1st Idea: Rotate
the axis system slightly6.838, Computational Geometry; Fall 2001
Point Location
Sergi Elizalde & David Pritchard
We can get rid of the assumption that no two distinct endpoints have the same x-coordinate.
Observation: The
vertical direction that we chose was immaterial.
1st Idea: Rotate
the axis system slightly
This can lead to numerical difficulties, and requires an extra pass through the data.
Improved Idea:
Apply affine mapping (shear transformation)
F(x,y)=(x+ey,y) for small enough e.
This mapping preserves straight lines, so any "insidedness" holds just as true as it did before we applied the shear.
