Correlation analysis can reveal the complex relationships that often exist among the variables in multivariate data. However, as the number of variables grows, it can be difficult to gain a good understanding of the correlation landscape and important intricate relationships might be missed. We previously introduced a technique that arranged the variables into a 2D layout, encoding their pairwise correlations. We then used this layout as a network for the interactive ordering of axes in parallel coordinate displays. Our current work expresses the layout as a correlation map and employs it for visual correlation analysis. In contrast to matrix displays where correlations are indicated at intersections of rows and columns, our map conveys correlations by spatial proximity which is more direct and more focused on the variables in play. We make the following new contributions, some unique to our map: (1) we devise mechanisms that handle both categorical and numerical variables within a unified framework, (2) we achieve scalability for large numbers of variables via a multi-scale semantic zooming approach, (3) we provide interactive techniques for exploring the impact of value bracketing on correlations, and (4) we visualize data relations within the sub-spaces spanned by correlated variables by projecting the data into a corresponding tessellation of the map.

Although the euclidean distance does well in measuring data distances within high-dimensional clusters, it does poorly when it comes to gauging intercluster distances. This significantly impacts the quality of global, low-dimensional space embedding procedures such as the popular multidimensional scaling (MDS) where one can often observe nonintuitive layouts. We were inspired by the perceptual processes evoked in the method of parallel coordinates which enables users to visually aggregate the data by the patterns the polylines exhibit across the dimension axes. We call the path of such a polyline its structure and suggest a metric that captures this structure directly in high-dimensional space. This allows us to better gauge the distances of spatially distant data constellations and so achieve data aggregations in MDS plots that are more cognizant of existing high-dimensional structure similarities. Our biscale framework distinguishes far-distances from near-distances. The coarser scale uses the structural similarity metric to separate data aggregates obtained by prior classification or clustering, while the finer scale employs the appropriate euclidean distance.

The navigation of high-dimensional data spaces remains challenging, making multivariate data exploration difficult. To be effective and appealing for mainstream application, navigation should use paradigms and metaphors that users are already familiar with. One such intuitive navigation paradigm is interactive route planning on a connected network. We have employed such an interface and have paired it with a prominent high-dimensional visualization paradigm showing the N-D data in undistorted raw form: parallel coordinates. In our network interface, the dimensions form nodes that are connected by a network of edges representing the strength of association between dimensions. A user then interactively specifies nodes/edges to visit, and the system computes an optimal route, which can be further edited and manipulated. In our interface, this route is captured by a parallel coordinate data display in which the dimension ordering is configured by the specified route. Our framework serves both as a data exploration environment and as an interactive presentation platform to demonstrate, explain, and justify any identified relationships to others. We demonstrate our interface within a business scenario and other applications.

Abstract Illustrative parallel coordinates (IPC) is a suite of artistic rendering techniques for augmenting and improving parallel coordinate (PC) visualizations. IPC techniques can be used to convey a large amount of information about a multidimensional dataset in a small area of the screen through the following approaches: (a) edge‐bundling through splines; (b) visualization of “branched ” clusters to reveal the distribution of the data; (c) opacity‐based hints to show cluster density; (d) opacity and shading effects to illustrate local line density on the parallel axes; and (e) silhouettes, shadows and halos to help the eye distinguish between overlapping clusters. Thus, the primary goal of this work is to convey as much information as possible in a manner that is aesthetically pleasing and easy to understand for non‐experts.

Professional designers and artists are quite cognizant of the rules that guide the design of effective color palettes, from both aesthetic and attention-guiding points of view. In the field of visualization, however, the use of systematic rules embracing these aspects has received less attention. The situation is further complicated by the fact that visualization often uses semi-transparencies to reveal occluded objects, in which case the resulting color mixing effects add additional constraints to the choice of the color palette. Color design forms a crucial part in visual aesthetics. Thus, the consideration of these issues can be of great value in the emerging field of illustrative visualization. We describe a knowledge-based system that captures established color design rules into a comprehensive interactive framework, aimed to aid users in the selection of colors for scene objects and incorporating individual preferences, importance functions, and overall scene composition. Our framework also offers new knowledge and solutions for the mixing, ordering and choice of colors in the rendering of semi-transparent layers and surfaces. All design rules are evaluated via user studies, for which we extend the method of conjoint analysis to task-based testing scenarios. Our framework's use of principles rooted in color design with application for the illustration of features in pre-classified data distinguishes it from existing systems which target the exploration of continuous-range density data via perceptual color maps.

Volumetric Subdivision (VS) is a powerful paradigm that enables volumetric sculpting and realistic volume deformations that give rise to the concept of "virtual clay". In VS, volumes are commonly represented as a space-filling set of deformed polyhedra, which can be further decomposed into a mesh of tetrahedra for rendering. Images can then be generated via tetrahedral projection or raycasting. A current shortcoming in VS-based operations is the need for a very high level of subdivision to represent fine detail in the mesh and to obtain a high-fidelity visualization. However, we have discovered that the subdivision process itself can be closely simulated with radial basis functions (RBFs), making it possible to replace the finer subdivision levels by a coarser aggregation of RBF kernels. This reduction to a simplified assembly of RBFs subsequently enables interactive rendering of volumetric subdivision shapes within a GPU-based volume splatting framework.

