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Overview of flow visualization
 The Visualization Handbook
, 2005
"... With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of flow visualization over the last two decades ..."
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Cited by 29 (14 self)
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With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of flow visualization over the last two decades, a number of challenges remain. Whilst the visualization of 2D flow has many good solutions, the visualization of 3D flow still poses many problems. Challenges such as domain coverage, speed of computation, and perception remain key directions for further research. Flow visualization with a focus on surfacebased techniques forms the basis of this literature survey, including surface construction techniques and visualization methods applied to surfaces. We detail our investigation into these algorithms with discussions of their applicability and their relative strengths and drawbacks. We review the most important challenges when considering such visualizations. The result is an uptodate overview of the current stateoftheart that highlights both solved and unsolved problems in this rapidly evolving branch of research.
Boundary Aligned Smooth 3D CrossFrame Field
"... Figure 1: Snapshots of the optimization procedure to construct a boundary aligned 3D crossframe field. The top row shows the internal streamlines. The next row contains another visualization with cubes spread by a parameterization along the current crossframe field and rotated by the current local ..."
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Cited by 11 (2 self)
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Figure 1: Snapshots of the optimization procedure to construct a boundary aligned 3D crossframe field. The top row shows the internal streamlines. The next row contains another visualization with cubes spread by a parameterization along the current crossframe field and rotated by the current local frame R(Φ). The corresponding number of iteration is shown at the bottom. In this paper, we present a method for constructing a 3D crossframe field, a 3D extension of the 2D crossframe field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface crossframe field (equivalent to a 4Way RotationalSymmetry vector field), symmetry for 3D crossframe fields cannot be formulated by simple oneparameter 2D rotations in the tangent planes. To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, we can formulate an efficient smoothness measure of the crossframe field. Through minimization of this measure under certain boundary conditions, we can construct a smooth 3D crossframe field that is aligned with the surface normal at the boundary. We visualize the resulting crossframe field through restrictions to the boundary surface, streamline tracing in the volume, and singularities. We also demonstrate the application of the 3D crossframe field to producing hexahedrondominant meshes for given volumes, and discuss its potential in highquality hexahedralization, much as its 2D counterpart has shown in quadrangulation.
Hexagonal global parameterization of arbitrary surfaces
 In: ACM SIGGRAPH ASIA 2010 Sketches
, 2010
"... Abstract—We introduce hexagonal global parameterization, a new type of surface parameterization in which parameter lines respect sixfold rotational symmetries (6RoSy). Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for tri ..."
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Abstract—We introduce hexagonal global parameterization, a new type of surface parameterization in which parameter lines respect sixfold rotational symmetries (6RoSy). Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for triangular remeshing. Our framework to construct a hexagonal parameterization, referred to as HEXCOVER, extends the QUADCOVER algorithm and formulates necessary conditions for hexagonal parameterization. We also provide an algorithm to automatically generate a 6RoSy field that respects directional and singularity features in the surface. We demonstrate the usefulness of our geometryaware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal remeshing. Index Terms—Surface parameterization, rotational symmetry, hexagonal global parameterization, triangular remeshing, pattern synthesis on surfaces, texture synthesis, geometry synthesis, regular patterns. 1
ImageSpace TextureBased OutputCoherent
"... Abstract—Imagespace Line Integral Convolution (LIC) is a popular scheme for visualizing surface vector fields due to its simplicity and high efficiency. To avoid inconsistencies or color blur during the user interactions, existing approaches employ surface parameterization or 3D volume texture sche ..."
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Cited by 4 (4 self)
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Abstract—Imagespace Line Integral Convolution (LIC) is a popular scheme for visualizing surface vector fields due to its simplicity and high efficiency. To avoid inconsistencies or color blur during the user interactions, existing approaches employ surface parameterization or 3D volume texture schemes. However, they often require expensive computation or memory cost, and cannot achieve consistent results in terms of both the granularity and color distribution on different scales. This paper introduces a novel imagespace surface flow visualization approach that preserves the coherence during user interactions. To make the noise texture under different viewpoints coherent, we propose to precompute a sequence of mipmap noise textures in a coarsetofine manner for consistent transition, and map the textures onto each triangle with randomly assigned and constant texture coordinates. Further, a standard imagespace LIC is performed to generate the flow texture. The proposed approach is simple and GPUfriendly, and can be easily combined with various texturebased flow visualization techniques. By leveraging viewpointdependent backward tracing and mipmap noise phase, our method can be incorporated with the Image Based Flow Visualization (IBFV) technique for coherent visualization of unsteady flows. We demonstrate consistent and highly efficient flow visualization on a variety of datasets.
