Outline for SM'99 talk

1. Define problem (6 slides)
   • What is MAT and why is it important?
   • Why is it difficult to compute?
   • Why is accuracy important? (4 slides, incl. images)
     • FP arith is not enough
     • each junction must be computed correctly
2. Previous work (2-3 slides)
3. Exact representations: MAPC library (2 slides)
   • Rational number
   • Algebraic number
   • Point in 2-D
   • Algebraic curve
   • Point in 3-D
4. Basic MAPC application: curve topology (2 slides)
5. MAT: High-level algorithm (2 slides)
6. Seam tracing by curve topology (1 slide)
7. Efficiency (3 slides)
   • Spatial decomposition
   • Linear programming
   • Replace 3-D Sturms by 2-D, and 2-D by 1-D
   • Floating-point estimation
   • Floating-point filters
   • Modular arithmetic
8. Results (3 slides)
   • Images
   • Timings

• Degeneracy
• Morphology classification
• Demmel's floating-point filter