Medial zones: Formulation and applications

Eftekharian, Ata A.; Ilieş, Horea T.

doi:10.1016/j.cad.2011.12.003

Cited by 2 publications

(5 citation statements)

References 39 publications

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“…Aichholzer et al (1996) used for the first time the straight skeletons to represent simple polygons. Geometric skeletons like medial axis and straight skeleton have been used in many applications such as contour interpolation (Barequet et al, 2004), automatic shape synthesis, and path planning (Eftekharian & Ilieş, 2012). The reason for this investigation is that, like Rules 3 and 4 in our approach, it introduces new auxiliary points between original points to find the shortest possible spanning network between points, considering angular bisector of polygons.…”

Section: Skeletonmentioning

confidence: 99%

Layout synthesis of fluid channels using generative graph grammars

Hooshmand

Campbell

2014

AIEDAM

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This paper presents a new technique for shape and topology optimization of fluid channels using generative design synthesis methods. The proposed method uses the generative abilities of graph grammars with simulation and analysis power of conventional computational fluid dynamics methods. The graph grammar interpreter GraphSynth is used to carry out graph transformations, which define different topologies for a given multiple-inlet multiple-outlet problem. After evaluating and optimizing the generated graphs, they are first transformed into meaningful three-dimensional shapes. These solutions are then analyzed by a computational fluid dynamics solver for final evaluation of the possible solutions. The effectiveness of the proposed method is checked by solving a variety of available test problems and comparing them with those found in the literature. Furthermore, by solving very complex large-scale problems, the robustness and effectiveness of the method is tested. To extend the work, future research directions are presented.

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Section: Skeletonmentioning

confidence: 99%

Layout synthesis of fluid channels using generative graph grammars

Hooshmand

Campbell

2014

AIEDAM

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“…Steps 1 and 3 above are summarized in Section 2.2 (see also Eftekharian & Ilieş, 2009); step 2 is discussed in Section 2.3, whereas the medial zones are summarized in Section 3 and described in detail in Eftekharian and Ilieş (2010). Section 4 illustrates the usefulness of our approach for several domains that simulate highly dynamic, topologically evolving domains.…”

Section: Summary Of the Approachmentioning

confidence: 99%

“…Consequently, by adjusting the value of a and the "nearness" metric, one can "grow" or "shrink" these medial zones. The effect of changing a on the resulting medial zone is illustrated in Figure 8b and c, as detailed in Eftekharian and Ilieş (2010).…”

Section: Medial Zones As Thick Skeletonsmentioning

confidence: 99%

“…However, converting the resulting approximate distance function into an “exact” distance function for such domains requires the computation of additional halfspaces as discussed above, which can only be computed approximately in many situations. The alternative that we take in this paper is to compute distance functions to each face bounding the 3-D domain, and combine them with the R-disjunction as described in more detail in Eftekharian and Ilieş (2010).…”

Section: Problem Formulationmentioning

confidence: 99%

“…This can effectively alter the planned path to accommodate specific geometric constraints such as approaching a refueling station or a sightseeing location. Furthermore, we exploit the concept of a medial zone that we introduced in Eftekharian and Ilieş (2010) to control the subset of the environment in which the roadmaps are being computed, and we show that, for the same domain, the resulting roadmaps are shorter and smoother than those obtained based solely on skeletons.…”

Section: Introductionmentioning

confidence: 99%

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A family of skeletons for motion planning and geometric reasoning applications

Eftekharian

Ilieş

2011

AIEDAM

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Link to this article: http://journals.cambridge.org/abstract_S0890060411000229How to cite this article: Ata A. Eftekharian and Horea T. Ilieş (2011). A family of skeletons for motion planning and geometric reasoning applications. AbstractThe task of planning a path between two spatial configurations of an artifact moving among obstacles is an important problem in practically all geometrically intensive applications. Despite the ubiquity of the problem, the existing approaches make specific limiting assumptions about the geometry and mobility of the obstacles, or those of the environment in which the motion of the artifact takes place. We present a strategy to construct a family of paths, or roadmaps, for two-and threedimensional solids moving in an evolving environment that can undergo drastic topological changes. Our approach is based on a potent paradigm for constructing geometric skeletons that relies on constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations. We describe a family of skeletons that have the same homotopy as that of the environment and contains the medial axis as a special case. Of importance, our skeletons can be designed so that they are "attracted to" or "repulsed by" prescribed spatial sites of the environment. Moreover, the R-function formulation suggests the new concept of a medial zone, which can be thought of as a "thick" skeleton with significant applications for motion planning and other geometric reasoning applications. Our approach can handle problems in which the environment is not fully known a priori, and intrinsically supports local and parallel skeleton computations for domains with rigid or evolving boundaries. Furthermore, our path planning algorithm can be implemented in any commercial geometric kernel, and has attractive computational properties. The capability of the proposed technique are explored through several examples designed to simulate highly dynamic environments.

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Medial zones: Formulation and applications

Cited by 2 publications

References 39 publications

Layout synthesis of fluid channels using generative graph grammars

Layout synthesis of fluid channels using generative graph grammars

A family of skeletons for motion planning and geometric reasoning applications

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