Intrinsic Morphing of Compatible Triangulations

Surazhsky, Vitaly; Gotsman, Craig

doi:10.1142/s0218654303000115

Cited by 43 publications

(23 citation statements)

References 17 publications

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“…The interpolation method is presented to improve the effect of boundary interpolation using rigid motion and compatible triangulation [23][24][25].…”

Section: Related Workmentioning

confidence: 99%

Morphing of Building Footprints Using a Turning Angle Function

Xie

2017

IJGI

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Abstract:We study the problem of morphing two polygons of building footprints at two different scales. This problem frequently occurs during the continuous zooming of interactive maps. The ground plan of a building footprint on a map has orthogonal characteristics, but traditional morphing methods cannot preserve these geographic characteristics at intermediate scales. We attempt to address this issue by presenting a turning angle function-based morphing model (TAFBM) that can generate polygons at an intermediate scale with an identical turning angle for each side. Thus, the orthogonal characteristics can be preserved during the entire interpolation. A case study demonstrates that the model yields good results when applied to data from a building map at various scales. During the continuous generalization, the orthogonal characteristics and their relationships with the spatial direction and topology are well preserved.

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“…The interpolation method is presented to improve the effect of boundary interpolation using rigid motion and compatible triangulation [23][24][25].…”

Section: Related Workmentioning

confidence: 99%

Morphing of Building Footprints Using a Turning Angle Function

Xie

2017

IJGI

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“…The approach of interpolating between intrinsic entities has further been employed by Surazshky and Gotsman [20]. They first compute compatible triangulations of the source and target polygons and then interpolate the mean value barycentric coordinates of the triangles by using a lengths and angle description.…”

Section: Multiresolution Morphingmentioning

confidence: 99%

“…Most morphing algorithms thus enforce manually the correspondence of a few selected points [3,16,10] or simply suppose that the problem is solved [20,18]. In [15] the vertex correspondance problem is solved using wavelets.…”

Section: Vertex Correspondencementioning

confidence: 99%

“…Morphing is also performed on elements describing the interior of a 2-D shape like triangles. Herein Floater and Gotsman [9] have used barycentric coordinates to morph compatible triangulations and Surazhsky and Gotsman [20] furthermore interpolate intrinsic components of these coordinates. Alexa et al [3] morph compatible triangulations by locally least-distorting maps.…”

Section: Introductionmentioning

confidence: 99%

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Multiresolution morphing for planar curves

et al. 2007

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We present a multiresolution morphing algorithm using "as-rigidas-possible" shape interpolation combined with an angle-length based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage that the details' orientation follows any deformation naturally. The multiresolution morphing algorithm consists of transforming separately the coarse and detail coefficients of the multiresolution decomposition. Thus all LoD (level of detail) applications like LoD display, compression, LoD editing etc. can be applied directly to all morphs without any extra computation. Furthermore, the algorithm can robustly morph between very large size polygons with many local details as illustrated in numerous figures. The intermediate morphs behave natural and least-distorting due to the particular intrinsic multiresolution representation.

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“…As the example in Figure 1 shows, it is not always possible to just add edges to G; sometimes additional vertices are necessary. The motivation for this work comes from the problem of morphing planar graphs, which has many applications [8,10,11,17,18] including computer animation. Imagine an animator who wishes to animate a scene in which a character's expression goes from neutral, to surprised, to happy (see Figure 2).…”

Section: Introductionmentioning

confidence: 99%

Compatible Connectivity Augmentation of Planar Disconnected Graphs

Aloupis

Barba

Carmi

et al. 2015

Discrete Comput Geom

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Abstract. Motivated by applications to graph morphing, we consider the following compatible connectivity-augmentation problem: We are given a labelled n-vertex planar graph, G, that has r ≥ 2 connected components, and k ≥ 2 isomorphic planar straight-line drawings, G 1 , . . . , G k , of G. We wish to augment G by adding vertices and edges to make it connected in such a way that these vertices and edges can be added to G 1 , . . . , G k as points and straight-line segments, respectively, to obtain k planar straight-line drawings isomorphic to the augmentation of G. We show that adding Θ(nr 1−1/k ) edges and vertices to G is always sufficient and sometimes necessary to achieve this goal. The upper bound holds for all r ∈ {2, . . . , n} and k ≥ 2 and is achievable by an algorithm whose running time is O(nr 1−1/k ) for k = O(1) and whose running time is O(kn 2 ) for general values of k. The lower bound holds for all r ∈ {2, . . . , n/4} and

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Intrinsic Morphing of Compatible Triangulations

Cited by 43 publications

References 17 publications

Morphing of Building Footprints Using a Turning Angle Function

Morphing of Building Footprints Using a Turning Angle Function

Multiresolution morphing for planar curves

Compatible Connectivity Augmentation of Planar Disconnected Graphs

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