Efficient Non-Parametric Surface Representations Using Active Sampling for Push Broom Laser Data

The μ-basis is a newly developed algebraic tool in curve and surface representations and it is used to analyze some essential geometric properties of curves and surfaces. However, the theoretical frame of μ-bases is still developing, especially of surfaces. We study the μ-basis of a rational surface V defined parametrically by P(t¯),t¯=(t1,t2) not being necessarily proper (or invertible). For applications using the μ-basis, an inversion formula for a given proper parametrization P(t¯) is obtained. In addition, the degree of the rational map ϕP associated with any P(t¯) is computed. If P(t¯) is improper, we give some partial results in finding a proper reparametrization of V. Finally, the implicitization formula is derived from P (not being necessarily proper). The discussions only need to compute the greatest common divisors and univariate resultants of polynomials constructed from the μ-basis. Examples are given to illustrate the computational processes of the presented results.

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A hierarchical extension to 3D non-parametric surface relief completion

Pattern Recognition ◽

10.1016/j.patcog.2011.04.021 ◽

2012 ◽

Vol 45 (1) ◽

pp. 172-185 ◽

Cited By ~ 6

Author(s):

Toby P. Breckon ◽

Robert B. Fisher

Keyword(s):

Surface Relief ◽

Parametric Surface ◽

Non Parametric

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Parametric Surfaced-Based Geological Reservoir Representation: A Computer Graphics Tool for Improved Decision Making in Immersive Environments

10.5194/egusphere-egu2020-9761 ◽

2020 ◽

Author(s):

Seyyedmohammad Moulaeifard ◽

Florian Wellmann

Keyword(s):

Decision Making ◽

Computer Graphics ◽

Subdivision Surfaces ◽

Control Points ◽

Parametric Surface ◽

Geological Modelling ◽

Spline Surfaces ◽

Geological Models ◽

Surface Representations ◽

Implicit Representations

Uncertainties are an inherent part of geological interpretation and immersive rendering has the potential to play a key role in gaining better insights. However, most 3D geological models have a limited possibility of manual, fast and smooth modification in order to make better decisions and interpretations. Here we present examples of parametric surface representations which use control points as a possibility to bring interactivity to geological modelling in immersive frameworks.In fact, using 2D surfaces of 3D solid objects is a typical representation of 3D models. Two of the major ways for surface representation in computer graphics are implicit representations and parametric surface representations. Parametric surface representations, unlike implicit representations, are based on control points. Manipulating these control points makes it easy and intuitive to modify geological models smoothly and fast, with a potential to more interactive decision-making.We present two different examples of parametric surface approaches; Spline Surfaces and Subdivision Surfaces. Spline surfaces, e.g. Bezier or NURBS surfaces, are a popular and common standard for CAD (Computer-Aided Design). Also, these surfaces are on the basis of parametric- based curves and a set of weighted control points. Subdivision Surfaces define smooth surfaces after a series of refinement which can be controlled by control points. Subdivision surfaces are not only a popular method for making free form models but also a common tool in animation, computer games and entertainment industry.Recently, research has been done based on using spline surfaces to model diverse geological structures and reservoirs. Similar to applications in computer graphics, using these methods in geological modelling can have specific considerations. Model refinement (e.g. adding new control points) and the requirement of many patches with geometrical constraints for the representation of complex geometries are some of the main difficulties of using spline surfaces. In this presentation, we will discuss several of these aspects and show two promising and controllable techniques for intuitive use of parametric surface-based representations in 3D geological and reservoir modelling.

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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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