- Colloquium this afternoon
- 4:00 - 5:00, Newton 201
- “Bodybuilding! ... for Mathematicians” + career reflections
- Extra credit for summaries
- Basic algorithm (for uniform samples)
loop: generate uniform random sample, s generate uniform random sample, x repeat until x < P(s) return s as sample value - Intuition:
- But PDFs aren’t always less than 1
- And probability distribution for picking x doesn’t have to be uniform
- Normal distribution: average of uniform distribution is normally distributed
- Ad hoc algorithms
- Low-discrepancy (uniform) samplers
- Because uniform random numbers aren’t evenly distributed
- Because uniform random numbers aren’t evenly distributed
- Glossy reflection via Monte Carlo integration
- Sample from a cosa distribution, i.e., P(x) ∝ cosax
- Series of 1-day labs based on (a version of) my 3rd ray tracer
- Derive sampler for cosine distribution
- Write sampler
- Isolate color computations from my ray tracer
- Reflections with 1 reflection ray
- Reflections with sample of reflection rays and MC integration
- Impact on next exam and initial project presentations
- Exam Monday April 13
- Presentations Wednesday & Friday April 15 & 17