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CSE 275 F04—Graphics with OpenGL

CSE 275 F04—Graphics with OpenGL. Dr. T. J. Peters, tpeters@cse.uconn.edu 486-5045 www.cse.uconn.edu/~tpeters. Use of plain text files for email No attachments Dynamic syllabus on home. CSE 275 F04—Graphics with OpenGL. Circle animation, due next week (5 pts)

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CSE 275 F04—Graphics with OpenGL

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  1. CSE 275 F04—Graphics with OpenGL Dr. T. J. Peters, tpeters@cse.uconn.edu 486-5045 www.cse.uconn.edu/~tpeters • Use of plain text files for email • No attachments • Dynamic syllabus on home

  2. CSE 275 F04—Graphics with OpenGL • Circle animation, due next week (5 pts) • 3 – 4 take home labs, (60 pts) • 2 tests, 9/30 & 11/04 (20 pts) • Final, (15 pts) • Alternate suggestions by Thurs, 9/2!!!!

  3. Computational Topology and Spline Surfaces T. J. Peters, University of Connecticut Thanks: I-TANGO Team

  4. Outline: Animation & Approximation • Animation for 3D • Spline intersection approximation (static) • Transition to molecules • Molecular dynamics and knots • Supportive theorems

  5. Role for Animation Towards Mathematical Discovery • ROTATING IMMORTALITY • www.bangor.ac.uk/cpm/sculmath/movimm.htm • Möbius Band in the form of a Trefoil Knot • Animation makes 3D more obvious • Simple surface here • Spline surfaces joined along boundaries

  6. INTERSECTIONS -- TOPOLOGY, ACCURACY, & NUMERICS FOR GEOMETRIC OBJECTS I-TANGO III NSF/DARPA

  7. Representation: Geometric Data • Two trimmed patches. • The data is inconsistent, and inconsistent with the associated topological data. • The first requirement is to specify the set defined by these inconsistent data.

  8. Rigorous Error Bounds • I-TANGO • Existing GK interface in parametric domain • Taylor’s theorem for theory • New model space error bound prototype • CAGD paper • Transfer to Boeing through GEML

  9. Topology • Computational Topology for Regular Closed Sets (within the I-TANGO Project) • Invited article, Topology Atlas • Entire team authors (including student) • I-TANGO interest from theory community

  10. Credits • Color image: UMass, Amherst, RasMol, web • Molecular Cartoons: T. Schlick, survey article, Modeling Superhelical DNA …, C. Opinion Struct. Biol., 1995

  11. Limitations • Tube of constant circular cross-section • Admitted closed-form engineering solution • More realistic, dynamic shape needed • Modest number of base pairs (compute bound) • Not just data-intensive snap-shots

  12. Opportunities • Join splines, but with care along boundaries • Establish numerical upper bounds • Maintain bounds during animation • Surfaces move • Boundaries move • Maintain bounds during simulation (FEA) • Functions to represent movement • More base pairs via higher order model

  13. Transition to Dynamics • Energy role • Embeddings • Knots encompass both

  14. Interest in Tool Similar to KnotPlot • Dynamic display of knots • Energy constraints incorporated for isotopy • Expand into molecular modeling • www.cs.ubc.ca/nest/imager/contributions/scharein/

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