Abstract We consider an eversion of a sphere driven by a gradient flow for elastic bending energy. We start with a halfway model which is an unstable Willmore sphere with 4-fold orientation-reversing rotational symmetry. The regular homotopy is automatically generated by flowing down the gradient of the energy from the halfway model to a round sphere, using the Surface Evolver. This flow is not yet fully understood; however, our numerical simulations give evidence that the resulting eversion is isotopic to one of Morin’s classical sphere eversions. These simulations were presented as real-time interactive animations in the CAVE automatic virtual environment at Supercomputing’95, as part of an experiment in distributed, parallel computing and broad-band, asynchronous networking. 1 A History of Sphere Eversions To evert a sphere is to turn it inside out by means of a continuous deformation, a regular homotopy, which allows the surface to pass through itself, but forbids more serious singularities where the curvature becomes

GeoSheet (version 1.0) is an interactive visualization tool for visualizing geometric algorithms in distributed environments. It provides features such as interactive visualization of program states for debugging, high-level graphical input/output manipulation facilities for geometric objects, reuse of existing data structures and algorithms implementation, and more importantly distributed executions on heterogeneous machines at different sites. To minimize development effort of the tool we make use of existing software packages available in public domain. Specifically we extend Xfig with a message-driven interface and a socket-based interprocess communication (IPC) mechanism. This extended-Xfig is the backbone of this version of the tool. Object-oriented programming methodology is used to construct the visualization interface. By deriving from traditional data type and algorithm libraries, our abstract GeoObject representation super-classes are easy to use, easy to construct, and hig...

Computer graphics has proven to be a very attractive tool for investigating low-dimensional algebraic manifolds and gaining intuition about their properties [9]. In principle, a computer image of any manifold described by algebraic

Virtual reality is an effective way (in many situations) for creating 3D visualisations, although the visualisations need to be designed with both 3D and virtual reality in mind to be most useful. Many issues are related to virtual realities, although these are often overlooked by users due to the issues being tightly integrated with the virtual worlds. Even though users can disregard such issues, it is important that designers of visualisations and virtual realities bear them in mind. Some of these issues are presented and discussed to enable designers to have a better idea of the aspects they should consider when creating such systems, with particular reference to visualisation with virtual reality. - 1. Introduction Software visualisation is an important tool in the maintainer's armoury. It is a technique that can, when designed and used effectively, aid him in his quest to understand existing program code. One way to achieve these visualisations is through the use of virtual re...

Hanson et al. [4] described mathematical visualization as "the art of creating concrete understanding from abstract mathematical objects and their transformations." Such artistry may be difficult to achieve because it demands both mathematical and graphical knowledge in one person, or excellent communication between members of a group of individuals with specific talents. Furthermore, it may also require the ability to exceed the limitations of one's own experience. This paper describes a computer-aided visualization system which aids users in finding meaningful imagery amidst the range of alternatives.

with relativistic and astrophysical visualization, which has been culminating in a substantial engagement for visualization in the Einstein Year 2005---the 100 anniversary of Einstein's publications on special relativity, the photoelectric effect, and Brownian motion. This paper focuses on explanatory and illustrative visualizations used to communicate aspects of the difficult theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. We discuss visualization strategies, motivated by physics education and didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular-science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Although our visualization tools build upon existing methods and implementations, these techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

Search and navigation in environments with four spatial dimensions were investigated using computer graphic methods for displaying large, immersive 4D environments interactively. After a short period of training with the computer interface, subjects started in a home room and were asked to run through a 4D environment in search of a randomly-positioned target. Subjects were instructed to return to the home room as rapidly as possible upon finding the target. Return times decreased with practice to a value close to optimal. Search for the target also improved in the way expected were subjects learning the layout of the environment. The results show that one can learn to search and navigate efficiently in environments with four spatial dimensions.

This dissertation examines how the computer can aid the creative human endeavour which is data visualization. That computers now critically aid many fields is apparent, as is evidenced by the breadth of contemporary research on this topic. Indeed, computers have contributed widely to the whole area of data comprehension, both in performing extensive computations and in producing visual representations of the results. Computers originally aided mathematicians who could both write the instructions necessary to direct the computer and interpret the resulting numbers. Even though modern computers include advanced graphical capabilities, many issues of access still remain: the users of data visualization software systems may not be experts in any computer-related field, yet they want to see visual representations of their data which allow them insight into their problems. For example, today's mathematicians who are generally expert in exploiting computational opportunities for experimentation may lack similar experience in opportunities for visual exploration. Of particular concern is how a computer-aided visualization tool can be designed to support

When asked what he thought of Western civilization, Mohandas Gandhi is reported to have replied that he thought it would be a good idea. How would a mathematician respond if asked about the mathematical basis of visualization... and does the answer matter?

papers, but a corresponding increase in the quality of each submission for conference. The authors represent a cross-section of international perspectives that include the United Kingdom, South-East Asia, the United States of America and Australia. All published papers were double blind peer-reviewed before acceptance into the conference for publication. There were a total of 13 papers submitted for review from which only 6 were accepted and presented. The 9 th Australian Information Warfare and Security Conference is one of four conferences that form the 2008 SECAU Security Congress. The congress reflects an overarching commitment to bringing together a broad spectrum of security topics under a single assembly in order to promote and develop a cross disciplinary approach to a continuum of security research. Conferences such as the 9 th Australian Information Warfare and Security Conference take a great deal of co-ordination, time and effort in order to bring together the right people in a common forum in order to advance the wider security understanding and to progress the various research directions. To that end, I express my thanks to the conference committee