38-Issue 1

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https://diglib.eg.org/handle/10.2312/2632737

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An Adaptive Multi‐Grid Solver for Applications in Computer Graphics
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Kazhdan, Misha; Hoppe, Hugues; Chen, Min and Benes, Bedrich
A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. We demonstrate the efficacy of our solver in applications including surface reconstruction, image stitching and Euclidean Distance Transform calculation.A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints.
Applying Visual Analytics to Physically Based Rendering
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Simons, G.; Herholz, S.; Petitjean, V.; Rapp, T.; Ament, M.; Lensch, H.; Dachsbacher, C.; Eisemann, M.; Eisemann, E.; Chen, Min and Benes, Bedrich
Physically based rendering is a well‐understood technique to produce realistic‐looking images. However, different algorithms exist for efficiency reasons, which work well in certain cases but fail or produce rendering artefacts in others. Few tools allow a user to gain insight into the algorithmic processes. In this work, we present such a tool, which combines techniques from information visualization and visual analytics with physically based rendering. It consists of an interactive parallel coordinates plot, with a built‐in sampling‐based data reduction technique to visualize the attributes associated with each light sample. Two‐dimensional (2D) and three‐dimensional (3D) heat maps depict any desired property of the rendering process. An interactively rendered 3D view of the scene displays animated light paths based on the user's selection to gain further insight into the rendering process. The provided interactivity enables the user to guide the rendering process for more efficiency. To show its usefulness, we present several applications based on our tool. This includes differential light transport visualization to optimize light setup in a scene, finding the causes of and resolving rendering artefacts, such as fireflies, as well as a path length contribution histogram to evaluate the efficiency of different Monte Carlo estimators.Few tools allow a user to gain insight into the algorithmic processes of physically‐based rendering. In this work, we present such a tool, which combines techniques from information visualization and visual analytics with physically based rendering.
Autonomous Particles for Interactive Flow Visualization
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Engelke, Wito; Lawonn, Kai; Preim, Bernhard; Hotz, Ingrid; Chen, Min and Benes, Bedrich
We present an interactive approach to analyse flow fields using a new type of particle system, which is composed of autonomous particles exploring the flow. While particles provide a very intuitive way to visualize flows, it is a challenge to capture the important features with such systems. Particles tend to cluster in regions of low velocity and regions of interest are often sparsely populated. To overcome these disadvantages, we propose an automatic adaption of the particle density with respect to local importance measures. These measures are user defined and the systems sensitivity to them can be adjusted interactively. Together with the particle history, these measures define a probability for particles to multiply or die, respectively. There is no communication between the particles and no neighbourhood information has to be maintained. Thus, the particles can be handled in parallel and support a real‐time investigation of flow fields. To enhance the visualization, the particles' properties and selected field measures are also used to specify the systems rendering parameters, such as colour and size. We demonstrate the effectiveness of our approach on different simulated vector fields from technical and medical applications.We present an interactive approach to analyse flow fields using a new type of particle system, which is composed of autonomous particles exploring the flow. While particles provide a very intuitive way to visualize flows, it is a challenge to capture the important features with such systems. Particles tend to cluster in regions of low velocity and regions of interest are often sparsely populated. To overcome these disadvantages, we propose an automatic adaption of the particle density with respect to local importance measures. These measures are user defined and the systems sensitivity to them can be adjusted interactively. Together with the particle history, these measures define a probability for particles to multiply or die, respectively. There is no communication between the particles and no neighbourhood information has to be maintained. Thus, the particles can be handled in parallel and support a real‐time investigation of flow fields. To enhance the visualization, the particles' properties and selected field measures are also used to specify the systems rendering parameters, such as colour and size. We demonstrate the effectiveness of our approach on different simulated vector fields from technical and medical applications.
Ballet
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Lawonn, Kai; Günther, Tobias; Chen, Min and Benes, Bedrich
Controllable Image‐Based Transfer of Flow Phenomena
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Bosch, Carles; Patow, Gustavo; Chen, Min and Benes, Bedrich
Modelling flow phenomena and their related weathering effects is often cumbersome due their dependence on the environment, materials and geometric properties of objects in the scene. Example‐based modelling provides many advantages for reproducing real textures, but little effort has been devoted to reproducing and transferring complex phenomena. In order to produce realistic flow effects, it is possible to take advantage of the widespread availability of flow images on the Internet, which can be used to gather key information about the flow. In this paper, we present a technique that allows the transfer of flow phenomena between photographs, adapting the flow to the target image and giving the user flexibility and control through specifically tailored parameters. This is done through two types of control curves: a fitted theoretical curve to control the mass of deposited material, and an extended colour map for properly adapting to the target appearance. In addition, our method filters and warps the input flow in order to account for the geometric details of the target surface. This leads to a fast and intuitive approach to easily transfer phenomena between images, providing a set of simple and intuitive parameters to control the process.
