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39
HardwareAccelerated Volume and Isosurface Rendering Based on CellProjection
, 2000
"... We present two beneficial rendering extensions to the Projected Tetrahedra (PT) algorithm by Shirley and Tuchman. These extensions are compatible with any cell sorting technique, for example the BSPXMPVO sorting algorithm for unstructured meshes. ..."
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Cited by 89 (13 self)
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We present two beneficial rendering extensions to the Projected Tetrahedra (PT) algorithm by Shirley and Tuchman. These extensions are compatible with any cell sorting technique, for example the BSPXMPVO sorting algorithm for unstructured meshes.
Anisotropic Diffusion of Surfaces and Functions on Surfaces
, 2003
"... We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated twomanifold surface meshes in R³ and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combin ..."
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Cited by 66 (7 self)
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We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated twomanifold surface meshes in R³ and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combine the C¹ limit representation of Loop’s subdivision for triangular surface meshes and vector functions on the surface mesh with the established diffusion model to arrive at a discretized version of the diffusion problem in the spatial direction. The time direction discretization then leads to a sparse linear system of equations. Iteratively solving the sparse linear system yields a sequence of faired (smoothed) meshes as well as faired functions.
Vector Field Design on Surfaces
 ACM Transactions on Graphics
, 2006
"... Figure 1: This figure shows various vector fields created on surfaces using our vector field design system. The vector field shown at the right was used to guide texture synthesis shown in Figure 12 (right). Vector field design on surfaces is necessary for many graphics applications: examplebased t ..."
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Cited by 51 (15 self)
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Figure 1: This figure shows various vector fields created on surfaces using our vector field design system. The vector field shown at the right was used to guide texture synthesis shown in Figure 12 (right). Vector field design on surfaces is necessary for many graphics applications: examplebased texture synthesis, nonphotorealistic rendering, and fluid simulation. A vector field design system should allow a user to create a large variety of complex vector fields with relatively little effort. In this paper, we present a vector field design system for surfaces that allows the user to control the number of singularities in the vector field and their placement. Our system combines basis vector fields to make an initial vector field that meets the user’s specifications. The initial vector field often contains unwanted singularities. Such singularities cannot always be eliminated, due to the PoincaréHopf index theorem. To reduce the effect caused by these singularities, our system allows a user to move a singularity to a more favorable location or to cancel a pair of singularities. These operations provide topological guarantees for the vector field in that they only affect the userspecified singularities. Other editing operations are also provided so that the user may change the topological and geometric characteristics of the vector field. We demonstrate our vector field design system for several applications: examplebased texture synthesis, painterly rendering of images, and pencil sketch illustrations of smooth surfaces.
Over Two Decades of IntegrationBased, Geometric Flow
 EUROGRAPHICS 2009 / M. PAULY AND G. GREINER, STAR  STATE OF THE ART REPORT
, 2009
"... Flow visualization is a fascinating subbranch of scientific visualization. With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of f ..."
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Cited by 35 (7 self)
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Flow visualization is a fascinating subbranch of scientific visualization. With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization which deals with large, timedependent, multivariate simulation datasets. In this paper, geometry based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the vector field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation, and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding object upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an uptodate overview of the current stateoftheart that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.
Topological segmentation in threedimensional vector fields
 IEEE Transactions on Visualization and Computer Graphics
, 2004
"... ..."
Anisotropic Diffusion of Subdivision Surfaces and Functions on Surfaces
 ACM TRANSACTIONS ON GRAPHICS
, 2002
"... We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated 2manifold surface meshes in R³ and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combi ..."
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Cited by 22 (6 self)
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We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated 2manifold surface meshes in R³ and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combine the C¹ limit representation of Loop's subdivision for triangular surface meshes and vector functions on the surface mesh with the established diffusion model to arrive at a discretized version of the diffusion problem in the spatial direction. The time
Display of Vector Fields Using a ReactionDiffusion Model
, 2004
"... Effective visualization of vector fields relies on the ability to control the size and density of the underlying mapping to visual cues used to represent the field. In this paper we introduce the use of a reactiondiffusion model, already well known for its ability to form irregular spatiotemporal ..."
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Cited by 21 (5 self)
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Effective visualization of vector fields relies on the ability to control the size and density of the underlying mapping to visual cues used to represent the field. In this paper we introduce the use of a reactiondiffusion model, already well known for its ability to form irregular spatiotemporal patters, to control the size, density, and placement of the vector field representation. We demonstrate that it is possible to encode vector field information (orientation and magnitude) into the parameters governing a reactiondiffusion model to form a spot pattern with the correct orientation, size, and density, creating an effective visualization. To encode direction we texture the spots using a light to dark fading texture. We also show that it is possible to use the reactiondiffusion model to visualize an additional scalar value, such as the uncertainty in the orientation of the vector field. An additional benefit of the reactiondiffusion visualization technique arises from its automatic density distribution. This benefit suggests using the technique to augment other vector visualization techniques. We demonstrate this utility by augmenting a LIC visualization with a reactiondiffusion visualization. Finally, the reactiondiffusion visualization method provides a technique that can be used for streamline and glyph placement.
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 17 (8 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.
Dye Advection without the Blur: A LevelSet Approach for Texture
 PROC. EUROGRAPHICS 2004
, 2004
"... Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noisebased dense vector field representations and is an important element in usercentric visual exploration processes. However, fast texturebased implementations of dy ..."
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Cited by 14 (4 self)
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Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noisebased dense vector field representations and is an important element in usercentric visual exploration processes. However, fast texturebased implementations of dye advection rely on linear interpolation operations that lead to severe diffusion artifacts. In this paper, a novel approach for dye advection is proposed to avoid this blurring and to achieve long and clearly defined streaklines or extended streaklike patterns. The interface between dye and background is modeled as a levelset within a signed distance field. The levelset evolution is governed by the underlying flow field and is computed by a semiLagrangian method. A reinitialization technique is used to counteract the distortions introduced by the levelset evolution and to maintain a levelset function that represents a local distance field. This approach works for 2D and 3D flow fields alike. It is demonstrated how the texturebased levelset representation lends itself to an efficient GPU implementation and therefore facilitates interactive visualization.
Discrete Surface Modeling using Geometric Flows
, 2003
"... We use various nonlinear geometric partial differential equations to efficiently solve several surface modeling problems, including surface blending, Nsided hole filling and freeform surface fitting. The nonlinear equations used include two second order flows (mean curvature flow and average mea ..."
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Cited by 9 (3 self)
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We use various nonlinear geometric partial differential equations to efficiently solve several surface modeling problems, including surface blending, Nsided hole filling and freeform surface fitting. The nonlinear equations used include two second order flows (mean curvature flow and average mean curvature flow), one fourth order flow (surface diffusion flow) and a sixth order flow. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.