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ABSTRACT: Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation, many of which are difficult or impossible to achieve via prior simulation-based methods.
IEEE transactions on visualization and computer graphics. 12/2011;
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ABSTRACT: Asymmetric tensor field visualization can provide important insight into fluid flows and solid deformations. Existing techniques for asymmetric tensor fields focus on the analysis, and simply use evenly-spaced hyperstreamlines on surfaces following eigenvectors and dual-eigenvectors in the tensor field. In this paper, we describe a hybrid visualization technique in which hyperstreamlines and elliptical glyphs are used in real and complex domains, respectively. This enables a more faithful representation of flow behaviors inside complex domains. In addition, we encode tensor magnitude, an important quantity in tensor field analysis, using the density of hyperstreamlines and sizes of glyphs. This allows colors to be used to encode other important tensor quantities. To facilitate quick visual exploration of the data from different viewpoints and at different resolutions, we employ an efficient image-space approach in which hyperstreamlines and glyphs are generated quickly in the image plane. The combination of these techniques leads to an efficient tensor field visualization system for domain scientists. We demonstrate the effectiveness of our visualization technique through applications to complex simulated engine fluid flow and earthquake deformation data. Feedback from domain expert scientists, who are also co-authors, is provided.
IEEE transactions on visualization and computer graphics. 12/2011; 17(12):1979-88.
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ABSTRACT: Morse decomposition provides a numerically stable topological representation of vector fields that is crucial for their rigorous interpretation. However, Morse decomposition is not unique, and its granularity directly impacts its computational cost. In this paper, we propose an automatic refinement scheme to construct the Morse Connection Graph (MCG) of a given vector field in a hierarchical fashion. Our framework allows a Morse set to be refined through a local update of the flow combinatorialization graph, as well as the connection regions between Morse sets. The computation is fast because the most expensive computation is concentrated on a small portion of the domain. Furthermore, the present work allows the generation of a topologically consistent hierarchy of MCGs, which cannot be obtained using a global method. The classification of the extracted Morse sets is a crucial step for the construction of the MCG, for which the Poincare´ index is inadequate. We make use of an upper bound for the Conley index, provided by the Betti numbers of an index pair for a translation along the flow, to classify the Morse sets. This upper bound is sufficiently accurate for Morse set classification and provides supportive information for the automatic refinement process. An improved visualization technique for MCG is developed to incorporate the Conley indices. Finally, we apply the proposed techniques to a number of synthetic and realworld simulation data to demonstrate their utility.
IEEE transactions on visualization and computer graphics. 06/2011; 18(5):767-82.
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ABSTRACT: We introduce hexagonal global parameterization, a new type of surface parameterization in which parameter lines respect sixfold rotational symmetries (6-RoSy). 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 6-RoSy field that respects directional and singularity features in the surface. We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal remeshing.
IEEE transactions on visualization and computer graphics. 06/2011; 18(6):865-78.
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ABSTRACT: In this paper, we introduce a new approach to computing a Morse decomposition of a vector field on a triangulated manifold surface. The basic idea is to convert the input vector field to a piecewise constant (PC) vector field, whose trajectories can be computed using simple geometric rules. To overcome the intrinsic difficulty in PC vector fields (in particular, discontinuity along mesh edges), we borrow results from the theory of differential inclusions. The input vector field and its PC variant have similar Morse decompositions. We introduce a robust and efficient algorithm to compute Morse decompositions of a PC vector field. Our approach provides subtriangle precision for Morse sets. In addition, we describe a Morse set classification framework which we use to color code the Morse sets in order to enhance the visualization. We demonstrate the benefits of our approach with three well-known simulation data sets, for which our method has produced Morse decompositions that are similar to or finer than those obtained using existing techniques, and is over an order of magnitude faster.
IEEE transactions on visualization and computer graphics. 05/2011; 18(6):938-51.
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ACM Trans. Graph. 01/2011; 30:141.
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ABSTRACT: Rotational symmetries have found uses in several computer graphics applications, such as global surface parameterization, geometry remeshing, texture and geometry synthesis, and non-photorealistic visualization of surfaces. The visualization of N-way rotational symmetry (N-RoSy) fields is a challenging problem due to the ambiguities in the N directions represented by an N-way symmetry. We provide an algorithm that allows faithful and interactive representation of N-RoSy fields in the plane and on surfaces, by adapting the well-known Line Integral Convolution (LIC) technique from vector and second-order tensor fields. Our algorithm captures the N directions associated with each point in a given field by decomposing the field into multiple different vector fields, generating LIC images of these fields, and then blending the results. To address the loss of contrast caused by the blending of images, we observe that the pixel values in LIC images closely approximate normally distributed random variables. This allows us to use concepts from probability theory to correct the loss of contrast without the need to perform any image analysis at each frame.
IEEE transactions on visualization and computer graphics. 09/2010;
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ACM Trans. Graph. 01/2010; 29:153.
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IEEE Trans. Vis. Comput. Graph. 01/2010; 16:95-108.
