Reflecting a Point About a Line
This is a pretty elementary operation in analytic geometry, but it’s come up in a few emails. Although the solution is available online, programmers often have problems with equations expressed in vector notation. That seems to be the common thread in the emails. I don’t have time for a comprehensive demo, so here is a quick Actionscript code snippet.
The problem at hand is how to reflect the point P2 about the line segment through points P0 and P1. Let R be the reflection of P2 about the line segment. I suspect the issue some people have problems with is the requirement to normalize the vector from P0 to P1.
If rx and ry are the x and ycomponents of R, then
var nx:Number = p1.x  p0.x; var ny:Number = p1.y  p0.y; var d:Number = Math.sqrt(nx*nx + ny*ny); nx /= d; ny /= d; var px:Number = p2.x  p0.x; var py:Number = p2.y  p0.y; var w:Number = nx*px + ny*py; var rx:Number = 2*p0.x  p2.x + 2*w*nx; var ry:Number = 2*p0.y  p2.y + 2*w*ny;
I’ll be using this method in an upcoming development, so we will have a chance to see it in action. In the mean time, I hope this helps the people who have been asking.

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