Guoning Chen

Interactive procedural street modeling

This sketch presents a solution to efficiently model the street networks of large urban areas. Parish and Müller [2001] were the first to note that the street network is the key to create a large urban model. While this algorithm created a high quality solution, the method does not allow to incorporate user-control. To address this limitation we provide a rather different alternative to street modeling that allows to integrate a wide variety of user input. The key idea is to use tensor fields to guide the generation of street graphs. A user can interactively edit a street graph by either modifying the underlying tensor field or by changing the graph directly. This allows for efficient modeling, because we can combine high-level and low-level modeling operations, constraints, and procedural methods. The major contributions are as follows: (1) We are the first to introduce a procedural approach to model urban street networks that combines interactive user-guided editing operations and procedural methods. (2) We are introducing a new methodology to graph modeling in general. The idea of tensor-guided graph modeling together with the tight integration of interactive editing and procedural modeling has not been explored previously in related modeling problems, such as modeling of bark, cracks, fracture, or trees.

Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition

Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper, we provide a new technique that allows for the systematic creation and cancellation of fixed points and periodic orbits. This technique enables vector field design and editing on the plane and surfaces with desired qualitative properties. The technique is based on Conley theory, which provides a unified framework that supports the cancellation of fixed points and periodic orbits. We also introduce a novel periodic orbit extraction and visualization algorithm that detects, for the first time, periodic orbits on surfaces. Furthermore, we describe the application of our periodic orbit detection and vector field simplification algorithms to engine simulation data demonstrating the utility of the approach. We apply our design system to vector field visualization by creating data sets containing periodic orbits. This helps us understand the effectiveness of existing visualization techniques. Finally, we propose a new streamline-based technique that allows vector field topology to be easily identified.

Efficient Morse Decompositions of Vector Fields

Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCGs, while fast, are overly conservative and usually result in MCGs that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCGs than existing techniques. Furthermore, the choice of tau provides a natural trade-off between the fineness of the MCGs and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.

Evenly Spaced Streamlines for Surfaces: An Image-Based Approach

We introduce a novel, automatic streamline seeding algorithm for vector fields defined on surfaces in 3D space. The algorithm generates evenly spaced streamlines fast, simply and efficiently for any general surface‐based vector field. It is general because it handles large, complex, unstructured, adaptive resolution grids with holes and discontinuities, does not require a parametrization, and can generate both sparse and dense representations of the flow. It is efficient because streamlines are only integrated for visible portions of the surface. It is simple because the image‐based approach removes the need to perform streamline tracing on a triangular mesh, a process which is complicated at best. And it is fast because it makes effective, balanced use of both the CPU and the GPU. The key to the algorithms speed, simplicity and efficiency is its image‐based seeding strategy. We demonstrate our algorithm on complex, real‐world simulation data sets from computational fluid dynamics and compare it with object‐space streamline visualizations.

Technical Section: Surface-based flow visualization

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. While 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 surface-based 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 up-to-date overview of the current state-of-the-art that highlights both solved and unsolved problems in this rapidly evolving branch of research.

Automatic Stream Surface Seeding: A Feature Centered Approach

The ability to capture and visualize information within the flow poses challenges for visualizing 3D flow fields. Stream surfaces are one of many useful integration based techniques for visualizing 3D flow. However seeding integral surfaces can be challenging. Previous research generally focuses on manual placement of stream surfaces. Little attention has been given to the problem of automatic stream surface seeding. This paper introduces a novel automatic stream surface seeding strategy based on vector field clustering. It is important that the user can define and target particular characteristics of the flow. Our framework provides this ability. The user is able to specify different vector clustering parameters enabling a range of abstraction for the density and placement of seeding curves and their associated stream surfaces. We demonstrate the effectiveness of this automatic stream surface approach on a range of flow simulations and incorporate illustrative visualization techniques. Domain expert evaluation of the results provides valuable insight into the users requirements and effectiveness of our approach.

Analysis of Recurrent Patterns in Toroidal Magnetic Fields

In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the fields topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactiveparallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.

Ovis: A Framework for Visual Analysisof Ocean Forecast Ensembles

We present a novel integrated visualization system that enables interactive visual analysis of ensemble simulations of the sea surface height that is used in ocean forecasting. The position of eddies can be derived directly from the sea surface height and our visualization approach enables their interactive exploration and analysis.The behavior of eddies is important in different application settings of which we present two in this paper. First, we show an application for interactive planning of placement as well as operation of off-shore structures using real-world ensemble simulation data of the Gulf of Mexico. Off-shore structures, such as those used for oil exploration, are vulnerable to hazards caused by eddies, and the oil and gas industry relies on ocean forecasts for efficient operations. We enable analysis of the spatial domain, as well as the temporal evolution, for planning the placement and operation of structures.Eddies are also important for marine life. They transport water over large distances and with it also heat and other physical properties as well as biological organisms. In the second application we present the usefulness of our tool, which could be used for planning the paths of autonomous underwater vehicles, so called gliders, for marine scientists to study simulation data of the largely unexplored Red Sea.

Mesh-Driven Vector Field Clustering and Visualization: An Image-Based Approach

Vector field visualization techniques have evolved very rapidly over the last two decades, however, visualizing vector fields on complex boundary surfaces from computational flow dynamics (CFD) still remains a challenging task. In part, this is due to the large, unstructured, adaptive resolution characteristics of the meshes used in the modeling and simulation process. Out of the wide variety of existing flow field visualization techniques, vector field clustering algorithms offer the advantage of capturing a detailed picture of important areas of the domain while presenting a simplified view of areas of less importance. This paper presents a novel, robust, automatic vector field clustering algorithm that produces intuitive and insightful images of vector fields on large, unstructured, adaptive resolution boundary meshes from CFD. Our bottom-up, hierarchical approach is the first to combine the properties of the underlying vector field and mesh into a unified error-driven representation. The motivation behind the approach is the fact that CFD engineers may increase the resolution of model meshes according to importance. The algorithm has several advantages. Clusters are generated automatically, no surface parameterization is required, and large meshes are processed efficiently. The most suggestive and important information contained in the meshes and vector fields is preserved while less important areas are simplified in the visualization. Users can interactively control the level of detail by adjusting a range of clustering distance measure parameters. We describe two data structures to accelerate the clustering process. We also introduce novel visualizations of clusters inspired by statistical methods. We apply our method to a series of synthetic and complex, real-world CFD meshes to demonstrate the clustering algorithm results.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.