Pathline glyphs

Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well‐established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph‐based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time‐dependent flow behavior. Zooming‐in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context‐preserving zoom lens and interactive pathline‐based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.     

Stream Line–Based Pattern Search in Flows

We propose a method that allows users to define flow features in form of patterns represented as sparse sets of stream line segments. Our approach finds similar occurrences in the same or other time steps. Related approaches define patterns using dense, local stencils or support only single segments. Our patterns are defined sparsely and can have a significant extent, i.e., they are integration‐based and not local. This allows for a greater flexibility in defining features of interest. Similarity is measured using intrinsic curve properties only, which enables invariance to location, orientation, and scale. Our method starts with splitting stream lines using globally consistent segmentation criteria. It strives to maintain the visually apparent features of the flow as a collection of stream line segments. Most importantly, it provides similar segmentations for similar flow structures. For user‐defined patterns of curve segments, our algorithm finds similar ones that are invariant to similarity transformations. We showcase the utility of our method using different 2D and 3D flow fields.     

Topological methods for 2D time-dependent vector fields based on stream lines and path lines

This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology, we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method of tracking all isolated closed stream lines. To get the path line oriented topology, we segment the vector field into areas of attracting, repelling, and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets.     

Sets of Globally Optimal Stream Surfaces for Flow Visualization

Stream surfaces are a well‐studied and widely used tool for the visualization of 3D flow fields. Usually, stream surface seeding is carried out manually in time‐consuming trial and error procedures. Only recently automatic selection methods were proposed. Local methods support the selection of a set of stream surfaces, but, contrary to global selection methods, they evaluate only the quality of the seeding lines but not the quality of the whole stream surfaces. Global methods, on the other hand, only support the selection of a single optimal stream surface until now. However, for certain flow fields a single stream surface is not sufficient to represent all flow features. In our work, we overcome this limitation by introducing a global selection technique for a set of stream surfaces. All selected surfaces optimize global stream surface quality measures and are guaranteed to be mutually distant, such that they can convey different flow features. Our approach is an efficient extension of the most recent global selection method for single stream surfaces. We illustrate its effectiveness on a number of analytical and simulated flow fields and analyze the quality of the results in a user study.     

Physics‐based Pathline Clustering and Exploration

Most existing unsteady flow visualization techniques concentrate on the depiction of geometric patterns in flow, assuming the geometry information provides sufficient representation of the underlying physical characteristics, which is not always the case. To address this challenge, this work proposes to analyse the time‐dependent characteristics of the physical attributes measured along pathlines which can be represented as a series of time activity curves (TAC). We demonstrate that the temporal trends of these TACs can convey the relation between pathlines and certain well‐known flow features (e.g. vortices and shearing layers), which enables us to select pathlines that can effectively represent the physical characteristics of interest and their temporal behaviour in the unsteady flow. Inspired by this observation, a new TAC‐based unsteady flow visualization and analysis framework is proposed. The centre of this framework is a new similarity measure that compares the similarity of two TACs, from which a new spatio‐temporal, hierarchical clustering that classifies pathlines based on their physical attributes, and a TAC‐based pathline exploration and selection strategy are proposed. A visual analytic system incorporating the TAC‐based pathline clustering and exploration is developed, which also provides new visualizations to support the user exploration of unsteady flow using TACs. This visual analytic system is applied to a number of unsteady flow in 2D and 3D to demonstrate its utility. The new system successfully reveals the detailed structure of vortices, the relation between shear layer and vortex formation, and vortex breakdown, which are difficult to convey with conventional methods.     

Animated 3D Line Drawings with Temporal Coherence

Producing traditional animation is a laborious task where the key drawings are first drawn by artists and thereafter inbetween drawings are created, whether it is by hand or computer‐assisted. Auto‐inbetweening of these 2D key drawings by computer is a non‐trivial task as 3D depths are missing. An alternate approach is to generate all the drawings by extracting lines directly from animated 3D models frame by frame, concatenating and rendering them together into an animation. However, animation quality generated using this straightforward method bears two problems. Firstly, the animation contains unsatisfactory visual artifacts such as line flickering and popping. This is especially pronounced when the lines are extracted using high‐order derivatives, such as ridges and valleys, from 3D models represented in triangle meshes. Secondly, there is a lack of temporal continuity as each drawing is generated without taking its neighboring drawings into consideration. In this paper, we propose an improved approach over the straightforward method by transferring extracted 3D line drawings of each frame into individual 3D lines and processing them along the time domain. Our objective is to minimize the visual artifacts and incorporate temporal relationship of individual lines throughout the entire animation sequence. This is achieved by creating correspondent trajectory of each line from each frame and applying global optimization on each trajectory. To realize this target, we present a fully automatic novel approach, which consists of (1) a line matching algorithm, (2) an optimizing algorithm, taking into account both the variations of numbers and lengths of 3D lines in each frame, and (3) a robust tracing method for transferring collections of line segments extracted from the 3D models into individual lines. We evaluate our approach on several animated model sequences to demonstrate its effectiveness in producing line drawing animations with temporal coherence.     

