- Today’s colloquium postponed
- Intersecting rays with transformed objects
- Apply inverse transformation to ray
- Apply inverse transformation to ray
- Can you in fact produce any triangle as a transformed canonical one?
- Proving that programming ideas such as this really will always work is an important but under-appreciated part of programming
- Idea: find coefficients for transformation matrix that will
turn vertices of canonical triangle into vertices of arbitrary one
- Problem: Need constraints on 3rd column to make transformation invertible
- Another idea: show how to construct a series of shears, dilations, rotations, and translations that can turn canonical triangle into any actual one.
- Finish proving that any triangle can be constructed by an
affine transformation applied to a canonical triangle
- Come to class with a proof in mind
- Start writing second ray tracer