A General Multi-step Algorithm for Voxel Traversing Along a Line

Traversing voxels along a three dimensional (3D) line is one of the most fundamental algorithms for voxel‐based applications. This paper presents a new 6‐connectivity integer algorithm for this task. The proposed algorithm accepts voxels having different sizes in x, y and z directions. To explain the idea of the proposed approach, a 2D algorithm is firstly considered and then extended in 3D. This algorithm is a multi‐step as up to three voxels may be added in one iteration. It accepts both integer and floating‐point input. The new algorithm was compared to other popular voxel traversing algorithms. Counting the number of arithmetic operations showed that the proposed algorithm requires the least amount of operations per traversed voxel. A comparison of spent CPU time using either integer or floating‐point arithmetic confirms that the proposed algorithm is the most efficient. This algorithm is simple, and in compact form which also makes it attractive for hardware implementation.     

Generalized Helicoids for Modeling Hair Geometry

In computer graphics, modeling the geometry of hair and hair‐like patterns such as grass and fur remains a significant challenge. Hair strands can exist in an extensive variety of arrangements and the choice of an appropriate representation for tasks such as hair synthesis, fitting, editing, or reconstruction from samples, is non‐trivial. To support such applications we present a novel mathematical representation of hair based on a class of minimal surfaces called generalized helicoids. This representation allows us to characterize the geometry of a single hair strand, as well as of those in its vicinity, by three intuitive curvature parameters and an elevation angle. We introduce algorithms for fitting piecewise generalized helicoids to unparameterized hair strands, and for interpolating hair between these fits. We showcase several applications of this representation including the synthesis of different hair geometries, wisp generation, hair interpolation from samples and hair‐style parametrization and reconstruction from real hair data.     

Uncertainty‐Aware Exploration of Continuous Parameter Spaces Using Multivariate Prediction

Systems projecting a continuous n‐dimensional parameter space to a continuous m‐dimensional target space play an important role in science and engineering. If evaluating the system is expensive, however, an analysis is often limited to a small number of sample points. The main contribution of this paper is an interactive approach to enable a continuous analysis of a sampled parameter space with respect to multiple target values. We employ methods from statistical learning to predict results in real‐time at any user‐defined point and its neighborhood. In particular, we describe techniques to guide the user to potentially interesting parameter regions, and we visualize the inherent uncertainty of predictions in 2D scatterplots and parallel coordinates. An evaluation describes a real‐world scenario in the application context of car engine design and reports feedback of domain experts. The results indicate that our approach is suitable to accelerate a local sensitivity analysis of multiple target dimensions, and to determine a sufficient local sampling density for interesting parameter regions.     

Fast Extraction of High‐quality Crease Surfaces for Visual Analysis

We present a novel algorithm for the efficient extraction and visualization of high‐quality ridge and valley surfaces from numerical datasets. Despite their rapidly increasing popularity in visualization, these so‐called crease surfaces remain challenging to compute owing to their strongly nonlinear and non‐orientable nature, and their complex boundaries. In this context, existing meshing techniques require an extremely dense sampling that is computationally prohibitive. Our proposed solution intertwines sampling and meshing steps to yield an accurate approximation of the underlying surfaces while ensuring the geometric quality of the resulting mesh. Using the computation power of the GPU, we propose a fast, parallel method for sampling. Additionally, we present a new front propagation meshing strategy that leverages CPU multiprocessing. Results are shown for synthetic, medical and fluid dynamics datasets.     

Implicit Brushes for Stylized Line‐based Rendering

We introduce a new technique called Implicit Brushes to render animated 3D scenes with stylized lines in realtime with temporal coherence. An Implicit Brush is defined at a given pixel by the convolution of a brush footprint along a feature skeleton; the skeleton itself is obtained by locating surface features in the pixel neighborhood. Features are identified via image‐space fitting techniques that not only extract their location, but also their profile, which permits to distinguish between sharp and smooth features. Profile parameters are then mapped to stylistic parameters such as brush orientation, size or opacity to give rise to a wide range of line‐based styles.     

Efficient Parallel Vectors Feature Extraction from Higher‐Order Data

The parallel vectors (PV) operator is a feature extraction approach for defining line‐type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher‐order data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higher‐order PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPU‐based prototype. We apply our method to higher‐order data obtained from discontinuous Galerkin fluid simulations.     

