Educational Software:
The full L-System interface (selectable by menu) is more appropriate for high school
and university students.
An L-system is a formal grammar (a set of rules and symbols) most famously used to model
the growth processes of plants. Changes to the library of preset parameters
will quickly yield beautiful fractal images of such variety that it is unlikely that
what you create has ever been seen before.
Abstract: The U.S. Air Force Space and Missile Systems Center (SMC) at the ground systems Research, Development, Test, and Evaluation (RDT&E) Support Complex (RSC) located at Kirtland AFB, has developed an in-house Trending Tool system. The system is used for archiving, graphing, and statistical analysis of State of Health (SOH) telemetry to support anomaly resolution and long-term trend analysis. This presentation examines strategies for user navigation through the very large data space, and a general case for small group development of in-house software rather than using Commercial Off-the-Shelf (COTS) software. In particular, the SOH telemetry, as opposed to general data, exhibits distribution qualities that allow for specialized data management. Furthermore, user access patterns have been identified across multiple satellite missions that can be leveraged to significant advantage.
Abstract: A fully automatic method of synthesizing isotropic textures on subdivision surfaces from sample images is presented. Both Gaussian and Laplacian pyramid representations of the sample texture are constructed. Texture synthesis proceeds coarse-to-fine, by incrementally inverting the Laplacian pyramid to produce an initial guess and refining this guess using non-parametric sampling. The sampling procedure uses a nearest neighbor search while preserving first-order statistics. The resulting texture is generated directly on the subdivision surface. Within the domain of isotropic textures, the proposed method offers improvements in faithful reproduction of a sample's appearance over a wide range of scales. The method can also be used to produce isotropic variants of anisotropic textures. Finally, while the sampling procedure we describe is not amenable to standard methods for nearest neighbor search in high dimensional spaces, an acceleration method is proposed that uses an eigenvector transform and a set of dynamic Kd-trees.
Abstract: This article represents an example of how computer software can be used to facilitate collaborative learning and the integration of mathematics and science. "Snap shots" from a pilot project, with thirty high school juniors who were involved in a university summer program, reveal how student-centered learning is facilitated by technology. This exploratory trial provides a glimpse of what the "classroom after next" might look like utilizing groupware in instructional settings.
Abstract: This paper introduces a new software tool, NonEuclid, which enables the user to easily perform ruler and compass constructions and measurements in Hyperbolic Geometry. The paper demonstrates how the software can be used to explore geometric patterns and theorems in Hyperbolic Geometry, as well as help to teach an axiomatic approach to geometry in general. A study of Hyperbolic Geometry can help students break away from long held pictorial definitions of geometric objects by offering a world in which the pictures are all changed; thereby helping students focus on the exact words in formal definitions of familiar objects such as squares, isosceles triangles, rhombuses.
Abstract: The paper presents an out-of-class writing method for helping students understand and internalize scientific concepts and theories. The proposed method breaks sharply form the typical writing assignments of summery reports and research papers. In particular, it focuses on careful student critiques of small segments of the given textbook, question articulation, development interconnections between class topics and concepts from other classes or life experience, student generated thought experiments, and imagination. The paper includes instructor guidelines and student hand-outs.