Sketchy rendering for information visualization

We present and evaluate a framework for constructing sketchy style information visualizations that mimic data graphics drawn by hand. We provide an alternative renderer for the Processing graphics environment that redefines core drawing primitives including line, polygon and ellipse rendering. These primitives allow higher-level graphical features such as bar charts, line charts, treemaps and node-link diagrams to be drawn in a sketchy style with a specified degree of sketchiness. The framework is designed to be easily integrated into existing visualization implementations with minimal programming modification or design effort. We show examples of use for statistical graphics, conveying spatial imprecision and for enhancing aesthetic and narrative qualities of visual- ization. We evaluate user perception of sketchiness of areal features through a series of stimulus-response tests in order to assess users’ ability to place sketchiness on a ratio scale, and to estimate area. Results suggest relative area judgment is compromised by sketchy rendering and that its influence is dependent on the shape being rendered. They show that degree of sketchiness may be judged on an ordinal scale but that its judgement varies strongly between individuals. We evaluate higher-level impacts of sketchiness through user testing of scenarios that encourage user engagement with data visualization and willingness to critique visualization de- sign. Results suggest that where a visualization is clearly sketchy, engagement may be increased and that attitudes to participating in visualization annotation are more positive. The results of our work have implications for effective information visualization design that go beyond the traditional role of sketching as a tool for prototyping or its use for an indication of general uncertainty

Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.Comment: 15 page

A model problem for conformal parameterizations of the Einstein constraint equations

We investigate the possibility that the conformal and conformal thin sandwich (CTS) methods can be used to parameterize the set of solutions of the vacuum Einstein constraint equations. To this end we develop a model problem obtained by taking the quotient of certain symmetric data on conformally flat tori. Specializing the model problem to a three-parameter family of conformal data we observe a number of new phenomena for the conformal and CTS methods. Within this family, we obtain a general existence theorem so long as the mean curvature does not change sign. When the mean curvature changes sign, we find that for certain data solutions exist if and only if the transverse-traceless tensor is sufficiently small. When such solutions exist, there are generically more than one. Moreover, the theory for mean curvatures changing sign is shown to be extremely sensitive with respect to the value of a coupling constant in the Einstein constraint equations.Comment: 40 pages, 4 figure

Development of integrated programs for Aerospace-vehicle Design (IPAD): Product program management systems

The Integrated Programs for Aerospace Vehicle Design (IPAD) is a computing system to support company-wide design information processing. This document presents a brief description of the management system used to direct and control a product-oriented program. This document, together with the reference design process (CR 2981) and the manufacture interactions with the design process (CR 2982), comprises the reference information that forms the basis for specifying IPAD system requirements

A study of electronic packages environmental control systems and vehicle thermal systems integration Quarterly report, Nov. 1966 - Jan. 1967

Heat balances of combined astrionic equipment and thermal conditioning subsystem of environmental control system, and vehicle configuration

Oscillatory approach to the singularity in vacuum T2T^2 symmetric spacetimes

A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.Comment: 2 pages submitted to the Ninth Marcel Grossmann Proceedings; v2, "all known cases" changed to "various known cases" in the first paragrap

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

Yang-Mills Flow and Uniformization Theorems

We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structure, and that the convergence of the flow to the fixed points is consistent with the Poincare Uniformization Theorem. We construct a similar system for the three-dimensional case. Here the connection is built from a Riemannian geometry, an SO(3) connection and two other 1-form fields which take their values in the SO(3) algebra. The flat connections include the eight homogeneous geometries relevant to the three-dimensional uniformization theorem conjectured by W. Thurston. The fixed points of the flow include, besides the flat connections (and their local deformations), non-flat solutions of the Yang-Mills equations. These latter "instanton" configurations may be relevant to the fact that generic 3-manifolds do not admit one of the homogeneous geometries, but may be decomposed into "simple 3-manifolds" which do.Comment: 21 pages, Latex, 5 Postscript figures, uses epsf.st