A ray in a corner (between two lines)

Author:
Ryan Hirst
Intersecting lines , with unit direction vectors , and normals . Let point on cast a ray in direction . What is the path of the ray?
NOTES: The index m of the last bounce is based on the following observation {link prev}. For and take Then the sequences are as follows:
  1. Given the (k-1)st reflection vector, the next reflection has direction: Or, in complex numbers:**
  2. Let the kth bounce fall at point Then the times are given by:
Simplifying the recursions, I obtain the formulas shown in the worksheet. But let me simplify a bit further... _______ Light>Reflection Prev: http://tube.geogebra.org/material/show/id/128176 Next: http://www.geogebratube.org/material/show/id/130551 **Rotation using Gauss numbers (Complex Algebra): http://tube.geogebra.org/material/show/id/115348