Meshless structural analyses of complex shape models using implicit surface representations

A novel technique for designing curves on surfaces is presented. The design specifications for this technique derive from other works on curvature continuous surface fairing. Briefly stated, the technique must provide a computationally efficient method for the design of surface curves that is applicable to a very general class of surface formulations. It must also provide means to define a smooth natural map relating two or more surface curves. The resulting technique is formulated as a geometric construction that maps a space curve onto a surface curve. It is designed to be coordinate independent and provides isoparametric maps for multiple surface curves. Generality of the formulation is attained by solving a tensorial differential equation formulated in terms of local differential properties of the surfaces. For an implicit surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This technique has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations.

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Coupling Explicit and Implicit Surface Representations for Generative 3D Modeling

Computer Vision – ECCV 2020 - Lecture Notes in Computer Science ◽

10.1007/978-3-030-58607-2_39 ◽

2020 ◽

pp. 667-683

Author(s):

Omid Poursaeed ◽

Matthew Fisher ◽

Noam Aigerman ◽

Vladimir G. Kim

Keyword(s):

3D Modeling ◽

Implicit Surface ◽

Surface Representations

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Radar Backscattering from Snowflakes: Comparison of Fractal, Aggregate, and Soft Spheroid Models

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-11-00004.1 ◽

2011 ◽

Vol 28 (11) ◽

pp. 1365-1372 ◽

Cited By ~ 65

Author(s):

Jani Tyynelä ◽

Jussi Leinonen ◽

Dmitri Moisseev ◽

Timo Nousiainen

Keyword(s):

Cross Sections ◽

Complex Shape ◽

Particle Sizes ◽

Shape Models ◽

Backscattering Cross Section ◽

W Band ◽

Mass Size ◽

Radar Backscattering ◽

Size Relation ◽

Good Agreement

Abstract The sensitivity of radar backscattering cross sections on different snowflake shapes is studied at C, Ku, Ka, and W bands. Snowflakes are simulated using two complex shape models, namely, fractal and aggregate, and a soft spheroid model. The models are tuned to emulate physical properties of real snowflakes, that is, the mass–size relation and aspect ratio. It is found that for particle sizes up to 5 mm and for frequencies from 5 to 35 GHz, there is a good agreement in the backscattering cross section for all models. For larger snowflakes at the Ka band, it is found that the spheroid model underestimates the backscattering cross sections by a factor of 10, and at W band by a factor of 50–100. Furthermore, there is a noticeable difference between spheroid and complex shape models in the linear depolarization ratios for all frequencies and particle sizes.

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On the Configuration of the Magnetic Field of β CrB

International Astronomical Union Colloquium ◽

10.1017/s0252921100080933 ◽

1976 ◽

Vol 32 ◽

pp. 613-622

Author(s):

I.A. Aslanov ◽

Yu.S. Rustamov

Keyword(s):

Magnetic Field ◽

Field Strength ◽

Radial Velocity ◽

Magnetic Field Strength ◽

Complex Shape ◽

Rotation Period ◽

Field Variation ◽

Magnetic Field Variation ◽

Secular Variations ◽

The Magnetic Field

SummaryMeasurements of the radial velocities and magnetic field strength of β CrB were carried out. It is shown that there is a variability with the rotation period different for various elements. The curve of the magnetic field variation measured from lines of 5 different elements: FeI, CrI, CrII, TiII, ScII and CaI has a complex shape specific for each element. This may be due to the presence of magnetic spots on the stellar surface. A comparison with the radial velocity curves suggests the presence of a least 4 spots of Ti and Cr coinciding with magnetic spots. A change of the magnetic field with optical depth is shown. The curve of the Heffvariation with the rotation period is given. A possibility of secular variations of the magnetic field is shown.

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Three-Dimensional Reconstruction of Native Androctonus Australis Hemocyanin

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100181014 ◽

1990 ◽

Vol 48 (1) ◽

pp. 452-453

Author(s):

Nicolas Boisset ◽

Jean-Christophe Taveau ◽

Jean Lamy ◽

Terence Wagenknecht ◽

Michael Radermacher ◽

...

Keyword(s):

Electron Microscopy ◽

Solid Body ◽

Body Surface ◽

Three Dimensional ◽

Staining Technique ◽

Three Dimensional Reconstruction ◽

Dimensional Reconstruction ◽

View Reconstruction ◽

Surface Representations ◽

Top View

Hemocyanin, the respiratory pigment of the scorpion Androctonus australis is composed of 24 kidney shaped subunits. A model of architecture supported by many indirect arguments has been deduced from electron microscopy (EM) and immuno-EM. To ascertain, the disposition of the subunits within the oligomer, the 24mer was submitted to three-dimensional reconstruction by the method of single-exposure random-conical tilt series.A sample of native hemocyanin, prepared with the double layer negative staining technique, was observed by transmisson electron microscopy under low-dose conditions. Six 3D-reconstructions were carried out indenpendently from top, side and 45°views. The results are composed of solid-body surface representations, and slices extracted from the reconstruction volume.The main two characters of the molecule previously reported by Van Heel and Frank, were constantly found in the solid-body surface representations. These features are the presence of two different faces called flip and flop and a rocking of the molecule around an axis passing through diagonnally opposed hexamers. Furthermore, in the solid-body surface of the top view reconstruction, the positions and orientations of the bridges connecting the half molecules were found in excellent agreement with those predicted by the model.

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