| Project | Geometry Creation Laboratory |
| Contact | Sha Xin Wei |
| Email | xinwei@stanford.edu |
| URL | |
Project
description | The conceptual purpose of this study is to understand what sort of geometric creation and performance can or cannot be supported computationally in a multi-modal writing system that spans freehand sketching, manipulable diagrams or graphics, mathematical text, symbolic and numeric computation, and simulation. The critical part of this project will be informed by insights from literature and performance as well as the mathematical sciences. Practically, this work benefits students of differential geometry or topology, people who need to work with nonlinear or multi-dimensional information, and animators and designers who wish to shape computational material using freehand sketches. A technical payoff of this project should be a richer set of representations of topological and geometric structures that provide good grips for a subsequent generation of computational material. |
Theoretical
background |
Some references:Allwein and Jon Barwise (eds.), Logical Reasoning with
Diagrams, Oxford University Press, 1996. David Barker-Plummer and Mark Greaves,
Architectures for Heterogeneous Reasoning On Interlinguae, CSLI 1996.Dubrovin,
Fomenko, Novikov, Modern Geometry -- Methods And Applications v I, II.L. Guibas,
Representations of topological structures.C. Gunn, A. Ortmann, U. Pinkall, K. Polthier,
U. Schwarz. Oorange: A Virtual Laboratory for Experimental Mathematics.
http://www-sfb288.math.tu-berlin.de/ oorange/ Oorange.html.
E. Husserl, Early writings; Logical Investigations; Crisis of European Sciences;Origins of Geometry.William P. Thurston. On proof and progress in mathematics. Bull. Amer. Math.Soc. (N.S.) v. 30 no. 2, 1994, 161--177.Robert Zeleznik, Kenneth P. Herndon and John F. Hughes. SKETCH, An Interface for Sketching 3D Scenes. |
| Challenges | The technical heart of the project is to develop a lightweight and extensible encoding of a minimal descriptive model M of "abstract" differential geometry: manifold, map, Lp space, curvature tensor, limit of an infinite sequence of maps, integral inequalities, etc. This model M will serve as a high-level knowledge representation easily read and written by geometers, but will also be writable by the graphical structure manipulation system. |
| Partnership | I'm looking for opportunities to observe students of differential geometry or topology at work as they informally work through problems on paper or on the board.I'm also looking for a sketching system which (1) has an easily modified but powerful gesture recognition subsystem, (2) has an open architecture so that it can commmunicate with external computational engines (like Mathematica or Matlab) via a fairly high-level protocol like MathLink. |