H.: Outputcoherent imagespace lic for surface flow visualization
 IEEE PacificVIS
"... Imagespace line integral convolution (LIC) is a popular approach for visualizing surface vector fields due to its simplicity and high efficiency. To avoid inconsistencies or color blur during the user interactions in the imagespace approach, some methods use surface parameterization or 3D volume ..."
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Imagespace line integral convolution (LIC) is a popular approach for visualizing surface vector fields due to its simplicity and high efficiency. To avoid inconsistencies or color blur during the user interactions in the imagespace approach, some methods use surface parameterization or 3D volume texture for the effect of smooth transition, which often require expensive computational or memory cost. Furthermore, those methods cannot achieve consistent LIC results in both granularity and color distribution on different scales. This paper introduces a novel imagespace LIC for surface flows that preserves the texture coherence during user interactions. To make the noise textures under different viewpoints coherent, we propose a simple texture mapping technique that is local, robust and effective. Meanwhile, our approach precomputes a sequence of mipmap noise textures in a coarsetofine manner, leading to consistent transition when the model is zoomed. Prior to perform LIC in the image space, the mipmap noise textures are mapped onto each triangle with randomly assigned texture coordinates. Then, a standard imagespace LIC based on the projected vector fields is performed to generate the flow texture. The proposed approach is simple and very suitable for GPU acceleration. Our implementation demonstrates consistent and highly efficient LIC visualization on a variety of datasets.
“Flow Visualization ” Juxtaposed With “Visualization of Flow”: Synergistic Opportunities Between Two Communities
"... Visualization is often employed as part of the simulation science pipeline. It is the window through which scientists examine their data for deriving new science, and the lens used to view modeling and discretization interactions within their simulations. We advocate that, as a component of the simu ..."
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Visualization is often employed as part of the simulation science pipeline. It is the window through which scientists examine their data for deriving new science, and the lens used to view modeling and discretization interactions within their simulations. We advocate that, as a component of the simulation science pipeline, visualization itself must be explicitly considered as part of the Validation and Verification (V&V) process. But what does this mean in a research area that has two “disciplinary ” homes – “flow visualization” within the computer science / computational science visualization area and “visualization of flow ” within the aeronautics community. Are aeronautics practitioners merely making use of algorithms developed within the visualization community that have now become “standard ” through their incorporation into various visualization tools, or rather does one find both development of algorithms and their usage for studying fundamental and engineering fluid mechanics in both communities, with possibly different focus. By narrowing the distance between research and development, and use of visualization techniques, one is left with a fertile ground for insights, and for increasing the reliability of results through V&V. In this paper, we explore “flow visualization ” from the perspective of the visualization community and “visualization of flow ” from the perspective of the aeronautics community in an attempt to understand how both communities can interact synergistically to bring visualization into the simulation science pipeline. We provide a brief review of the stateoftheart in flow visualization from the perspective of both communities, discuss advances in research areas such as color maps/perception and uncertainty visualization about which the AIAA community should be aware, provide some observations from both perspectives on visualizations currently published in two of the communities ’ representative journals (IEEE TVCG and AIAA Journal), and then conclude by highlighting some areas of possible synergistic interaction that might benefit both communities.
An Operator Approach to Tangent Vector Field Processing
"... Figure 1: Using our framework various vector field design goals can be easily posed as linear constraints. Here, given three symmetry maps: rotational (S1), bilateral (S2) and front/back (S3), we can generate a symmetric vector field using only S1 ..."
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Figure 1: Using our framework various vector field design goals can be easily posed as linear constraints. Here, given three symmetry maps: rotational (S1), bilateral (S2) and front/back (S3), we can generate a symmetric vector field using only S1
Functional Fluids on Surfaces
"... Figure 1: Jet flow (left) and shear layer flow (right) on curved surfaces. Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an inc ..."
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Figure 1: Jet flow (left) and shear layer flow (right) on curved surfaces. Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its timevarying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step, we advance scalar vorticity along two consecutive, stationary velocity fields. This approach leads to a variational integrator in the space continuous setting. In addition, using this approach, the update rule amounts to manipulating functions on the surface using linear operators, which can be discretized efficiently using the recently introduced functional approach to vector fields. Combining these time and space discretizations leads to a conceptually and algorithmically simple approach, which is efficient, timereversible and conserves vorticity by construction. We further demonstrate that our method exhibits no numerical dissipation and is able to reproduce intricate phenomena such as vortex shedding from boundaries.