Markus Meister December 1, 1975 - December 24, 1998

Trajectory

> Would you create a trajectory/projection of what you think Markus might have
> done, where he might have gone with who he was as you knew him. The special
> aspects that only you, of the people here, were likely to know. Also, could
> we invite his other professors to join in this projection.

I'll make a stab at it...

Markus loved mathematical sophistication and complexity, indeed, he sometimes loved complexity for its own sake. I had gotten him started on looking at subdivision surfaces, and in particular I had him read Jos Stam's papers on exact computation of limit points for subdivision surfaces (in which he found and then corrected an error), but that didn't seem to lead to any obvious further interest for him. I'd also encouraged him when he expressed interest in taking the "Theory of Manifolds" course in the mathematics department, even though it was a graduate course intended for future mathematicians, not CS students.

As he began to learn about bundles, parallelizability, and frame bundles, not to mention Grassmannians, I explained to him how certain user-interface ideas could be described in bundle terms; in particular, Ken Shoemake's "double the angle" virtual sphere rotation interface can be seen as a "blowing up" of a singularity in the exponential map on SO(3), and the notion of "motion by local frames" (i.e., controls that let you "move in the x-direction that I carried along with me") having no singularities can be seen as an explicit parallelization of a frame bundle. I was delighted to see him not only grasp these things, but apparently find the mathematics more transparent on account of the graphics application.

My hope for his research was that he could take some of these ideas (which are admittedly ill-formed in my mind) and extend them to build new and better interfaces (we had talked about a twin-joystick camera controller for viewing in 4-space, for example) for all sorts of tasks. My guess is that having done some of that, he'd have found some other problem that interested him, and to which topology could be applied, and that I'd have been able to sit back and just watch.

The last project that I'd gotten him interested in was an extended axis-angle interpolation scheme, generalizing some work that I'd done with some Caltech folks in 1991/92. The questions he asked, as I tried to explain my ideas, showed me that I'd not thought through the ideas nearly enough. In trying to formulate answers to his questions, I've come to understand rather more about what I'd been thinking of doing. That was one of the pleasures of working with Markus: he knew a good question when he saw one, and was never afraid to ask it.

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Not exactly what you requested, but the closest I can come...hope it suits...

-Spike