cse 275 f04—graphics with opengl
DESCRIPTION
CSE 275 F04—Graphics with OpenGL. Dr. T. J. Peters, [email protected] 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) - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/1.jpg)
CSE 275 F04—Graphics with OpenGL
Dr. T. J. Peters, [email protected]
486-5045www.cse.uconn.edu/~tpeters
• Use of plain text files for email• No attachments• Dynamic syllabus on home
![Page 2: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/2.jpg)
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!!!!
![Page 3: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/3.jpg)
Computational Topology and Spline Surfaces
T. J. Peters, University of Connecticut
Thanks: I-TANGO Team
![Page 4: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/4.jpg)
Outline: Animation & Approximation
• Animation for 3D• Spline intersection approximation (static)• Transition to molecules• Molecular dynamics and knots• Supportive theorems
![Page 5: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/5.jpg)
![Page 6: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/6.jpg)
Role for Animation Towards
• 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
Mathematical Discovery
![Page 7: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/7.jpg)
![Page 8: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/8.jpg)
INTERSECTIONS -- TOPOLOGY,
ACCURACY, &
NUMERICS FOR
GEOMETRIC
OBJECTS
I-TANGO III
NSF/DARPA
![Page 9: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/9.jpg)
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.
![Page 10: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/10.jpg)
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
![Page 11: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/11.jpg)
• 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
Topology
![Page 12: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/12.jpg)
![Page 13: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/13.jpg)
![Page 14: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/14.jpg)
![Page 15: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/15.jpg)
![Page 16: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/16.jpg)
Credits
• Color image: UMass, Amherst, RasMol, web
• Molecular Cartoons: T. Schlick, survey article, Modeling Superhelical DNA …, C. Opinion Struct. Biol., 1995
![Page 17: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/17.jpg)
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
![Page 18: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/18.jpg)
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
![Page 19: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/19.jpg)
Transition to Dynamics
•Energy role
•Embeddings
•Knots encompass both
![Page 20: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/20.jpg)
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/
![Page 21: CSE 275 F04—Graphics with OpenGL](https://reader036.vdocument.in/reader036/viewer/2022062521/56814cf6550346895dba0081/html5/thumbnails/21.jpg)