Abstract The graphical depiction of uncertainty information is emerging as a problem of great importance. Scientific data sets are not considered complete without indications of error, accuracy, or levels of confidence. The visual portrayal of this information is a challenging task. This work takes inspiration from graphical data analysis to create visual representations that show not only the data value, but also important characteristics of the data including uncertainty. The canonical box plot is reexamined and a new hybrid summary plot is presented that incorporates a collection of descriptive statistics to highlight salient features of the data. Additionally, we present an extension of the summary plot to two dimensional distributions. Finally, a use‐case of these new plots is presented, demonstrating their ability to present high‐level overviews as well as detailed insight into the salient features of the underlying data distribution.

Many courses on the history of computing are designed for a general student audience, and as such, include fewer technical details than one might find in a typical CS course. While this approach is appropriate in some contexts, it risks losing the interest of the students who could perhaps benefit most from the subject-namely, future computer scientists. This paper describes a technically-oriented History of Computing course which we taught at the University of Utah in 2008. Like other History of Computing courses, ours included a significant amount of writing and discussion. However, inasmuch as our course was created specifically for CS students, we also incorporated several "hands-on" programming exercises and demonstrations, giving students actual experience with the computing environments of the past. Students and faculty alike have responded enthusiastically to this dual-faceted approach.

Abstract This work introduces a technique for interactive walk‐throughs of non‐photorealistically rendered (NPR) scenes using three‐dimensional (3D) line primitives to define architectural features of the model, as well as indicate textural qualities. Line primitives are not typically used in this manner in favour of texture mapping techniques which can encapsulate a great deal of information in a single texture map, and take advantage of GPU optimizations for accelerated rendering. However, texture mapped images may not maintain the visual quality or aesthetic appeal that is possible when using 3D lines to simulate NPR scenes such as hand‐drawn illustrations or architectural renderings. In addition, line textures can be modified interactively, for instance changing the sketchy quality of the lines. The technique introduced here extracts feature edges from a model, and using these edges, generates a reduced set of line textures which indicate material properties while maintaining interactive frame rates. A clipping algorithm is presented to enable 3D lines to reside only in the interior of the 3D model without exposing the underlying triangulated mesh. The resulting system produces interactive illustrations with high visual quality that are free from animation artifacts.

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. To addresses the difficulties mentioned heretofore, we present the Sliding Windows Algorithm (SWA), a new blossoming based algorithm for the multiplication of two B-spline curves, two B-spline surfaces, or any two general multivariate B-splines.

Radial visualization, or the practice of displaying data in a circular or elliptical pattern, is an increasingly common technique in information visualization research. In spite of its prevalence, little work has been done to study this visualization paradigm as a methodology in its own right. We provide a historical review of radial visualization, tracing it to its roots in centuries-old statistical graphics. We then identify the types of problem domains to which modern radial visualization techniques have been applied. A taxonomy for radial visualization is proposed in the form of seven design patterns encompassing nearly all recent works in this area. From an analysis of these patterns, we distill a series of design considerations that system builders can use to create new visualizations that address aspects of the design space that have not yet been explored. It is hoped that our taxonomy will provide a framework for facilitating discourse among researchers and stimulate the development of additional theories and systems involving radial visualization as a distinct design metaphor.

Surveys and opinion polls are extremely popular in the media, especially in the months preceding a general election. However, the available tools for analyzing poll results often require specialized training. Hence, data analysis remains out of reach for many casual computer users. Moreover, the visualizations used to communicate the results of surveys are typically limited to traditional statistical graphics like bar graphs and pie charts, both of which are fundamentally noninteractive. We present a simple interactive visualization that allows users to construct queries on large tabular data sets, and view the results in real time. The results of two separate user studies suggest that our interface lowers the learning curve for naive users, while still providing enough analytical power to discover interesting correlations in the data.

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines, is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. We present the Sliding Windows Algorithm (SWA), a new blossoming based algorithm for B-spline multiplication that addresses the difficulties mentioned heretofore.

Symbolic computation of NURBS plays an important role in many areas of NURBS-based geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider include zero curvatures and critical curvatures of plane curves, various ruled surfaces related to space curves, and point/curve bisectors and curve/curve bisectors.

This paper introduces the rational forward difference operator for differential computation on a rational Bezier patch based on its control mesh. With this rational version of the forward difference operator, and by ignoring the appropriate dependent (on lower order derivatives) terms of various derivatives, the derivatives themselves have the same expressions as their polynomial counterparts; the curvature and torsion, and the first and second fundamental forms, all have very similar expressions as those equations from classical differential geometry. This new approach also allows straightforward generalization to higher dimensional rational Bezier patches, the special co-dimension 1 case of which is treated with the result of the first and second fundamental forms.

We present an approach for automatically generating complete process plans, including fixturing and CNC code, from high level shape feature part descriptions. The demonstration system is targeted at a broadly useful class of machined prismatic parts which includes sculpted exterior profiles and features requiring four and five axis indexing for manufacture. The approach introduces a set of process plan templates which are schemas for a family of process plans embodying a variety of fixturing strategies. The knowledge built into the process plan templates can adapt existing part hole features to be used for fixturing, can modify the workpiece to enable fixturing, and can create custom fixturing components for stages of the process plan. The process plan template system automatically transforms a given part design into a complete process plan. The user can provide optional guidance for this transformation and also can edit the resulting process plan to further extend the usefulness of this approach through customization. Domain knowledge in the process plan then automatically generates CNC code for a target machining center. This research is implemented as an experimental subsystem within our Alpha 1 modeling and manufacturing testbed environment, and has been used to design and manufacture working components for outside client applications.

