Ray-Triangle Intersection (cont.)
- Simplifying:
- Letting \rho = 1 - \sigma - \tau
\bs{p}(\sigma, \tau) = \bs{r} +
\sigma (\bs{s} - \bs{r}) + \tau (\bs{t} - \bs{r})
- Intersection of the Ray and the Plane:
- Substituting the parametric form of the ray,
\bs{o} + t \bs{d}, for \bs{p} yields:
\bs{o} + t \bs{d} = \bs{r} +
\sigma (\bs{s} - \bs{r}) + \tau (\bs{t} - \bs{r})
- Using the Paramters:
- The point is in the interior if and only if
\sigma > 0, \tau > 0, and
(\sigma + \tau) \lt 1