Volumetric Rendering on Wavelet-Based Adaptive Grid
Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analys...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/7/7/245 |
| _version_ | 1827597200833642496 |
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| author | Alexei V. Vezolainen Gordon Erlebacher Oleg V. Vasilyev David A. Yuen |
| author_facet | Alexei V. Vezolainen Gordon Erlebacher Oleg V. Vasilyev David A. Yuen |
| author_sort | Alexei V. Vezolainen |
| collection | DOAJ |
| description | Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes. |
| first_indexed | 2024-03-09T03:26:06Z |
| format | Article |
| id | doaj.art-15a756d890924701829fe281b2886d56 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T03:26:06Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-15a756d890924701829fe281b2886d562023-12-03T15:02:15ZengMDPI AGFluids2311-55212022-07-017724510.3390/fluids7070245Volumetric Rendering on Wavelet-Based Adaptive GridAlexei V. Vezolainen0Gordon Erlebacher1Oleg V. Vasilyev2David A. Yuen3NPO Geoved LLC, 196644 Saint Petersburg, RussiaDepartment of Scientific Computing, Florida State University, Tallahassee, FL 32306, USAKeldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047 Moscow, RussiaDepartment of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USANumerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.https://www.mdpi.com/2311-5521/7/7/245adaptive meshvolumetric renderingvolume renderingwavelet compressionscientific visualization |
| spellingShingle | Alexei V. Vezolainen Gordon Erlebacher Oleg V. Vasilyev David A. Yuen Volumetric Rendering on Wavelet-Based Adaptive Grid Fluids adaptive mesh volumetric rendering volume rendering wavelet compression scientific visualization |
| title | Volumetric Rendering on Wavelet-Based Adaptive Grid |
| title_full | Volumetric Rendering on Wavelet-Based Adaptive Grid |
| title_fullStr | Volumetric Rendering on Wavelet-Based Adaptive Grid |
| title_full_unstemmed | Volumetric Rendering on Wavelet-Based Adaptive Grid |
| title_short | Volumetric Rendering on Wavelet-Based Adaptive Grid |
| title_sort | volumetric rendering on wavelet based adaptive grid |
| topic | adaptive mesh volumetric rendering volume rendering wavelet compression scientific visualization |
| url | https://www.mdpi.com/2311-5521/7/7/245 |
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