Incremental Polygonization of Implicit Surfaces

Galin, Éric; Akkouche, Samir

doi:10.1006/gmod.1999.0514

Cited by 28 publications

(21 citation statements)

References 19 publications

(34 reference statements)

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“…At present, there are many research work done by researchers about polygonization of implicit surface [4][5][6][7][8], and most of them are about how to approximate implicit surface by triangle mesh with high quality and high performance.Surface tracking meethod is a family of polygonization techniques, e.g., Hartmann's algorithm [9], which also known as continuation method, it iteratively create a triangulation from a seed point by marching the surface. These approaches can achieve good results by generating meshes of evenly sized and quasi-equilateral triangles.…”

Section: Introductionmentioning

confidence: 99%

Parallel Polygonization of Implicit Surfaces

Yang

Chen

Pang

2010

2010 International Symposium on Intelligence Information Processing and Trusted Computing

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In this paper, we present an effective parallel algorithm for polygonizing implicit surfaces. The algorithm can produces triangulation approximation of implicit surface with adaptive size of triangles according to the local curvature of the surface. Our algorithm first divides an given implicit surface into eight parts by subdividing its bounding box. Then, the algorithm finds a seed point for each part on the surface and builds a seed mesh centered at the point. The seed mesh is the expanded by using the wave-front method and the surfacetracking approach. The local approximations of eight parts can be constructed in parallel way. Our algorithm finally merges the local meshes to a global approximation of the implicit surface. Resulted triangulations contain triangles with various sizes, i.e. smaller triangles for high curvature areas and larger triangles for flat areas, on the surface. Compared with the existing polygonization methods, our method has more fast speed and can guarantee quality of resulted meshes very well. Our method can be used in the real-time environment for rapid visualization of implicit surfaces.

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Section: Introductionmentioning

confidence: 99%

Parallel Polygonization of Implicit Surfaces

Yang

Chen

Pang

2010

2010 International Symposium on Intelligence Information Processing and Trusted Computing

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“…In both cases, field functions with compact supports are of primary interest since they localize the field function interactions when they are composed. This leads to more predictable and controllable shape behaviors and allows us to benefit from great accelerations based on the bounding box of their support [9,10,11]. This is why this work focuses on compact field functions.…”

Section: Introductionmentioning

confidence: 99%

Adequate inner bound for geometric modeling with compact field functions

Canezin¹,

Guennebaud²,

Barthe³

2013

Computers & Graphics

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Recent advances in implicit surface modeling now provide highly controllable blending effects. These effects rely on the field functions of R 3 → R in which the implicit surfaces are defined. In these fields, there is an outside part in which blending is defined and an inside part. The implicit surface is the interface between these two parts. As recent operators often focus on blending, most efforts have been made on the outer part of field functions and little attention has been paid on the inner part. Yet, the inner fields are important as soon as difference and intersection operators are used. This makes its quality as crucial as the quality of the outside.In this paper, we analyze these shortcomings, and deduce new constraints on field functions such that differences and intersections can be seamlessly applied without introducing discontinuities or field distortions. In particular, we show how to adapt state of the art gradient-based union and blending operators to our new constraints. Our approach enables a precise control of the shape of both the inner or outer field boundaries. We also introduce a new set of asymmetric operators tailored for the modeling of fine details while preserving the integrity of the resulting fields.

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“…The process repeats, until the minimum cell size is reached. An interactive system utilizing this method was described in [21]. The initial cell size restriction was successfully handled by octree growing.…”

Section: Existing Polygonization Methodsmentioning

confidence: 99%

“…The second task, is local updating the polygonal mesh at the interactive rate following either an interactive operation modifying a part of the shape (e.g., [20], [21]) or simulating the change of the eye focal length when shifting the gaze from the whole shape to a little part of it (e.g., [24]). We propose a few different solutions to these problems in our work.…”

Section: Problems Of Interactive Polygonizationmentioning

confidence: 99%

Interactive function-based artistic shape modeling

Levinski

Sourin

First International Symposium on Cyber Worlds, 2002. Proceedings.

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This paper addresses interactive function-based shape modeling where relatively small formulas are used rather than thousands of polygons. Interactive modification of the function model with concurrent visualization of the respective polygonal mesh lets us provide both the interactivity and any required level of detail leading to photo-realistic appearance of the resulting shapes. We have proposed a rendering method capable of handling local shape modifications with any desired precision. Also, we have proposed a few methods, which let us accelerate the final function evaluation-a common bottleneck for the function-based shape modeling. Finally, we describe applications of the interactive function-based shape modeling to photo-realistic virtual embossing and carving.

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Incremental Polygonization of Implicit Surfaces

Cited by 28 publications

References 19 publications

Parallel Polygonization of Implicit Surfaces

Parallel Polygonization of Implicit Surfaces

Adequate inner bound for geometric modeling with compact field functions

Interactive function-based artistic shape modeling

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