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Visualization Of Meshless Simulations Using Fourier Volume Rendering
"... Fourier volume rendering is a volume visualization technique previously applied to regular grid data. We adapt this technique to deal directly with meshless data, with the intended application of visualizing simulations which use meshless methods to solve the underlying equations of the simulation. ..."
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Fourier volume rendering is a volume visualization technique previously applied to regular grid data. We adapt this technique to deal directly with meshless data, with the intended application of visualizing simulations which use meshless methods to solve the underlying equations of the simulation. Because we consider a general class of meshless data, the technique is applicable to the data produced by many meshless methods such as Kansa’s method, symmetric collocation, and smoothed particle hydrodynamics. We discuss the technique’s implementation on graphics hardware, and demonstrate its usefulness in visualizing data produced by both astrophysical and fluid dynamics simulations. 1
2.2 Discrete Fourier Transform............................ 6
"... We present an introduction to spectral transformations on surfaces from a differential geometric perspective. We show that the Fourier series has an extension to smooth surfaces and that for triangulated surfaces, spectral transforms can be defined which approximate the Fourier coefficients of the u ..."
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We present an introduction to spectral transformations on surfaces from a differential geometric perspective. We show that the Fourier series has an extension to smooth surfaces and that for triangulated surfaces, spectral transforms can be defined which approximate the Fourier coefficients of the underlying smooth manifold. This construction, which is based on a discrete approximation to the differential Laplacian operator, is compared to transforms
Continuous Fourier Volume Rendering of Irregularly Sampled Data Using Anisotropic RBFs
, 2008
"... We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolat ..."
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We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric basis function (RBF) that may be anisotropically scaled. While in the frequency domain, we can apply low, band, and highpass filters and arbitrary magnification and minification of the dataset before performing an inverse 2D Fourier transform to obtain the Xray projection. Our algorithm is particularly amenable to implementation on commodity programmable graphics boards, and can interactively render Xrays for datasets on the order of tens of thousands of points. We describe the theoretical considerations to properly sample the frequency spectrum of anisotropic RBFs to avoid aliasing in the resulting Xray and present a practical method for datasets with high sampling requirements. A significant benefit of our algorithm is that it can be applied to anisotropic RBFs that have been fitted to data through optimization techniques, allowing the incorporation of advanced datasensitive constraints, such as smoothness, sharpness, and feature preservation.
An Investigation of Fourier Domain Fluid Simulation
, 2003
"... Motivated by the reduced rendering cost of the Fourier Volume Rendering method, we construct a NavierStokes fluid flow simulation that operates entirely in the frequency domain. We show results from a practical implementation and compare with Jos Stam's spatial domain and FFTbased simulations. We ..."
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Motivated by the reduced rendering cost of the Fourier Volume Rendering method, we construct a NavierStokes fluid flow simulation that operates entirely in the frequency domain. We show results from a practical implementation and compare with Jos Stam's spatial domain and FFTbased simulations. We break