A rendering is an abstraction that favors, preserves, or even emphasizes some qualities while sacrificing, suppressing, or omitting other characteristics that are not the focus of attention.Most computer graphics rendering activities have been concerned with photorealism, i.e., trying to emulate an image that looks like a highquality photograph.This laudable goal is useful and appropriate in many applications, but not in technical illustration where elucidation of structure and technical information is the preeminent motivation.This calls for a different kind of abstraction in which technical communication is central, but art and appearance are still essential instruments toward this end.Work that has been done on computer generated technical illustrations has focused on static images, and has not included all of the techniques used to hand draw technical illustrations.A paradigm for the display of technical illustrations in a dynamic environment is presented.This display environment includes all of the benefits of computer generated technical illustrations, such as a clearer picture of shape, structure, and material composition than traditional computer graphics methods.It also includes the three-dimensional interactive strength of modem display systems.This is accomplished by using new algorithms for real time drawing of silhouette curves, algorithms which solve a number of the problems inherent in previous methods.We incorporate current non-photorealistic lighting methods, and augment them with new shadowing algorithms based on accepted techniques used by artists and studies carried out in human perception.This paper, all of the images, and a mpeg video clip are available at http

We present a solution to the general problem of characterizing shadows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a spline function.Studying generalized prism-like constructions generated by the emitter and the occluder in a fourdimensional (shadow) space reveals a simpler intrinsic structure of the shadow as compared to the more complicated 2D projection onto a receiver.A closed form expression for the spline shadow irradiance function is derived by twice applying Stokes' theorem to reduce an evaluation over a 4D domain to an explicit formula involving only 2D faces on the receiver, derived from the scene geometry.This leads to a straightforward computational algorithm and an interactive implementation.Moreover, this approach can be extended to scenes involving multiple emitters and occluders, as well as curved emitters, occluders, and receivers.Spline functions are constructed from these prism-like objects.We call them generalized polyhedral splines because they extend the classical polyhedral splines to include curved boundaries and a density function.The approach can be applied to more general problems such as some of those occurring in radiosity, and other related topics.

Article Free Access Share on Solid modeling(Panel Session) Authors: David Gossard MIT MITView Profile , Richard Riesenfeld University of Utah University of UtahView Profile , Herbert Voelcker University of Rochester University of RochesterView Profile , Tony Woo University of Michigan University of MichiganView Profile , Chairman: Ronald N. Goldman Control Data Corporation Control Data CorporationView Profile Authors Info & Claims SIGGRAPH '83: Proceedings of the 10th annual conference on Computer graphics and interactive techniquesJuly 1983 Pages 163–165https://doi.org/10.1145/800059.801146Published:01 July 1983Publication History 0citation349DownloadsMetricsTotal Citations0Total Downloads349Last 12 Months3Last 6 weeks0 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 SiteeReaderPDF

Two algorithms for parametric piecewise polynomial evaluation and generation are described. The mathematical development of these algorithms is shown to generalize to new algorithms for obtaining curve and surface intersections and for the computer display of parametric curves and surfaces.

Abstract The design and implementation of a symbolic input end computation package and its application to the development of several new surface interpolation schemes are described. Capabilities such as the composition of operators and symbolic differentiation have been incorporated into the system. This allows, in particular, the specification of Boolean sum projectors. The new schemes which have been implemented include an interpolant to randomly spaced data and a 'shape operator1 which has quadratic precision.

The accompanying film shows some general sessions of working with an interactive graphics system to design free-form curves and surfaces. In particular, it demonstrates the use of a very general B-spline curve package that allows the user to specify desired attributes like degree, shape, type of parametrization, and periodicity. Other schemes that show the use of tension as a parameter in design will ge presented.

The m th degree Bernstein polynomial approximation to a function ƒ defined over [0, 1] is Σ m μ =0 ƒ( μ / m ) φ μ ( s ), where the weights φ μ ( s ) are binomial density functions. The Bernstein approximations inherit many of the global characteristics of ƒ, like monotonicity and convexity, and they always are at least as “smooth” as ƒ, where “smooth” refers to the number of undulations, the total variation, and the differentiability class of ƒ. Historically, their relatively slow convergence in the L ∞ -norm has tended to discourage their use in practical applications. However, in a large class of problems the smoothness of an approximating function is of greater importance than closeness of fit. This is especially true in connection with problems of computer-aided geometric design of curves and surfaces where aesthetic criteria and the intrinsic properties of shape are major considerations. For this latter class of problems, P. Bézier of Renault has successfully exploited the properties of parametric Bernstein polynomials. The purpose of this paper is to analyze the Bézier techniques and to explore various extensions and generalizations. In a sequel, the authors consider the extension of the results contained herein to free-form curve and surface design using polynomial splines . These B-spline methods have several advantages over the techniques described in the present paper.