Home About us Contact
|
Home About us Contact | ||
|
|
||
Linear Interpolation (linear + interpolation)
Selected AbstractsResampling Feature and Blend Regions in Polygonal Meshes for Surface Anti-AliasingCOMPUTER GRAPHICS FORUM, Issue 3 2001Mario Botsch Efficient surface reconstruction and reverse engineering techniques are usually based on a polygonal mesh representation of the geometry: the resulting models emerge from piecewise linear interpolation of a set of sample points. The quality of the reconstruction not only depends on the number and density of the sample points but also on their alignment to sharp and rounded features of the original geometry. Bad alignment can lead to severe alias artifacts. In this paper we present a sampling pattern for feature and blend regions which minimizes these alias errors. We show how to improve the quality of a given polygonal mesh model by resampling its feature and blend regions within an interactive framework. We further demonstrate sophisticated modeling operations that can be implemented based on this resampling technique. [source] Green's function interpolations for prestack imagingGEOPHYSICAL PROSPECTING, Issue 1 2000Manuela Mendes A new interpolation method is presented to estimate the Green's function values, taking into account the migration/inversion accuracy requirements and the trade-off between resolution and computing costs. The fundamental tool used for this technique is the Dix hyperbolic equation (DHE). The procedure, when applied to evaluate the Green's function for a real source position, uses the DHE to derive the root-mean-square velocity, vRMS, from the precomputed traveltimes for the nearest virtual sources, and by linear interpolation generates vRMS for the real source. Then, by applying the DHE again, the required traveltimes and geometrical spreading can be estimated. The inversion of synthetic data demonstrates that the new interpolation yields excellent results which give a better qualitative and quantitative resolution of the imaging sections, compared with those carried out by conventional linear interpolation. Furthermore, the application to synthetic and real data demonstrates the ability of the technique to interpolate Green's functions from widely spaced virtual sources. Thus the proposed interpolation, besides improving the imaging results, also reduces the overall CPU time and the hard disk space required, hence decreasing the computational effort of the imaging algorithms. [source] A uniform nodal strain tetrahedron with isochoric stabilizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009M. W. Gee Abstract A stabilized node-based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity. The element is based on linear interpolation of a classical displacement-based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior, especially in the regime of near-incompressibility where classical linear tetrahedral elements perform very poorly. This uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature. We present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on an isochoric,volumetric splitting of the stress tensor. We demonstrate that by stabilizing the isochoric energy contributions only, reintroduction of volumetric locking through the stabilization can be avoided. The isochoric,volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] Time accurate consistently stabilized mesh-free methods for convection dominated problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2003Antonio Huerta Abstract The behaviour of high-order time stepping methods combined with mesh-free methods is studied for the transient convection,diffusion equation. Particle methods, such as the element-free Galerkin (EFG) method, allow to easily increase the order of consistency and, thus, to formulate high-order schemes in space and time. Moreover, second derivatives of the EFG shape functions can be constructed with a low extra cost and are well defined, even for linear interpolation. Thus, consistent stabilization schemes can be considered without loss in the convergence rates. Copyright © 2003 John Wiley & Sons, Ltd. [source] A new modification of the immersed-boundary method for simulating flows with complex moving boundariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2006Jian Deng Abstract In this paper, a new immersed-boundary method for simulating flows over complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. The present method is based on a finite-difference approach on a staggered mesh together with a fractional-step method. It must be noted that the immersed boundary is generally not coincident with the position of the solution variables on the grid, therefore, an appropriate strategy is needed to construct a relationship between the curved boundary and the grid points nearby. Furthermore, a momentum forcing is added on the body boundaries and also inside the body to satisfy the no-slip boundary condition. The immersed boundary is represented by a series of interfacial markers, and the markers are also used as Lagrangian forcing points. A linear interpolation is then used to scale the Lagrangian forcing from the interfacial markers to the corresponding grid points nearby. This treatment of the immersed-boundary is used to simulate several problems, which have been validated with previous experimental results in the open literature, verifying the accuracy of the present method. Copyright © 2006 John Wiley & Sons, Ltd. [source] Inter-particle contact heat transfer model: an extension to soils at elevated temperaturesINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 2 2005W. H. Leong Abstract A simple ,inter-particle contact heat transfer' model for predicting effective thermal conductivity of soils at moderate temperatures (0,30°C) has been extended up to 90°C. The extended model accounts for latent heat transport by water vapour diffusion in soil air above the permanent wilting point; below that point, the soil thermal conductivity is approximated by linear interpolation without latent heat effect. By and large the best results are obtained when the latent heat is used only in the ,self consistent approximation' model with an overall root mean square error of 35% for all soils under consideration or 26% when excluding volcanic soils. This option can also be applied to moderate temperatures at which the enhanced heat transfer is negligibly small. Copyright © 2005 John Wiley & Sons, Ltd. [source] Comparison of 1- and 2-Marker Techniques for Calculating System Magnification Factor for Angiographic Measurement of Intracranial VesselsJOURNAL OF NEUROIMAGING, Issue 4 2005A. A. Divani PhD ABSTRACT Background and Purpose. Accurate estimation of an intracranial vessel size is crucial during a diagnostic or therapeutic angiography procedure. The use of 1 or 2 external markers of known size is previously proposed to manually estimate the magnification factor (MF) of an intracranial vessel. The authors evaluated the use of different external marker techniques commonly used during angiographic measurements. Methods. Forty-three intracranial vessels in 17 patients were measured using 1-and 2-marker techniques. To obtain the MF, 2 metallic markers were attached to the frontal-temporal regions. The MFs for the targeted vessels were obtained from the x-ray films by measuring the image sizes of the markers and their positions with respect to the target vessel. Results. Using a phantom, the errors resulted from (a) linear interpolation of MFs, (b) linear interpolation of inverse MFs, and (c) using the MFs of 1 marker, which were 1.23% to 2.23%, 0.8% to 1.55%, and 3.85% to 14.62%, respectively. A similar trend was observed for the measurement of cerebral arteries. Conclusion. The use of 2 markers can result in a more accurate estimation of the vessel size. The use of only 1 external marker can lead to substantial error based on the location of the target vessel. Optimizing image acquisition is also crucial for accurate determination of vessel size. [source] Importance of interpolation when constructing double-bootstrap confidence intervalsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000Peter Hall We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error. [source] | ||||||||||