article.
Abstract: A boundary surface information creating method comprising an input step of inputting object boundary surface information (11) into a computer, a grid sampling step of determining cut points (13) at which a boundary surface cuts edges of a predetermined rectangular parallel piled grid (12) and a normal vector (14) of the boundary surface at the cut point and storing them as primary data (15) in a storage unit, a D-polyhedron data creating step of creating D-polyhedron data (16) on a D-polyhedron composed of only triangles by connecting adjacent cut points through line segments and by sequentially defining triangles, and a V-polyhedron data creating step of creating V-polyhedron data (17) on a V-polyhedron defined by intersection of infinite planes which pass through the cut points and on which the normal vector conforms to the normal. One of the D-polyhedron data and the V-polyhedron data is created from the primary data (15) and the other is created as a dual of the one.
1 citations
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References
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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.
Abstract: We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
13,231 citations
11,285 citations
"Dual/Primal mesh optimization for p..." refers methods in this paper
...Similar to [10] we use the singular value decomposition [17] to find a minimum-norm least squares solution to (1)....
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03 Aug 1997
TL;DR: This work has developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models, and which also supports non-manifold surface models.
Abstract: Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface and object representations
3,564 citations