Morphing stick figures using optimized compatible triangulations

Surazhsky, Vitaly; Gotsman, Craig

doi:10.1109/pccga.2001.962856

Cited by 10 publications

(12 citation statements)

References 17 publications

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“…Apart from this grand challenge our algorithms could be improved in a number of ways. First, ensuring that self-intersections do not occur during a morph can be accomplished by utilizing the algorithm of Surazhsky and Gotsman (2001b) to compute non-linear trajectories to morph points. Further investigation would be necessary to avoid intersections between different polylines in a network.…”

Section: Discussionmentioning

confidence: 99%

“…We give a heuristic method in Section 3.3.4 that may be implemented to avoid some typical cases of selfintersections, namely if a pair of corresponding segments would intersect; intersections may still occur in some cases between two different parts of the same polyline or between different polylines in a network. The method of Surazhsky and Gotsman (2001b), who give a solution to the trajectory problem, provides a workaround to this issue by computing more complex but therefore intersection-free trajectories given our solution to the correspondence problem. Since self-intersections were not an issue in the examples of our case study we refrained from including their method in our prototype implementation.…”

Section: Model and Algorithmmentioning

confidence: 99%

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Morphing polylines: A step towards continuous generalization

Nöllenburg¹,

Merrick

Wolff

et al. 2008

Computers, Environment and Urban Systems

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We study the problem of morphing between two polylines that represent linear geographical features like roads or rivers generalized at two different scales. This problem occurs frequently during continuous zooming in interactive maps. Situations in which generalization operators like typification and simplification replace, for example, a series of consecutive bends by fewer bends are not always handled well by traditional morphing algorithms. We attempt to cope with such cases by modeling the problem as an optimal correspondence problem between characteristic parts of each polyline. A dynamic programming algorithm is presented that solves the matching problem in O(nm) time, where n and m are the respective numbers of characteristic parts of the two polylines. In a case study we demonstrate that the algorithm yields good results when being applied to data from mountain roads, a river and a region boundary at various scales.

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Section: Discussionmentioning

confidence: 99%

Section: Model and Algorithmmentioning

confidence: 99%

Morphing polylines: A step towards continuous generalization

Nöllenburg¹,

Merrick

Wolff

et al. 2008

Computers, Environment and Urban Systems

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show abstract

“…For example, the triangulations in which simple polygons are embedded are constructed by compatibly triangulating the interior of the polygons and an annular region in the exterior of the polygon between the polygon boundary and a fixed convex enclosure. See Surazhsky and Gotsman 2001] for more details. These works have yet to be extended to morph planar figures with arbitrary (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…for image warping), then a fixed common convex boundary might be restrictive. Fortunately, using the methods of Surazhsky and Gotsman 2001], it is possible to overcome this by embedding the source and target triangulations with different boundaries, in two larger triangulations with a common fixed boundary. In practice this is done by compatibly triangulating the annulus between the original and new boundary, possibly introducing Steiner vertices.…”

Section: Discussionmentioning

confidence: 99%

Controllable morphing of compatible planar triangulations

Surazhsky¹,

Gotsman²

2001

ACM Trans. Graph.

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Two planar triangulations with a correspondence between the pair of vertex sets are compatible (isomorphic) if they are topologically equivalent. This work describes methods for morphing compatible planar triangulations with identical convex boundaries in a manner that guarantees compatibility throughout the morph. These methods are based on a fundamental representation of a planar triangulation as a matrix that unambiguously describes the triangulation. Morphing the triangulations corresponds to interpolations between these matrices.We show that this basic approach can be extended to obtain better control over the morph, resulting in valid morphs with various natural properties. Two schemes, which generate the linear trajectory morph if it is valid, or a morph with trajectories close to linear otherwise, are presented. An efficient method for verification of validity of the linear trajectory morph between two triangulations is proposed. We also demonstrate how to obtain a morph with a natural evolution of triangle areas and how to find a smooth morph through a given intermediate triangulation.

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“…14 These coordinates reflect the shapes of triangles in a way similar to coordinates 17,18,19,16 produce triangulations that may have long, skinny and close to degenerate triangles together with many additional (Steiner ) vertices. Moreover, the resulting compatible triangulations must usually be refined in order to create more natural morphing sequences.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Morphing of Compatible Triangulations

Surazhsky

Gotsman

2003

Int. J. Shape Model.

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Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentric coordinates representation of planar triangulations, and thus, guarantees compatibility of all intermediate triangulations. The intrinsic properties are preserved by interpolating angles and edge lengths components of mean value barycentric coordinates, rather than interpolating the barycentric coordinates themselves. As a result, the method generates a natural-looking and guaranteed intersection-free morphing sequence.

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Morphing stick figures using optimized compatible triangulations

Abstract: Abstract

Cited by 10 publications

References 17 publications

Morphing polylines: A step towards continuous generalization

Morphing polylines: A step towards continuous generalization

Controllable morphing of compatible planar triangulations

Intrinsic Morphing of Compatible Triangulations

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