Denoising Deep Monte Carlo Renderings
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Vicini, D.; Adler, D.; Novák, J.; Rousselle, F.; Burley, B.; Chen, Min and Benes, Bedrich
We present a novel algorithm to denoise deep Monte Carlo renderings, in which pixels contain multiple colour values, each for a different range of depths. Deep images are a more expressive representation of the scene than conventional flat images. However, since each depth bin receives only a fraction of the flat pixel's samples, denoising the bins is harder due to the less accurate mean and variance estimates. Furthermore, deep images lack a regular structure in depth—the number of depth bins and their depth ranges vary across pixels. This prevents a straightforward application of patch‐based distance metrics frequently used to improve the robustness of existing denoising filters. We address these constraints by combining a flat image‐space non‐local means filter operating on pixel colours with a cross‐bilateral filter operating on auxiliary features (albedo, normal, etc.). Our approach significantly reduces noise in deep images while preserving their structure. To our best knowledge, our algorithm is the first to enable efficient deep‐compositing workflows with denoised Monte Carlo renderings. We demonstrate the performance of our filter on a range of scenes highlighting the challenges and advantages of denoising deep images.
Editorial 2019 CGF 38-1
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Chen, Min; Benes, Bedrich; Chen, Min and Benes, Bedrich
Filtered Quadrics for High‐Speed Geometry Smoothing and Clustering
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Legrand, Hélène; Thiery, Jean‐Marc; Boubekeur, Tamy; Chen, Min and Benes, Bedrich
Modern 3D capture pipelines produce dense surface meshes at high speed, which challenge geometric operators to process such massive data on‐the‐fly. In particular, aiming at instantaneous feature‐preserving smoothing and clustering disqualifies global variational optimizers and one usually relies on high‐performance parallel kernels based on simple measures performed on the positions and normal vectors associated with the surface vertices. Although these operators are effective on small supports, they fail at properly capturing larger scale surface structures. To cope with this problem, we propose to enrich the surface representation with filtered quadrics, a compact and discriminating range space to guide processing. Compared to normal‐based approaches, this additional vertex attribute significantly improves feature preservation for fast bilateral filtering and mode‐seeking clustering, while exhibiting a linear memory cost in the number of vertices and retaining the simplicity of convolutional filters. In particular, the overall performance of our approach stems from its natural compatibility with modern fine‐grained parallel computing architectures such as graphics processor units (GPU). As a result, filtered quadrics offer a superior ability to handle a broad spectrum of frequencies and preserve large salient structures, delivering meshes on‐the‐fly for interactive and streaming applications, as well as quickly processing large data collections, instrumental in learning‐based geometry analysis.
FitConnect: Connecting Noisy 2D Samples by Fitted Neighbourhoods
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Ohrhallinger, S.; Wimmer, M.; Chen, Min and Benes, Bedrich
We propose a parameter‐free method to recover manifold connectivity in unstructured 2D point clouds with high noise in terms of the local feature size. This enables us to capture the features which emerge out of the noise. To achieve this, we extend the reconstruction algorithm , which connects samples to two (noise‐free) neighbours and has been proven to output a manifold for a relaxed sampling condition. Applying this condition to noisy samples by projecting their ‐nearest neighbourhoods onto local circular fits leads to multiple candidate neighbour pairs and thus makes connecting them consistently an NP‐hard problem. To solve this efficiently, we design an algorithm that searches that solution space iteratively on different scales of . It achieves linear time complexity in terms of point count plus quadratic time in the size of noise clusters. Our algorithm extends seamlessly to connect both samples with and without noise, performs as local as the recovered features and can output multiple open or closed piecewise curves. Incidentally, our method simplifies the output geometry by eliminating all but a representative point from noisy clusters. Since local neighbourhood fits overlap consistently, the resulting connectivity represents an ordering of the samples along a manifold. This permits us to simply blend the local fits for denoising with the locally estimated noise extent. Aside from applications like reconstructing silhouettes of noisy sensed data, this lays important groundwork to improve surface reconstruction in 3D. Our open‐source algorithm is available online.We propose a parameter‐free method to recover manifold connectivity in unstructured 2D point clouds with high noise in terms of the local feature size. This enables us to capture the features which emerge out of the noise. To achieve this, we extend the reconstruction algorithm , which connects samples to two (noise‐free) neighbours and has been proven to output a manifold for a relaxed sampling condition. Applying this condition to noisy samples by projecting their ‐nearest neighbourhoods onto local circular fits leads to multiple candidate neighbour pairs and thus makes connecting them consistently an NP‐hard problem. To solve this efficiently, we design an algorithm that searches that solution space iteratively on different scales of . It achieves linear time complexity in terms of point count plus quadratic time in the size of noise clusters.