Radial Basis Functions (RBFs) have become a popular rendering primitive, both in surface and in volume rendering. This paper focuses on volume visualization, giving rise to 3D kernels. RBFs are especially convenient for the representation of scattered and irregularly distributed point samples, where the RBF kernel is used as a blending function for the space in between samples. Common representations employ radially symmetric RBFs, and various techniques have been introduced to render these, also with efficient implementations on programmable graphics hardware (GPUs). In this paper, we extend the existing work to more generalized, ellipsoidal RBF kernels, for the rendering of scattered volume data. We devise a post-shaded kernel-centric rendering approach, specifically designed to run efficiently on GPUs, and we demonstrate our renderer using datasets from subdivision volumes and computational science.

We present a novel surface reconstruction algorithm that can recover high-quality surfaces from noisy and defective data sets without any normal or orientation information. A set of new techniques is introduced to afford extra noise tolerability, robust orientation alignment, reliable outlier removal, and satisfactory feature recovery. In our algorithm, sample points are first organized by an octree. The points are then clustered into a set of monolithically singly-oriented groups. The inside/outside orientation of each group is determined through a robust voting algorithm. We locally fit an implicit quadric surface in each octree cell. The locally fitted implicit surfaces are then blended to produce a signed distance field using the modified Shepard's method. We develop sophisticated iterative fitting algorithms to afford improved noise tolerance both in topology recognition and geometry accuracy. Furthermore, this iterative fitting algorithm, coupled with a local model selection scheme, provides a reliable sharp feature recovery mechanism even in the presence of bad input.

Subdivision has gained popularity in computer graphics and shape modeling during the past two decades, yet volumetric subdivision has received much less attention. In this paper, we develop a new subdivision scheme, which can interpolate all of the initial control points in 3D and generate a continuous volume in the limit. We devise a set of solid subdivision rules to facilitate a simple subdivision procedure. The conversion between the subdivided mesh and a simplicial complex is straightforward and effective, which can be directly utilized in solid meshing, finite element simulation, and other numerical processes. In principle, our solid subdivision process is a combination of simple linear interpolations in 3D. Affine operations of neighboring control points produce new control points in the next level, yet inherit the original control points and achieve the interpolatory effect. A parameter is offered to control the tension between control points. The interpolatory property of our solid subdivision offers many benefits, which are desirable in many design applications and physics simulations, including intuitive manipulation on control points and ease of constraint enforcement in numerical procedures. We outline a proof that can guarantee the convergence and C/sup 1/ continuity of our volumetric subdivision and limit volumes in regular cases. In addition to solid subdivision, we derive special rules to generate C/sup 1/ surfaces as B-reps and to model shapes of non-manifold topology. Several examples demonstrate the ability of our subdivision to handle complex manifolds easily. Numerical experiments and future research suggestions for extraordinary cases are also presented.

Article Share on Virtual clay: a real-time sculpting system with haptic toolkits Authors: Kevin T. McDonnell State Univ. of New York, Stony Brook State Univ. of New York, Stony BrookView Profile , Hong Qin State Univ. of New York, Stony Brook State Univ. of New York, Stony BrookView Profile , Robert A. Wlodarczyk State Univ. of New York, Stony Brook State Univ. of New York, Stony BrookView Profile Authors Info & Claims I3D '01: Proceedings of the 2001 symposium on Interactive 3D graphicsMarch 2001 Pages 179–190https://doi.org/10.1145/364338.364395Online:01 March 2001Publication History 92citation1,570DownloadsMetricsTotal Citations92Total Downloads1,570Last 12 Months38Last 6 weeks7 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

This paper presents a sculptured solid modeling system founded upon dynamic Catmull-Clark subdivision-based solids of arbitrary topology. Our primary contribution is that we integrate the geometry of sculptured free-form solids with the powerful physics-based modeling framework by augmenting pure geometric entities with material properties such as mass, damping, and stiffness distributions and with physical behaviors such as elasticity, plasticity, and natural deformation under external forces. Our novel dynamic model of free-form solids frees users from having to deal with low-level central point operations and permits them to interact with subdivision-based virtual clay in a more natural and intuitive fashion via "forces".

We present CEASAR, a centerline extraction algorithm that delivers smooth, accurate and robust results. Centerlines are needed for accurate measurements of length along winding tubular structures. Centerlines are also required in automatic virtual navigation through human organs, such as the colon or the aorta, as they are used to control movement and orientation of the virtual camera. We introduce a concise but general definition of a centerline, and provide an algorithm that finds the centerline accurately and rapidly. Our algorithm is provably correct for general geometries. Our solution is fully automatic, which frees the user from having to engage in data preprocessing. For a number of test datasets, we show the smooth and accurate centerlines computed by our CEASAR algorithm on a single 194 MHz MIPS R10000 CPU within five minutes.