An Illustrative Visualization Framework for 3D Vector Fields

Most 3D vector field visualization techniques suffer from the problem of visual clutter, and it remains a challenging task to effectively convey both directional and structural information of 3D vector fields. In this paper, we present a novel visualization framework that combines the advantages of clustering methods and illustrative rendering techniques to generate a concise and informative depiction of complex flow structures. Given a 3D vector field, we first generate a number of streamlines covering the important regions based on an entropy measurement. Then we decompose the streamlines into different groups based on a categorization of vector information, wherein the streamline pattern in each group is ensured to be coherent or nearly coherent. For each group, we select a set of representative streamlines and render them in an illustrative fashion to enhance depth cues and succinctly show local flow characteristics. The results demonstrate that our approach can generate a visualization that is relatively free of visual clutter while facilitating perception of salient information of complex vector fields.     

Analytic Curve Skeletons for 3D Surface Modeling and Processing

We present a new curve skeleton model designed for surface modeling and processing. This skeleton is defined as the geometrical integration of a piecewise harmonic parameterization defined over a disk‐cylinder surface decomposition. This decomposition is computed using a progressive Region Graph reduction based on both geometric and topological criteria which can be iteratively optimized to improve region boundaries. The skeleton has an analytical form with regularity inherited from the surface one. Such a form offers well‐defined surface‐skeleton and skeleton‐surface projections. The resulting skeleton satisfies quality criteria which are relevant for skeleton‐based modeling and processing. We propose applications that benefit from our skeleton model, including local thickness editing, inset surface creation for shell mapping, as well as a new mid‐scale feature preserving smoothing.     

An Evaluation of Glyph Perception for Real Symmetric Traceless Tensor Properties

A perceptual study of four tensor glyphs for symmetric, real, traceless tensors was performed. Each glyph encodes three properties of the system: Orientation, uniaxiality (alignment along the direction of orientation), and biaxiality (alignment along a vector orthogonal to the orientation). Thirty users over two studies were asked to identify these three properties for each glyph type under a variety of permutations in order to evaluate the effectiveness of visually communicating the properties; response time was also measured. We discuss the significant differences found between the methods as guidance to the use of these glyphs for traceless tensor visualization.     

Surface Patches from Unorganized Space Curves

Recent 3D sketch tools produce networks of three‐space curves that suggest the contours of shapes. The shapes may be non‐manifold, closed three‐dimensional, open two‐dimensional, or mixed. We describe a system that automatically generates intuitively appealing piecewise‐smooth surfaces from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both the automatic and the semi‐automatic parts of the system use a linear algebra representation of the set of surface patches to track the topology. On complicated inputs from ILoveSketch [ [BBS08] ], our system allows the user to build the desired surface with just a few mouse‐clicks.     

Pathway Preserving Representation of Metabolic Networks

Improvements in biological data acquisition and genomes sequencing now allow to reconstruct entire metabolic networks of many living organisms. The size and complexity of these networks prohibit manual drawing and thereby urge the need of dedicated visualization techniques. An efficient representation of such a network should preserve the topological information of metabolic pathways while respecting biological drawing conventions. These constraints complicate the automatic generation of such visualization as it raises graph drawing issues. In this paper we propose a method to lay out the entire metabolic network while preserving the pathway information as much as possible. That method is flexible as it enables the user to define whether or not node duplication should be performed, to preserve or not the network topology. Our technique combines partitioning, node placement and edge bundling to provide a pseudo‐orthogonal visualization of the metabolic network. To ease pathway information retrieval, we also provide complementary interaction tools that emphasize relevant pathways in the entire metabolic context.     

Goal‐based Caustics

We propose a novel system for designing and manufacturing surfaces that produce desired caustic images when illuminated by a light source. Our system is based on a nonnegative image decomposition using a set of possibly overlapping anisotropic Gaussian kernels. We utilize this decomposition to construct an array of continuous surface patches, each of which focuses light onto one of the Gaussian kernels, either through refraction or reflection. We show how to derive the shape of each continuous patch and arrange them by performing a discrete assignment of patches to kernels in the desired caustic. Our decomposition provides for high fidelity reconstruction of natural images using a small collection of patches. We demonstrate our approach on a wide variety of caustic images by manufacturing physical surfaces with a small number of patches.     