Flexible Use of Temporal and Spatial Reasoning for Fast and Scalable CPU Broad‐Phase Collision Detection Using KD‐Trees
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Serpa, Ygor Rebouças; Rodrigues, Maria Andréia Formico; Chen, Min and Benes, Bedrich
Realistic computer simulations of physical elements such as rigid and deformable bodies, particles and fractures are commonplace in the modern world. In these simulations, the broad‐phase collision detection plays an important role in ensuring that simulations can scale with the number of objects. In these applications, several degrees of motion coherency, distinct spatial distributions and different types of objects exist; however, few attempts have been made at a generally applicable solution for their broad phase. In this regard, this work presents a novel broad‐phase collision detection algorithm based upon a hybrid SIMD optimized KD‐Tree and sweep‐and‐prune, aimed at general applicability. Our solution is optimized for several objects distributions, degrees of motion coherence and varying object sizes. These features are made possible by an efficient and idempotent two‐step tree optimization algorithm and by selectively enabling coherency optimizations. We have tested our solution under varying scenario setups and compared it to other solutions available in the literature and industry, up to a million simulated objects. The results show that our solution is competitive, with average performance values two to three times better than those achieved by other state‐of‐the‐art AABB‐based CPU solutions.Realistic computer simulations of physical elements such as rigid and deformable bodies, particles and fractures are commonplace in the modern world. In these simulations, the broad‐phase collision detection plays an important role in ensuring that simulations can scale with the number of objects. In these applications, several degrees of motion coherency, distinct spatial distributions and different types of objects exist; however, few attempts have been made at a generally applicable solution for their broad phase. In this regard, this work presents a novel broad‐phase collision detection algorithm based upon a hybrid SIMD optimized KD‐Tree and sweep‐and‐prune, aimed at general applicability. Our solution is optimized for several objects distributions, degrees of motion coherence and varying object sizes. These features are made possible by an efficient and idempotent two‐step tree optimization algorithm and by selectively enabling coherency optimizations.
Functional Maps Representation On Product Manifolds
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Rodolà, E.; Lähner, Z.; Bronstein, A. M.; Bronstein, M. M.; Solomon, J.; Chen, Min and Benes, Bedrich
We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.
Generation and Visual Exploration of Medical Flow Data: Survey, Research Trends and Future Challenges
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Oeltze‐Jafra, S.; Meuschke, M.; Neugebauer, M.; Saalfeld, S.; Lawonn, K.; Janiga, G.; Hege, H.‐C.; Zachow, S.; Preim, B.; Chen, Min and Benes, Bedrich
Simulations and measurements of blood and airflow inside the human circulatory and respiratory system play an increasingly important role in personalized medicine for prevention, diagnosis and treatment of diseases. This survey focuses on three main application areas. (1) Computational fluid dynamics (CFD) simulations of blood flow in cerebral aneurysms assist in predicting the outcome of this pathologic process and of therapeutic interventions. (2) CFD simulations of nasal airflow allow for investigating the effects of obstructions and deformities and provide therapy decision support. (3) 4D phase‐contrast (4D PC) magnetic resonance imaging of aortic haemodynamics supports the diagnosis of various vascular and valve pathologies as well as their treatment. An investigation of the complex and often dynamic simulation and measurement data requires the coupling of sophisticated visualization, interaction and data analysis techniques. In this paper, we survey the large body of work that has been conducted within this realm. We extend previous surveys by incorporating nasal airflow, addressing the joint investigation of blood flow and vessel wall properties and providing a more fine‐granular taxonomy of the existing techniques. From the survey, we extract major research trends and identify open problems and future challenges. The survey is intended for researchers interested in medical flow but also more general, in the combined visualization of physiology and anatomy, the extraction of features from flow field data and feature‐based visualization, the visual comparison of different simulation results and the interactive visual analysis of the flow field and derived characteristics.Simulations and measurements of blood and airflow inside the human circulatory and respiratory system play an increasingly important role in personalized medicine for prevention, diagnosis and treatment of diseases. This survey focuses on three main application areas. (1) Computational fluid dynamics (CFD) simulations of blood flow in cerebral aneurysms assist in predicting the outcome of this pathologic process and of therapeutic interventions. (2) CFD simulations of nasal airflow allow for investigating the effects of obstructions and deformities and provide therapy decision support. (3) 4D phase‐contrast (4D PC) magnetic resonance imaging of aortic haemodynamics supports the diagnosis of various vascular and valve pathologies as well as their treatment. An investigation of the complex and often dynamic simulation and measurement data requires the coupling of sophisticated visualization, interaction and data analysis techniques.
