A Comparison of Algorithms for the Triangulation Refinement Problem

Rivara, María‐Cecilia; Inostroza, Patricio

doi:10.1007/978-1-4757-9805-0_7

Cited by 3 publications

(3 citation statements)

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“…The Real-time Optimally Adapting Meshes (ROAM) triangulation method presented in [13] is conceptually very close to [34]. However, it is strictly based on the notion of a triangle bin-tree hierarchy as shown in Figure 21, which is a special case of the longest side bisection triangle refinement method described in [51,52]. This method recursively refines triangles by splitting their longest edge at the base vertex (see also Figure 11).…”

Section: Triangle Bin-treesmentioning

confidence: 99%

“…The partitioning consists of replacing a triangular region σ with two triangular regions obtained by splitting σ at the midpoint of its longest edge [51,52]. To guarantee that a conforming mesh is always generated after a bisection, the two triangular regions sharing σ 's longest edge are split at the same time.…”

Section: Combining Regular and Irregular Triangulationsmentioning

confidence: 99%

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Survey of semi-regular multiresolution models for interactive terrain rendering

2007

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Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform.In this survey, we analyze multi-resolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accuracy.

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Section: Triangle Bin-treesmentioning

confidence: 99%

Section: Combining Regular and Irregular Triangulationsmentioning

confidence: 99%

Survey of semi-regular multiresolution models for interactive terrain rendering

2007

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“…Addressing this aw, Rivara 179,180 proposed the following recursive algorithm: bisect a triangle in need of re nement b y adding a diagonal from the opposite vertex to the midpoint of the longest edge, then re ne its neighbor the same way. Bisections may propagate for some way across the triangulation, but this algorithm|now called Rivara r e nement|always terminates, since each bisection splits a longer edge.…”

Section: Mesh Improvement Techniquesmentioning

confidence: 99%

Mesh Generation and Optimal Triangulation

Bern

Eppstein

1995

Lecture Notes Series on Computing

278

178

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We survey the computational geometry relevant to nite element mesh generation. We especially focus on optimal triangulations of geometric domains in two-and three-dimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices Steiner points. We brie y survey the heuristic algorithms used in some practical mesh generators.

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