Curve Density Estimates

In this work, we present a technique based on kernel density estimation for rendering smooth curves. With this approach, we produce uncluttered and expressive pictures, revealing frequency information about one, or, multiple curves, independent of the level of detail in the data, the zoom level, and the screen resolution. With this technique the visual representation scales seamlessly from an exact line drawing, (for low‐frequency/low‐complexity curves) to a probability density estimate for more intricate situations. This scale‐independence facilitates displays based on non‐linear time, enabling high‐resolution accuracy of recent values, accompanied by long historical series for context. We demonstrate the functionality of this approach in the context of prediction scenarios and in the context of streaming data.     

Detecting Symmetries and Curvilinear Arrangements in Vector Art

Understanding symmetries and arrangements in existing content is the first step towards providing higher level content aware editing capabilities. Such capabilities may include edits that both preserve existing structure as well as synthesize entirely new structures based on the extracted pattern rules. In this paper we show how to detect regular symmetries and arrangement along curved segments in vector art. We determine individual elements in the art by using the transformation similarity for sequences of sample points on the input curves. Then we detect arrangements of those elements along an arbitrary curved path. We can un-warp the arrangement path to detect symmetries near the path. We introduce novel applications inform of editing elements that are arranged along a curved path. This includes their sliding along the path, changing of their spacing, or their scale. We also allow the user to brush the elements that the system recognized along new paths.     

Investigative Visual Analysis of Global Terrorism

Recent increases in terrorist activity around the world have made analyzing and understanding such activities more critical than ever. With the help of organizations such as the National Center for the Study of Terrorism and Responses to Terrorism (START), we now have detailed historical information on each terrorist event around the world since 1970. However, due to the size and complexity of the data, identifying terrorists' patterns and trends has been difficult. To better enable investigators in understanding terrorist activities, we propose a visual analytical system that focuses on depicting one of the most fundamental concepts in investigative analysis, the five W's (who, what, where, when, and why). Views in our system are highly correlated, and each represents one of the W's. With this approach, an investigator can interactively explore terrorist activities efficiently and discover reasons of attacks (why) by identifying patterns temporally (when), geo‐spatially (where), between multiple terrorist groups (who), and across different methods or modes of attacks (what). By coupling a global perspective with the details gleaned from asking these five questions, the system allows analysts to think both tactically and strategically.     

Interpolatory and Mixed Loop Schemes

This paper presents a new interpolatory Loop scheme and an unified and mixed interpolatory and approximation subdivision scheme for triangular meshes. The former which is C¹ continuous as same as the modified Butterfly scheme has better effect in some complex models. The latter can be used to solve the “popping effect” problem when switching between meshes at different levels of resolution. The scheme generates surfaces coincident with the Loop subdivision scheme in the limit condition having the coefficient k equal 0. When k equal 1, it will be changed into a new interpolatory subdivision scheme. Eigen‐structure analysis demonstrates that subdivision surfaces generated using the new scheme are C¹ continuous. All these are achieved only by changing the value of a parameter k. The method is a completely simple one without constructing and solving equations. It can achieve local interpolation and solve the “popping effect” problem which are the method's advantages over the modified Butterfly scheme.     

Visualization of vessel movements

We propose a geographical visualization to support operators of coastal surveillance systems and decision making analysts to get insights in vessel movements. For a possibly unknown area, they want to know where significant maritime areas, like highways and anchoring zones, are located. We show these features as an overlay on a map. As source data we use AIS data: Many vessels are currently equipped with advanced GPS devices that frequently sample the state of the vessels and broadcast them. Our visualization is based on density fields that are derived from convolution of the dynamic vessel positions with a kernel. The density fields are shown as illuminated height maps. Combination of two fields, with a large and small kernel provides overview and detail. A large kernel provides an overview of area usage revealing vessel highways. Details of speed variations of individual vessels are shown with a small kernel, highlighting anchoring zones where multiple vessels stop. Besides for maritime applications we expect that this approach is useful for the visualization of moving object data in general.     

Energy-Based Image Deformation

We present a general approach to shape deformation based on energy minimization, and applications of this approach to the problems of image resizing and 2D shape deformation. Our deformation energy generalizes that found in the prior art, while still admitting an efficient algorithm for its optimization. The key advantage of our energy function is the flexibility with which the set of "legal transformations" may be expressed; these transformations are the ones which are not considered to be distorting. This flexibility allows us to pose the problems of image resizing and 2D shape deformation in a natural way and generate minimally distorted results. It also allows us to strongly reduce undesirable foldovers or self-intersections. Results of both algorithms demonstrate the effectiveness of our approach.     

Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram

We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT) . Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD) , defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation-based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd -tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O ( m log n ), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi-Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state-of-art approaches.