Gradient‐Guided Local Disparity Editing
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Scandolo, Leonardo; Bauszat, Pablo; Eisemann, Elmar; Chen, Min and Benes, Bedrich
Stereoscopic 3D technology gives visual content creators a new dimension of design when creating images and movies. While useful for conveying emotion, laying emphasis on certain parts of the scene, or guiding the viewer's attention, editing stereo content is a challenging task. Not respecting comfort zones or adding incorrect depth cues, for example depth inversion, leads to a poor viewing experience. In this paper, we present a solution for editing stereoscopic content that allows an artist to impose disparity constraints and removes resulting depth conflicts using an optimization scheme. Using our approach, an artist only needs to focus on important high‐level indications that are automatically made consistent with the entire scene while avoiding contradictory depth cues and respecting viewer comfort.
Increasing the Spatial Resolution of BTF Measurement with Scheimpflug Imaging
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Havran, V.; Hošek, J.; Němcová, Š.; Čáp, J.; Chen, Min and Benes, Bedrich
We present an improved way of acquiring spatially varying surface reflectance represented by a bidirectional texture function (BTF). Planar BTF samples are measured as images at several inclination angles which puts constraints on the minimum depth of field of cameras used in the measurement instrument. For standard perspective imaging, we show that the size of a sample measured and the achievable spatial resolution are strongly interdependent and limited by diffraction at the lens' aperture. We provide a formula for this relationship. We overcome the issue of the required depth of field by using Scheimpflug imaging further enhanced by an anamorphic attachment. The proposed optics doubles the spatial resolution of images compared to standard perspective imaging optics. We built an instrument prototype with the proposed optics that is portable and allows for measurement on site. We show rendered images using the visual appearance measured by the instrument prototype.
Incremental Labelling of Voronoi Vertices for Shape Reconstruction
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Peethambaran, J.; Parakkat, A.D.; Tagliasacchi, A.; Wang, R.; Muthuganapathy, R.; Chen, Min and Benes, Bedrich
We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves. The proposed framework has been thoroughly evaluated for its usefulness using various test data. Results indicate that even sparsely and non‐uniformly sampled curves with outliers or collection of curves are faithfully reconstructed by the proposed algorithm.We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves.
Issue Information CGF38-1
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Chen, Min and Benes, Bedrich
Learning A Stroke‐Based Representation for Fonts
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Balashova, Elena; Bermano, Amit H.; Kim, Vladimir G.; DiVerdi, Stephen; Hertzmann, Aaron; Funkhouser, Thomas; Chen, Min and Benes, Bedrich
Designing fonts and typefaces is a difficult process for both beginner and expert typographers. Existing workflows require the designer to create every glyph, while adhering to many loosely defined design suggestions to achieve an aesthetically appealing and coherent character set. This process can be significantly simplified by exploiting the similar structure character glyphs present across different fonts and the shared stylistic elements within the same font. To capture these correlations, we propose learning a stroke‐based font representation from a collection of existing typefaces. To enable this, we develop a stroke‐based geometric model for glyphs, a fitting procedure to reparametrize arbitrary fonts to our representation. We demonstrate the effectiveness of our model through a manifold learning technique that estimates a low‐dimensional font space. Our representation captures a wide range of everyday fonts with topological variations and naturally handles discrete and continuous variations, such as presence and absence of stylistic elements as well as slants and weights. We show that our learned representation can be used for iteratively improving fit quality, as well as exploratory style applications such as completing a font from a subset of observed glyphs, interpolating or adding and removing stylistic elements in existing fonts.
