- Math dept scholarship applications available
- See notice on dept home page, http://www.geneseo.edu/math/home
- Colloquia
- Dawood, “Mathematical Methods in Equity Research”
- Thursday, February 19, 3:00 - 4:00, Newton 203
- Dickerson, “Mathematics Majors’ Understandings of the
Concept of Mathematical Definition”
- Monday, February 23, 4:00 - 5:00, Newton 201
- Extra credit for summaries
- Dawood, “Mathematical Methods in Equity Research”
- Speeding up ray tracer?
- Use profiler!
- Replace loops with vectorized computation!
- Move code out of loops where possible
- Evaluate common subexpressions only once
- Spheres
- Use canonical sphere with equation x2 + y2 + z2 = 1, plug in x, y, and z coordinates from ray, and solve for t
- Ray coordinates have form sx + tdx, etc.
- With 2 real solutions, use smaller positive one for t
- Two complex solutions mean ray misses sphere
- Cylinders
- Use canonical cylinder aligned with z axis such that x2 + y2 = 1
- But need to consider whether cylinder is infinite (unlikely) or has bounds on z coordinates, and whether its ends are closed or open
- Closed ends involve more complicated code for intersections,
because ray can intersect in an end plane, whereas for open
cylinders intersections are only with sides
- Can you also handle distorted version of these shapes, e.g., ellipsoids, non-right-circular cylinders, etc?
- Ray-plane intersections
- And note that first exam is coming up in a week