1 / 28

Floating Point Geometric Algorithms

Floating Point Geometric Algorithms. for Scientific Visualization. T. J. Peters www.cse.uconn.edu/~tpeters and E. L. F. Moore. Rotate Molecule?. UMass, RasMol. Molecular Modeling?. Joining Geometry. Static Images. “A picture is worth a thousand words.”. BUT ,.

cade
Download Presentation

Floating Point Geometric Algorithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Floating Point Geometric Algorithms for Scientific Visualization T. J. Peters www.cse.uconn.edu/~tpeters and E. L. F. Moore

  2. Rotate Molecule?

  3. UMass, RasMol

  4. Molecular Modeling?

  5. Joining Geometry

  6. Static Images “A picture is worth a thousand words.” BUT, http://commfaculty.fullerton.edu/lester/writings/ad.html

  7. Dynamic Scientific Visualization Approximately 11M translations per hour: 100 translations per frame, at 30 frames per second

  8. Documented Animation Issues • Geri’s game: along boundary joins. • Resolution was data-specific. • Short time span was favorable DeRose, Kass and Truong, Subdivision surfaces in character animation, SIGGRAPH '98

  9. Practical Animation Response • Accumulated error versus Maya alternative. • Used at BlueSky Studios (Ice Age II)

  10. Approximation & Knots • Approximate & compare knot types: But recognizing unknot in NP (Hass, L, P, 1998)!! • Approximation as operation in geometric design • Preserve original knot type (even if unknown).

  11. Unknot

  12. Bad Approximation! Self-intersect?

  13. Good Approximation! Respects Embedding Via Curvature (local) Separation (global) (recognizing unknot in NP; Hass, L, P, 1998)

  14. Approximation by PL interpolation problem solved !* Nr(B) B • Construct the boundary of an open neighborhood Nr(B)of curve B • The boundary (a pipe surface) will have a radius r, with the following conditions* • no local self-intersections • no global self-intersections *

  15. Applications !

  16. Subdivision for graphics • Integration with sub-systems. • Generation of vertices. • Performance benefits. • Motion driven by chemistry and physics.

  17. The Class of Unknotted Spline Curves with Knotted Control Polygons • Planar Degree 10 Bézier Curve P0 P9 P8 P1 P10 P5 P3 P2 P7 P6 P4 • note: the control polygon is self-intersecting

  18. The Class of Unknotted Spline Curves with Knotted Control Polygons • 3D Degree 10 Bézier Curve P9 P0 P8 P1 P10 P5 P3 P2 P7 P6 • note: the control polygon is knotted

  19. Algorithm for Isotopic Subdivision (cubic) Subdividing B until its control polygon is contained in Nr(B). a. Compute number of subdivisions required* b. Test to ensure there are no self-intersections Nr(B) Pk+2 B Pk+1 Pk+2 lk+2 lk+1 Pk qk,f lk+3 lk qk,i Cubic: no local knotting *

  20. Algorithm for Isotopic Subdivision 1. Computing r for B Find minimum of a. separation distance [c(s) – c(t)] • c'(s) = 0 [c(s) – c(t)] • c'(t) = 0 b. radius of curvature 2r Cubic b-spline curve

  21. Min distance with Newton's method

  22. Additional High Performance Issues Example: Blue Gene L, Macro-Molecule • Over 100,000 processors, with local geometry. • Join across all nodes (surfaces & curves). • Output to light-weight graphics clients raises bandwidth & architectural concerns. Andersson-Peters-Stewart, IJCGA 00 & CAGD 98

  23. Credits • ROTATING IMMORTALITY • www.bangor.ac.uk/cpm/sculmath/movimm.htm • KnotPlot • www.cs.ubc.ca/nest/imager/ contributions/scharein/KnotPlot.html

  24. Acknowledgements, NSF • I-TANGO,May 1, 2002, #DMS-0138098. • SGER: Computational Topology for Surface Reconstruction, NSF, October 1, 2002, #CCR - 0226504. • Computational Topology for Surface Approximation, September 15, 2004, #FMM -0429477. • IBM Faculty Award, 2005

More Related