Fully Dynamic Constrained Delaunay Triangulations

Kallmann, Marcelo; Bieri, Hanspeter; Thalmann, Daniel

doi:10.1007/978-3-662-07443-5_15

Cited by 51 publications

(41 citation statements)

References 23 publications

(33 reference statements)

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“…This can include performing right angle rectification, line collinearity adjustment, snapping of dangles from shortening, and removal of overhanging dangles. The second step is to construct a Triangulated Irregular Network (TIN) using Constrained Delaunay Triangulation (CDT) (Chew, 1987;Kallmann et al, 2003), where the vertices of structural lines are adopted as points and the structural lines themselves are used for constraining the generated TINs. Two neighbouring TINs are iteratively merged by removing the shared edges that have no corresponding structural lines.…”

Section: Methodsmentioning

confidence: 99%

“…The generated TINs cannot intersect or cross over the structural lines. The endpoints of the structural lines act as points for constructing TINs on the 2D horizontal plane but are constrained by the structural lines themselves using Constrained Delaunay Triangulation (Chew, 1987;Kallmann et al, 2003) to avoid triangles crossing the structural lines. …”

Section: Constrained Delaunay Triangulationmentioning

confidence: 99%

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A Line-Based 3d Roof Model Reconstruction Algorithm: Tin-Merging and Reshaping (Tmr)

Rau

2012

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Three-dimensional building model is one of the major components of a cyber-city and is vital for the realization of 3D GIS applications. In the last decade, the airborne laser scanning (ALS) data is widely used for 3D building model reconstruction and object extraction. Instead, based on 3D roof structural lines, this paper presents a novel algorithm for automatic roof models reconstruction. A line-based roof model reconstruction algorithm, called TIN-Merging and Reshaping (TMR), is proposed. The roof structural line, such as edges, eaves and ridges, can be measured manually from aerial stereo-pair, derived by feature line matching or inferred from ALS data. The originality of the TMR algorithm for 3D roof modelling is to perform geometric analysis and topology reconstruction among those unstructured lines and then reshapes the roof-type using elevation information from the 3D structural lines. For topology reconstruction, a line constrained Delaunay Triangulation algorithm is adopted where the input structural lines act as constraint and their vertex act as input points. Thus, the constructed TINs will not across the structural lines. Later at the stage of Merging, the shared edge between two TINs will be check if the original structural line exists. If not, those two TINs will be merged into a polygon. Iterative checking and merging of any two neighboured TINs/Polygons will result in roof polygons on the horizontal plane. Finally, at the Reshaping stage any two structural lines with fixed height will be used to adjust a planar function for the whole roof polygon. In case ALS data exist, the Reshaping stage can be simplified by adjusting the point cloud within the roof polygon. The proposed scheme reduces the complexity of 3D roof modelling and makes the modelling process easier. Five test datasets provided by ISPRS WG III/4 located at downtown Toronto, Canada and Vaihingen, Germany are used for experiment. The test sites cover high rise buildings and residential area with diverse roof type. For performance evaluation, the adopted roof structural lines are manually measured from the provided stereo-pair. Experimental results indicate a nearly 100% success rate for topology reconstruction was achieved provided that the 3D structural lines can be enclosed as polygons. On the other hand, the success rate at the Reshaping stage is dependent on the complexity of the rooftop structure. Thus, a visual inspection and semi-automatic adjustment of roof-type is suggested and implemented to complete the roof modelling. The results demonstrate that the proposed scheme is robust and reliable with a high degree of completeness, correctness, and quality, even when a group of connected buildings with multiple layers and mixed roof types is processed.

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Section: Methodsmentioning

confidence: 99%

Section: Constrained Delaunay Triangulationmentioning

confidence: 99%

A Line-Based 3d Roof Model Reconstruction Algorithm: Tin-Merging and Reshaping (Tmr)

Rau

2012

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…Whenever a CDT is kept with O(n) cells, discrete search algorithms can compute channels (or corridors) containing a solution path in optimal times. The funnel algorithm [Chazelle 1982;Lee and Preparata 1984;Hershberger and Snoeyink 1994] has emerged as an efficient way to extract the shortest path inside a triangulated channel [Kallmann et al 2003;Demyen 2007;Geraerts 2010].…”

Section: Triangulationsmentioning

confidence: 99%

“…The approach described by Kallmann et al [2003] is followed where a same id is associated to all the constraints forming one polygonal obstacle. The insertion routine will process all constraints of an obstacle at once, and then return the id that is assigned to the obstacle.…”

Section: Dynamic Updatesmentioning

confidence: 99%

Dynamic and Robust Local Clearance Triangulations

Kallmann

2014

ACM Trans. Graph.

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The Local Clearance Triangulation (LCT) of polygonal obstacles is a cell decomposition designed for the efficient computation of locally shortest paths with clearance. This paper presents a revised definition of LCTs, new theoretical results and optimizations, and new algorithms introducing dynamic updates and robustness. Given an input obstacle set with n vertices, a theoretical analysis is proposed showing that LCTs generate a triangular decomposition of O(n) cells, guaranteeing that discrete search algorithms can compute paths in optimal times. In addition, several examples are presented indicating that the number of triangles is low in practice, close to 2n, and a new technique is described for reducing the number of triangles when the maximum query clearance is known in advance. Algorithms for repairing the local clearance property dynamically are also introduced, leading to efficient LCT updates for addressing dynamic changes in the obstacle set. Dynamic updates automatically handle intersecting and overlapping segments with guaranteed robustness, using techniques that combine one exact geometric predicate with adjustment of illegal floating point coordinates. The presented results demonstrate that LCTs are efficient and highly flexible for representing dynamic polygonal environments with clearance information.

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“…Kallmann et al 9 construct a NavMesh using the constrained Delaunay triangulation. 10 Tozour 11 describes a different approach using the 3-D triangle mesh of a scene to create convex polygons representing the navigable area. The polygons in the mesh can be triangles, quads, or arbitrary convex polygons.…”

Section: Background and Related Workmentioning

confidence: 99%

Adaptive grids: an image-based approach to generate navigation meshes

Akaydın

Güdükbay

2013

Opt. Eng.

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Abstract. We propose adaptive grids, an image-based approach for constructing navigation meshes, which are used for path planning. A cellular navigation mesh, called an adaptive grid, is constructed from a top-view range image of a three-dimensional urban model. A navigation graph can then be extracted from this adaptive grid for path planning. We compare our approach with two popular navigation mesh-generation approaches and obtain promising results in terms of path accuracy and memory cost.

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Fully Dynamic Constrained Delaunay Triangulations

Cited by 51 publications

References 23 publications

A Line-Based 3d Roof Model Reconstruction Algorithm: Tin-Merging and Reshaping (Tmr)

A Line-Based 3d Roof Model Reconstruction Algorithm: Tin-Merging and Reshaping (Tmr)

Dynamic and Robust Local Clearance Triangulations

Adaptive grids: an image-based approach to generate navigation meshes

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