MegaViews: Scalable Many‐View Rendering With Concurrent Scene‐View Hierarchy Traversal
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Kol, Timothy R.; Bauszat, Pablo; Lee, Sungkil; Eisemann, Elmar; Chen, Min and Benes, Bedrich
We present a scalable solution to render complex scenes from a large amount of viewpoints. While previous approaches rely either on a scene or a view hierarchy to process multiple elements together, we make full use of both, enabling sublinear performance in terms of views and scene complexity. By concurrently traversing the hierarchies, we efficiently find shared information among views to amortize rendering costs. One example application is many‐light global illumination. Our solution accelerates shadow map generation for virtual point lights, whose number can now be raised to over a million while maintaining interactive rates.
MyEvents: A Personal Visual Analytics Approach for Mining Key Events and Knowledge Discovery in Support of Personal Reminiscence
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Parvinzamir, F.; Zhao, Y.; Deng, Z.; Dong, F.; Chen, Min and Benes, Bedrich
Reminiscence is an important aspect in our life. It preserves precious memories, allows us to form our own identities and encourages us to accept the past. Our work takes the advantage of modern sensor technologies to support reminiscence, enabling self‐monitoring of personal activities and individual movement in space and time on a daily basis. This paper presents MyEvents, a web‐based personal visual analytics platform designed for non‐computing experts, that allows for the collection of long‐term location and movement data and the generation of event mementos. Our research is focused on two prominent goals in event reminiscence: (1) selection subjectivity and human involvement in the process of self‐knowledge discovery and memento creation; and (2) the enhancement of event familiarity by presenting target events and their related information for optimal memory recall and reminiscence. A novel multi‐significance event ranking model is proposed to determine significant events in the personal history according to user preferences for event category, frequency and regularity. The evaluation results show that MyEvents effectively fulfils the reminiscence goals and tasks.Reminiscence is an important aspect in our life. It preserves precious memories, allows us to form our own identities and encourages us to accept the past. Our work takes the advantage of modern sensor technologies to support reminiscence, enabling self‐monitoring of personal activities and individual movement in space and time on a daily basis. This paper presents MyEvents, a web‐based personal visual analytics platform designed for non‐computing experts, that allows for the collection of long‐term location and movement data and the generation of event mementos. Our research is focused on two prominent goals in event reminiscence: (1) selection subjectivity and human involvement in the process of self‐knowledge discovery and memento creation; and (2) the enhancement of event familiarity by presenting target events and their related information for optimal memory recall and reminiscence. A novel multi‐significance event ranking model is proposed to determine significant events in the personal history according to user preferences for event category, frequency and regularity. The evaluation results show that MyEvents effectively fulfils the reminiscence goals and tasks.
On Visualizing Continuous Turbulence Scales
(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Liu, Xiaopei; Mishra, Maneesh; Skote, Martin; Fu, Chi‐Wing; Chen, Min and Benes, Bedrich
Turbulent flows are multi‐scale with vortices spanning a wide range of scales continuously. Due to such complexities, turbulence scales are particularly difficult to analyse and visualize. In this work, we present a novel and efficient optimization‐based method for turbulence structure visualization with scale decomposition directly in the Kolmogorov energy spectrum. To achieve this, we first derive a new analytical objective function based on integration approximation. Using this new formulation, we can significantly improve the efficiency of the underlying optimization process and obtain the desired filter in the Kolmogorov energy spectrum for scale decomposition. More importantly, such a decomposition allows a ‘continuous‐scale visualization’ that enables us to efficiently explore the decomposed turbulence scales and further analyse the turbulence structures in a continuous manner. With our approach, we can present scale visualizations of direct numerical simulation data sets continuously over the scale domain for both isotropic and boundary layer turbulent flows. Compared with previous works on multi‐scale turbulence analysis and visualization, our method is highly flexible and efficient in generating scale decomposition and visualization results. The application of the proposed technique to both isotropic and boundary layer turbulence data sets verifies the capability of our technique to produce desirable scale visualization results.Turbulent flows are multi‐scale with vortices spanning a wide range of scales continuously. Due to such complexities, turbulence scales are particularly difficult to analyse and visualize. In this work, we present a novel and efficient optimization‐based method for turbulence structure visualization with scale decomposition directly in the Kolmogorov energy spectrum. To achieve this, we first derive a new analytical objective function based on integration approximation. Using this new formulation, we can significantly improve the efficiency of the underlying optimization process and obtain the desired filter in the Kolmogorov energy spectrum for scale decomposition. More importantly, such a decomposition allows a ‘continuous‐scale visualization’ that enables us to efficiently explore the decomposed turbulence scales and further analyse the turbulence structures in a continuous manner. With our approach, we can present scale visualizations of direct numerical simulation data sets continuously over the scale domain for both isotropic and boundary layer turbulent flows.

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