Distance between parallel lines under transformation

Numsgil · 2013-01-30T19:23:36

I have a line (with points A, B on the line), and a distance 'h' to a parallel line. Under an affine transformation, the lines should stay parallel, but the distance between them might change. How can I get the new distance between the lines? My thinking right now is to construct a point on the red line, transform that point with the affine transformation, and then find the distance of that new point to the transformed black line AB. But is there a more direct way to calculate the new distance?

Math and Physics Programming

Started by Numsgil January 29, 2013 07:33 PM

9 comments, last by clb 12 years ago

clb

2,153

January 30, 2013 07:23 PM

Numsgil: You are absolutely correct.

For the case of no shear, it should hold. For the case with shear, I think it's possible to arrive to a closed expression by deriving the distance between the lines under the operation by the affine map, but that's indeed a more detailed examination.