基于单幅折反射全向图的水平直线3维重建

与传统的利用立体视觉原理进行3维重建不同,在研究基于单幅全向图像重建空间水平直线问题的基础上,首先指出基于直线在全向图中的两个像点即可重建该水平直线,然后通过分析和推导空间水平直线在全向成像系统中的成像特点,有效简化了全向图中的水平直线检测;针对现有“四点定位”方法的不足,提出了一种基于“主像点/非主像点”的水平直线重建算法,并详细分析了像点提取精度对直线重建结果的影响。实验表明,在不同的像点提取精度下,对于不同空间水平直线,该重建算法均能取得较好结果。     

Decomposition of complex line drawings with hidden lines for 3D planar-faced manifold object reconstruction

Three-dimensional object reconstruction from a single 2D line drawing is an important problem in computer vision. Many methods have been presented to solve this problem, but they usually fail when the geometric structure of a 3D object becomes complex. In this paper, a novel approach based on a divide-and-conquer strategy is proposed to handle the 3D reconstruction of a planar-faced complex manifold object from its 2D line drawing with hidden lines visible. The approach consists of four steps: 1) identifying the internal faces of the line drawing, 2) decomposing the line drawing into multiple simpler ones based on the internal faces, 3) reconstructing the 3D shapes from these simpler line drawings, and 4) merging the 3D shapes into one complete object represented by the original line drawing. A number of examples are provided to show that our approach can handle 3D reconstruction of more complex objects than previous methods.     

An Exploratory Technique for Coherent Visualization of Time‐varying Volume Data

The selection of an appropriate global transfer function is essential for visualizing time‐varying simulation data. This is especially challenging when the global data range is not known in advance, as is often the case in remote and in‐situ visualization settings. Since the data range may vary dramatically as the simulation progresses, volume rendering using local transfer functions may not be coherent for all time steps. We present an exploratory technique that enables coherent classification of time‐varying volume data. Unlike previous approaches, which require pre‐processing of all time steps, our approach lets the user explore the transfer function space without accessing the original 3D data. This is useful for interactive visualization, and absolutely essential for in‐situ visualization, where the entire simulation data range is not known in advance. Our approach generates a compact representation of each time step at rendering time in the form of ray attenuation functions, which are used for subsequent operations on the opacity and color mappings. The presented approach offers interactive exploration of time‐varying simulation data that alleviates the cost associated with reloading and caching large data sets.     

Energy Aware Color Sets

We present a design technique for colors with the purpose of lowering the energy consumption of the display device. Our approach is based on a screen space variant energy model. The result of our design is a set of distinguishable iso-lightness colors guided by perceptual principles. We present two variations of our approach. One is based on a set of discrete user-named (categorical) colors, which are analyzed according to their energy consumption. The second is based on the constrained continuous optimization of color energy in the perceptually uniform CIELAB color space. We quantitatively compare our two approaches with a traditional choice of colors, demonstrating that we typically save approximately 40 percent of the energy. The color sets are applied to examples from the 2D visualization of nominal data and volume rendering of 3D scalar fields.     

Algorithms for matching 3D line sets

Matching two sets of lines is a basic tool that has applications in many computer vision problems such as scene registration, object recognition, motion estimation, and others. Line sets may be composed of infinitely long lines or finite length line segments. Depending on line lengths, three basic cases arise in matching sets of lines: 1) finite-finite, 2) finite-infinite, and 3) infinite-infinite. Case 2 has not been treated in the literature. For Cases 1 and 3, existing algorithms for matching 3D line sets are not completely satisfactory in that they either solve special situations, or give approximate solutions, or may not converge, or are not invariant with respect to coordinate system transforms. In this paper, we present new algorithms that solve exactly all three cases for the general situation. The algorithms are provably convergent and invariant to coordinate transforms. Experiments with synthetic and real 3D image data are reported.     

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines

In recent years the work on vector field visualization has been concentrated on LIC-based methods. In this paper we propose an alternative solution for the visualization of unsteady flow fields. Our approach is based on the computation of temporal series of correlated images. While other methods are based on pathlines and try to correlate successive images at the pixel level, our approach consists in correlating instantaneous visualizations of the vector field at the streamline level. For each frame a feed forward algorithm computes a set of evenly-spaced streamlines as a function of the streamlines generated for the previous frame. This is achieved by establishing a correspondence between streamlines at successive time steps. A cyclical texture is mapped onto every streamline and textures of corresponding streamlines at different time steps are correlated together so that, during the animation, they move along the streamlines, giving the illusion that the flow is moving in the direction defined by the streamline. Our method gives full control on the image density so that we are able to produce smooth animations of arbitrary density, covering the field of representations from sparse, that is classical streamline-based images, to dense, that is texture-like images.     