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ABSTRACT: The visualization community is currently witnessing strong advances in topology-based flow visualization research. Numerous
algorithms have been pro posed since the introduction of this class of approaches in 1989. Yet despite the many advances in
the field, topology-based flow visualization methods have, until now, failed to penetrate industry. Application domain experts
are still, in general, not using topological analysis and visualization in daily practice. We present a range of state-of-the
art topology-based flow visualization methods such as vortex core line extraction, singularity and separatrix extraction,
and periodic orbit extraction techniques, and apply them to real-world data sets. Applications include the visual ization
of engine simulation data such as in-cylinder flow, cooling jacket flow, as well as flow around a spinning missile. The novel
application of periodic orbit extraction to the boundary surface of a cooling jacket is presented. Based on our experiences,
we then describe what we believe needs to be done in order to bring topological flow visualization methods to industry-level
software applications. We believe this discussion will inspire useful directions for future work.
07/2009: pages 161-176;
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Proceedings of the 2009 Computer Graphics International Conference, CGI 2009, Victoria, British Columbia, Canada, May 26-29, 2009; 01/2009
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Comput. Graph. Forum. 01/2009; 28:1618-1631.
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2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2009), 20-25 June 2009, Miami, Florida, USA; 01/2009
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ACM Trans. Graph. 01/2008; 27.
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ACM Trans. Graph. 01/2007; 26:55.
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ABSTRACT: For some graphics applications, object interiors and hard-tosee regions contribute little to the final images and need not be processed. In this paper, we define a view-independent visibility measure on mesh surfaces based on the visibility function between the surfaces and a surrounding sphere of cameras. We demonstrate the usefulness of this measure with a visibility-guided simplification algorithm.
12/2002;
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ABSTRACT: Aging highway infrastructure requires effective rating methodologies to prioritize bridges for rehabilitation and repair. To aid engineers in decision making regarding bridge maintenance, a three-dimensional 3D visualization system is developed for rating reinforced concrete deck-girder bridge. Color codings show the most probable mode of failure for girder cross sections under combined moment-shear forces and allow an engineer to determine a rehabilitation strategy. The visualization system relies on 3D finite-element analyses using the open source framework OpenSees, making the system readily extensible to a wide range of bridge types and loading scenarios, as well as emergent reliability-based rating methodologies. Important features of the visualization system are emphasized, including the use of lighting and feature edge detection to improve the visual quality of a bridge model. Recent developments in scientific visualization are discussed for potential application to civil engineering problems.
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ABSTRACT: In this chapter we define the topology of 2D asymmetric tensor fields in terms of two graphs corresponding to the eigenvalue and eigenvector analysis for the tensor fields, respectively. Asymmetric tensor field topology can not only yield a concise repre-sentation of the field, but also provide a framework for spatial-temporal tracking of field features. Furthermore, inherent topological constraints in asymmetric tensor fields can be identified unambiguously through these graphs. We also describe ef-ficient algorithms to compute the topology of a given 2D asymmetric tensor field. We demonstrate the utility of our graph representations for asymmetric tensor field topology with fluid simulation data sets.
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ABSTRACT: Fluid simulation on interacting deformable surfaces is a challenging problem that has many applications. In this paper, we present a framework in which artistic as well as physically realistic flows can be generated on surfaces during deformation and collision. Our simulation system provides comprehensive control over the motion and deformation of an object as well as the movement and density of the fluid on the surface. At the heart of our system is a numerical solver that allows viscous and incompressible flows to be directly generated on surfaces using concepts from differential geometry, such as geodesic polar maps and parallel transport. This solver is fast and stable even when the object undergoes deforma-tion or collides with other surfaces. We also propose rules that allow deformation and collisions to im-pact fluid flows in a physically realistic manner. By combining these rules with a set of comprehensive design functionalities, we develop a system in which the user can specify shape deformation, collision, and fluid flow in a unified framework. We demonstrate the capability of our system with a number exam-ple scenarios.
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ABSTRACT: Visualization of 3D, unsteady (4D) flow is very difficult due to both perceptual challenges and the large size of 4D vector field data. Here, we describe the use of integral surfaces for visualization of CFD simulation data. By "integral" surfaces we mean surfaces based on massless particles that are integrated according to the underlying flow. Traditionally, in-tegral curves, e.g., streamlines, pathlines, and streaklines are used to visualize 3D and 4D flow. However, integral surfaces offer clear benefits over integral curves when visualizing flow. Despite the clear benefits that stream, path, and streak surfaces bring when visualiz-ing 4D vector fields, their use in both industry and for research has not proliferated. This is due, in part, to the complexity of integral surface construction algorithms. We introduce algorithms for the construction of stream, path, and streak surfaces that are fast and do not rely on any complicated data structures or surface parametrization. Our surface construction algorithms generate the surfaces using a quadrangular mesh. The algorithms can be applied to large data sets because they are based on local operations performed on quad primitives. The algorithms offer a combination of speed for exploration of 3D, unsteady flow and high precision. Thus they are suitable for inclusion into any visualization application. We demon-strate the techniques on a series of simulation data sets and show a number of benefits that stem naturally from them. We also introduce interaction techniques in order to address the perceptual challenges associated with visualizing 3D, time-dependent CFD simulation data.
