Chris Hartman

The minimax sphere eversion

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 TM automatic virtual environment at Supercomputing’95, as part of an experiment in distributed, parallel computing and broad-band, asynchronous networking.

Computing Sphere Eversions

We consider several tools for computing and visualizing sphere eversions. First, we discuss a family of rotationally symmetric eversions driven computationally by minimizing the Willmore bending energy. Next, we describe programs to compute and display the double locus of an immersed surface and to track this along a homotopy. Finally, we consider ways to implement computationally the various eversions originally drawn by hand; this requires interpolation of splined curves in time and space.

ODES: an overlapping dense sub-graph algorithm

SUMMARY Enumeration of the dense sub-graphs of a graph is of interest in community discovery and membership problems, including dense sub-graphs that overlap each other. Described herein is ODES (Overlapping DEnse Sub-graphs), pthreads parallelized software to extract all overlapping maximal sub-graphs whose densities are greater than or equal to a specified cutoff density of at least 1/2. AVAILABILITY AND IMPLEMENTATION http://dense.sf.net

Thresholds for Path Colorings of Planar Graphs

A graph is path k-colorable if it has a vertex k-coloring in which the subgraph induced by each color class is a disjoint union of paths. A graph is path k-choosable if, whenever each vertex is assigned a list of k colors, such a coloring exists in which each vertex receives a color from its list.

Enumeration and Classification of 12-Bar Planar Simple-Jointed Kinematic Chains Using a Hierarchical Approach

The complete set of 12-bar planar simple-jointed kinematic chains is enumerated using the stratified or hierarchical representation, of Fang and Freudenstien (1990) in which post-priori isomorphism testing is not needed. This is achieved by directly enumerating the simplified and contracted graphs from which the kinematic chains are built up. The number obtained is compared with those from previous studies, and the list is catagorized by the link sets and by the numbers of major vertices and edges in the simplified graphs. A major feature of the technique is the use of an efficient rote-based technique for eliminating degenerate chains.Copyright

Painting in space

The goal of our research is to enable artists to interact with the world of their imagination; to create art by moving, molding, and shaping virtual forms as if by their own bodies. We show a print that represents a scene painted into virtual reality and tell how the scene and the subsequent print were done. There will be some discussion of the meaning of the work, the intent of the artist and the relationship between the art and the technology used to create it. The print seen here is both a picture of an exotic place and the artistic fruit of research into how to embody the user in virtual reality. Our approach is based on the premise that embodiment is an appropriate direction for developing tools to facilitate artistic expression. It is also a premise of this research that the constraints requisite to creating art will also result in tools that serve the visualization community in general.

Uniquely Tree-saturated Graphs

Let H be a graph. A graph G is uniquely H-saturated if G contains no subgraph isomorphic to H, but for every edge e in the complement of G (i.e., for each “nonedge” of G),

Bounds on the metric and partition dimensions of a graph

G+e