Refolding planar polygons

Iben, Hayley N.; O’Brien, James F.; Demaine, Erik D.

doi:10.1145/1186223.1186341

Cited by 5 publications

(7 citation statements)

References 6 publications

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“…Connelly et al [2003] proved that a simple polygon with fixed edge lengths can be morphed from one configuration to another preserving edge lengths and remaining simple. A stronger result shows that it is possible to morph between any two polygons, preserving planarity and with edge lengths changing monotonically [Iben et al 2009]. …”

Section: Maintaining Edge Directionsmentioning

confidence: 99%

Morphing orthogonal planar graph drawings

Biedl

Lubiw

Petrick

et al. 2013

ACM Trans. Algorithms

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We give an algorithm to morph between two planar orthogonal drawings of a graph, preserving planarity and orthogonality. The morph uses a quadratic number of steps, where each step is a linear morph (a linear interpolation between two drawings). This is the first algorithm to provide planarity-preserving morphs with well-behaved complexity for a significant class of graph drawings. Our method is to morph until each edge is represented by a sequence of segments, with corresponding segments parallel in the two drawings. Then, in a result of independent interest, we morph such parallel planar orthogonal drawings, preserving edge directions and planarity.

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Section: Maintaining Edge Directionsmentioning

confidence: 99%

Morphing orthogonal planar graph drawings

Biedl

Lubiw

Petrick

et al. 2013

ACM Trans. Algorithms

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“…In [26], Connelly et al prove that there are no locked 2D polygonal linkages. Upon this discovery, Cantarella et al [27] propose an energydriven approach to unfold such linkages, and Iben et al [28] propose an extended approach to interpolate arbitrary polygonal linkage configurations. The research of linkage folding/unfolding greatly inspired our research.…”

Section: Linkage Unfolding In Computational Geometrymentioning

confidence: 99%

“…We employ the same strategy proposed in [28]. At every step, instead of changing both postures, we update the posture with the higher energy, P h , towards the other posture, P l .…”

Section: Leveraging Linear Interpolationmentioning

confidence: 99%

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An Energy-Driven Motion Planning Method for Two Distant Postures

Wang

Komura

2015

IEEE Trans. Visual. Comput. Graphics

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Abstract-In this paper, we present a local motion planning algorithm for character animation. We focus on motion planning between two distant postures where linear interpolation leads to penetrations. Our framework has two stages. The motion planning problem is first solved as a Boundary Value Problem (BVP) on an energy graph which encodes penetrations, motion smoothness and user control. Having established a mapping from the configuration space to the energy graph, a fast and robust local motion planning algorithm is introduced to solve the BVP to generate motions that could only previously be computed by global planning methods. In the second stage, a projection of the solution motion onto a constraint manifold is proposed for more user control. Our method can be integrated into current keyframing techniques. It also has potential applications in motion planning problems in robotics.

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“…For example, [GS01] achieve this by equivalently triangulating the source and target shapes, and extending the triangulation to a common convex domain. [IOD09] preform intersection free morphing by combining a non‐convex energy which prohibits intersection with a ‘user supplied’ energy which determines the properties of the morph. In contrast to intersection free morphing, a regular homotopy prohibits local intersections, but allows global intersections which may occur naturally in planar images ( e.g ., Figures , ).…”

Section: Previous Workmentioning

confidence: 99%

Homotopic Morphing of Planar Curves

Dym

Shtengel

Lipman

2015

Computer Graphics Forum

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This paper presents an algorithm for morphing between closed, planar piecewise‐C1 curves. The morph is guaranteed to be a regular homotopy, meaning that pinching will not occur in the intermediate curves. The algorithm is based on a novel convex characterization of the space of regular closed curves and a suitable symmetric length‐deviation energy. The intermediate curves constructed by the morphing algorithm are guaranteed to be regular due to the convexity and feasibility of the problem. We show that our method compares favorably with standard curve morphing techniques, and that these methods sometimes fail to produce a regular homotopy, and as a result produce an undesirable morph. We explore several applications and extensions of our approach, including morphing networks of curves with simple connectivity, morphing of curves with different turning numbers with minimal pinching, convex combination of several curves, and homotopic morphing of b‐spline curves via their control polygon.

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Refolding planar polygons

Cited by 5 publications

References 6 publications

Morphing orthogonal planar graph drawings

Morphing orthogonal planar graph drawings

An Energy-Driven Motion Planning Method for Two Distant Postures

Homotopic Morphing of Planar Curves

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