Physically based morphing of point‐sampled surfaces

Bao, Yunfan; Guo, Xiaohu; Qin, Hong

doi:10.1002/cav.100

Cited by 17 publications

(10 citation statements)

References 24 publications

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“…This method can provide very uniform results even if the source and target meshes are quite different, but it requires the solution of a nonlinear equation and again, it is not easy to create consistent tetrahedral meshes in 3D. Bao et al [31] also used a similar idea for point cloud morphing. Although many morphing methods use different algorithms, they are typically guided by the same physical principle -that of keeping the shape as rigid as possible as it changes.…”

Section: Related Workmentioning

confidence: 97%

As-Rigid-As-Possible Surface Morphing

Liu

Yan

Martin

2011

J. Comput. Sci. Technol.

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This paper presents a new morphing method based on the "as-rigid-as-possible" approach. Unlike the original as-rigid-as-possible method, we avoid the need to construct a consistent tetrahedral mesh, but instead require a consistent triangle surface mesh and from it create a tetrahedron for each surface triangle. Our new approach has several significant advantages. It is much easier to create a consistent triangle mesh than to create a consistent tetrahedral mesh. Secondly, the equations arising from our approach can be solved much more efficiently than the corresponding equations for a tetrahedral mesh. Finally, by incorporating the translation vector in the energy functional controlling interpolation, our new method does not need the user to arbitrarily fix any vertex to obtain a solution, allowing artists automatic control of interpolated mesh positions.

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Section: Related Workmentioning

confidence: 97%

As-Rigid-As-Possible Surface Morphing

Liu

Yan

Martin

2011

J. Comput. Sci. Technol.

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“…Chao et al [CPSS10] make use of the distance between the differential of a deformation and the rotation group to establish a geometric model for elasticity. [BGQ05] focuses on finding an ideal transformation via physics-based energy optimization. [BGQ05] focuses on finding an ideal transformation via physics-based energy optimization.…”

Section: Related Workmentioning

confidence: 99%

Planar Shape Interpolation Based On Teichmüller Mapping

Nian

Chen

2016

Computer Graphics Forum

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0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 t = 0 t = 0.333 t = 0.666 t = 1 Figure 1: Interpolation between a horse and a dinosaur. From left to right: source (t = 0), intermediate shapes (t = 0.333 and t = 0.666),target (t = 1), and the conformal distortion graph which depicts the normalized conformal distortion for 1000 most distorted triangles along the time variable t. As it can be seen from the texture image that circles in the source shape gradually become ellipses in the intermediate shapes, and that the conformal distortion of the map is almost linear with respect to t. Abstract Shape interpolation is a classical problem in computer graphics and has been widely investigated inthe past two decades. Ideal shape interpolation should be natural and smooth which have good properties such as affine and conformal reproduction, bounded distortion, no fold-overs, etc. In this paper, we present a new approach for planar shape interpolation based on Teichmüller maps -a special type of maps in the class of quasi-conformal maps. The algorithm consists of two steps. In the first step, a Teichmüller map is computed from the source shape to the target shape, and then the Beltrami coefficient is interpolated such that the conformal distortion is linear with respect to the time variable. In the second step, the intermediate shape is reconstructed by solving the Beltrami equation locally over each triangle and then stitching the mapped triangles by conformal transformations. The new approach preserves all the good properties mentioned above and produces more natural and more uniform intermediate shapes than the start-of-the-art methods. Especially, the conformal distortion changes linearly with respect to the time variable. Experiment results show that our method can produce appealing results regardless of interpolating between the same or different objects.interpolation which includes the interpolation of the interior of the domain. In this paper, we only deal with shape blending of 2D domains. Figure 1 illustrates an example.Given a source shape and a target shape, the ultimate goal of shape blending is to generate a sequence of intermediate shapes with some good properties, such as intersection free (no foldovers), bounded distortion, affine reproduction and smoothness. Different methods differ by the quantities they choose to interpolate. However, most methods can't satisfy all the above properties, especially bounded distortion property and intersection free. Recent-

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“…The approach solves the time dependant implicit function which minimizes the supremum of the gradient during the morph. Bao et al [31] presented a morphing process between two homeomorphic point-set surfaces by optimizing an energy function. Among boundary based approaches, Sun et al [32] proposed to interpolate polyhedral models using intrinsic shape parameters, such as dihedral angles and edge lengths.…”

Section: D Metamorphosis Of Implicit Surfacesmentioning

confidence: 99%

Metamorphosis of Periodic Surface Models

Cheng

Wang

2009

Volume 5: 35th Design Automation Conference, Parts a and B

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A phase transition is a geometric and topological transformation process of materials from one phase to another, each of which has a unique and homogeneous physical property. Providing an initial guess of transition path for further physical simulation studies is highly desirable in materials design. In this paper, we present a metamorphosis scheme for periodic surface (PS) models by interpolation in the PS parameter space. The proposed approach creates multiple potential transition paths for further selection based on three smoothness criteria. The goal is to search for a smooth transformation in phase transition analysis.

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Physically based morphing of point‐sampled surfaces

Cited by 17 publications

References 24 publications

As-Rigid-As-Possible Surface Morphing

As-Rigid-As-Possible Surface Morphing

Planar Shape Interpolation Based On Teichmüller Mapping

Metamorphosis of Periodic Surface Models

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