Efficient coding for 3D shape data considering normal vectors on the surface model

Abstract Recently, along with the improvements of geometry modeling methods using sketch-based interface, there have been a lot of developments in research about generating surface model from 3D curves. However, surfacing a 3D curve network remains an ambiguous problem due to the lack of geometric information. In this paper, we propose a new algorithm for estimating the normal vectors of the 3D curves which accord closely with user intent. Bending energy is defined by utilizing RMF(Rotation-Minimizing Frame) of 3D curve, and we estimated this minimal energy frame as the one that accords design intent. The proposed algorithm is demonstrated with surface model creation of various curve networks. The algorithm of estimating geometric information in 3D curves which is proposed in this paper can be utilized to extract new information in the sketch-based modeling process. Also, a new framework of 3D modeling can be expected through the fusion between curve network and surface creating algorithm.

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Tensorial Minkowski functionals of triply periodic minimal surfaces

Interface Focus ◽

10.1098/rsfs.2012.0007 ◽

2012 ◽

Vol 2 (5) ◽

pp. 623-633 ◽

Cited By ~ 11

Author(s):

Walter Mickel ◽

Gerd E. Schröder-Turk ◽

Klaus Mecke

Keyword(s):

Surface Model ◽

Minkowski Functionals ◽

Periodic Minimal Surface ◽

Triply Periodic ◽

Interfacial Surface ◽

Fundamental Understanding ◽

Triply Periodic Minimal Surface ◽

Weighted Integrals ◽

Normal Vectors

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.

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4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data

10.36227/techrxiv.13629260 ◽

2021 ◽

Author(s):

HAMID LAGA ◽

Marcel Padilla ◽

Ian H. Jermyn ◽

Sebastian Kurtek ◽

Mohammed Bennamoun ◽

...

Keyword(s):

Statistical Analysis ◽

Building Blocks ◽

Shape Space ◽

Spatiotemporal Variability ◽

3D Shape ◽

Execution Rates ◽

And Performance ◽

Body Shapes ◽

Spatiotemporal Registration ◽

Shape Data

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of subjects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered onto each others. Also, different deforming subjects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus, they need to be temporally aligned onto each others. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemmanian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories, or 1D curves, embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the L2 metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a Euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates, (2) the computation of geodesics between 4D surfaces, (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces, and (4) the synthesis of random 4D surfaces. We demonstrate the utility and performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

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4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data

10.36227/techrxiv.13629260.v1 ◽

2021 ◽

Author(s):

HAMID LAGA ◽

Marcel Padilla ◽

Ian H. Jermyn ◽

Sebastian Kurtek ◽

Mohammed Bennamoun ◽

...

Keyword(s):

Statistical Analysis ◽

Building Blocks ◽

Shape Space ◽

Spatiotemporal Variability ◽

3D Shape ◽

Execution Rates ◽

And Performance ◽

Body Shapes ◽

Spatiotemporal Registration ◽

Shape Data

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of subjects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered onto each others. Also, different deforming subjects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus, they need to be temporally aligned onto each others. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemmanian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories, or 1D curves, embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the L2 metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a Euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates, (2) the computation of geodesics between 4D surfaces, (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces, and (4) the synthesis of random 4D surfaces. We demonstrate the utility and performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

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Experimental Investigation of Behavior of Impinging Liquid Jet in a Shallow Pool by 3D-LIF

Volume 3: Student Paper Competition; Thermal-Hydraulics; Verification and Validation ◽

10.1115/icone2020-16233 ◽

2020 ◽

Author(s):

Sota Yamamura ◽

Fumihito Kimura ◽

Hiroyuki Yoshida ◽

Akiko Kaneko ◽

Yutaka Abe

Keyword(s):

Liquid Film ◽

3D Visualization ◽

Liquid Jet ◽

Water Pool ◽

Molten Material ◽

3D Shape ◽

The Core ◽

Severe Accidents ◽

Jet Velocity ◽

Shape Data

Abstract In some scenarios of severe accidents, the core materials melt and fall into a water pool in the lower plenum as a jet. The molten material jet is broken up, and heat transfer between molten material and coolant occurs. The aim of this study is to clarify the behavior of liquid jet falling into a shallow pool. In a previous study, it is clarified that, in a shallow pool, the jet spread radially after bottoming, and the atomization occurs with high flow velocity in a shallow pool. the detail of atomization and the spreading of the jet cannot be measured by the limitation of a 2D visualization method. In this study, a 3D-LIF method is used to obtain the detail 3D shape data of the jet. The 3D visualization of the jet is conducted. Using 3D shape data, the liquid film and the atomized droplet are measured. The initial jet velocity is selected as a parameter. As a result, following knowledge is obtained. The thickness of liquid film increases suddenly, and the radius of thin liquid flow increases with the increase of the initial jet velocity. The number of atomized droplets increases with the increase of the initial jet velocity. However, the size of the droplets are not influenced by the initial jet velocity.

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