A 2-point algorithm for 3D reconstruction of horizontal lines from a single omni-directional image

Reconstruction of 3D scenes with abundant straight line features has many applications in computer vision and robot navigation. Most approaches to this problem involve stereo techniques, in which a solution to the correspondence problem between at least two different images is required. In contrast, 3D reconstruction of straight horizontal lines from a single 2D omni-directional image is studied in this paper. The authors show that, for symmetric non-central catadioptric systems, a 3D horizontal line can be estimated using only two points extracted from a single image of the line. One of the two points is the symmetry point of the image curve of horizontal line, and the other is a generic point on the image curve. This paper improves on several prior works, including horizontal line detection in omni-directional image and line reconstruction from four viewing rays, but is simpler than those methods while being more robust. We evaluate how the precision of feature point extraction can affect line reconstruction accuracy, and discuss preliminary experimental results.     

Efficient and robust 3D line drawings using difference-of-Gaussian

Line drawings are widely used for sketches, animations, and technical illustrations because they are effective and easy to draw. The existing computer-generated lines, such as suggestive contours, apparent ridges, and demarcating curves, adopt the two-pass framework: in the first pass, certain geometric features or properties are extracted or computed in the object space; then in the second pass, the line drawings are rendered by iterating each polygonal face or edge. It is known these approaches are very sensitive to the mesh quality, and usually require appropriate preprocessing operations (e.g. smoothing, remeshing, etc.) to the input meshes. This paper presents a simple yet robust approach to generate view-dependent line drawings for 3D models. Inspired by the image edge detector, we compute the difference-of-Gaussian of illumination on the 3D model. With moderate assumption, we show all the expensive computations can be done in the pre-computing stage. Our method naturally integrates object- and image-spaces in that we compute the geometric features in the object space and then adopt a simple fragment shader to render the lines in the image space. As a result, our algorithm is more efficient than the existing object-space approaches, since the lines are generated in a single pass without iterating the mesh edges/faces. Furthermore, our method is more flexible and robust than the existing algorithms in that it does not require the preprocessing on the input 3D models. Finally, the difference-of-Gaussian operator can be extended to the anisotropic setting guided by local geometric features. The promising experimental results on a wide range of real-world models demonstrate the effectiveness and robustness of our method.     

What the back of the object looks like: 3D reconstruction from line drawings without hidden lines

The human vision system can interpret a single 2D line drawing as a 3D object without much difficulty even if the hidden lines of the object are invisible. Many reconstruction methods have been proposed to emulate this ability, but they cannot recover the complete object if the hidden lines of the object are not shown. This paper proposes a novel approach to reconstructing a complete 3D object, including the shape of the back of the object, from a line drawing without hidden lines. First, we develop theoretical constraints and an algorithm for the inference of the topology of the invisible edges and vertices of an object. Then we present a reconstruction method based on perceptual symmetry and planarity of the object. We show a number of examples to demonstrate the success of our approach.     

3D Reconstruction from 2D Line Drawings only with Visible Vertices and Edges

The human vision system can reconstruct a 3D object easily from single 2D line drawings even if the hidden lines of the object are invisible. Now, there are many methods have emulated this ability, but when the hidden lines of the object are invisible, these methods cannot reconstruct a complete 3D object. Therefore, we put forward a new algorithm to settle this hard problem. Our approach consists of two steps： （1） infer the invisible vertices and edges to complete the line drawing, （2） propose a vertex-based optimization method to reconstruct a 3D object.     

Combined Vector Field Approach for 2D and 3D Arbitrary Twice Differentiable Curved Path Following with Constrained UAVs

Path following is an essential requirement for unmanned aerial vehicles (UAVs). Path following problems of 2-dimensional (2D) straight lines and planar circles have been studied and many approaches have been proposed during the past few years. In this paper the problem of following arbitrary twice differentiable curved paths in both 2D and 3D spaces is investigated. Based on the Helmholtz theorem, respective combined guidance vector fields for any given 2D and 3D arbitrary twice differentiable curved paths are constructed by trading off the respective conservative and solenoidal vector fields making use of the defined distance between the UAV and the desired path. Conditions for the two combined vector fields to be globally feasible are given. UAV input constraints and constant wind disturbance are assumed to be present. By tracking the constructed combined vector fields, a saturated course rate controller for 2D curved path following and a jointly saturated course rate and climb rate controller for 3D curved path following are designed. The Lyapunov stability of the saturated course rate controller for 2D curved path following is proved. Numerical simulations are given to assess the proposed approach.