- Proof that you can
- General ideas
- Canonical vertices to instance vertices?
- Coordinate system transformations to add information?
- Specific proof outline
- Matrix we found Monday provides the canonical-to-instance transformation, but isn’t invertible
- Try to fill in the 3rd column so the determinant is non-0
- Constraints associated with requiring the instance triangle to really be a triangle, rather than degenerating to a point or line segment, ensure that at least 1 of the cross-product terms in the determinant is non-0
- So pick a, b, and c coefficients to give non-negative
products with their cross-product terms, e.g., based on
signs of cross products, and the resulting determinant has
to be positive, i.e., non-0
- Fleshing this out with background literature, implementation, etc. could be an at-least-minimally publishable (e.g., at GREAT Day) course project
- General ideas
- Write second ray tracer