TotallyUnrelatedMathQuestions

Thought I'd pay a little visit back to the RoboWiki in an unashamed attempt to recruit some help for a little project I have going. It's a little hard to explain the problem, but I think I'm up to the task. Say you have a rectangular piece of elastic with a dot on it, and you stretch the four corners of the rectangle out different directions. Given the coordinates of the 4 corners and the point, I need to figure the coordinates of the point when the rectangle is unstretched. Any ideas? --Simonton

Well... I might be able to help but I have a couple questions to clarify the problem. Are you assuming the sides of the elastic rectangle stay straight unlike a truly realistic elastic which becomes thinner when stretched? I'm guessing you assume stretching is linear as well? I think I have an understanding of how to do this if the answer is yes to both of those :) -- Rednaxela

The answer is yes to both, though the latter is a simplifying assumption ;). --Simonton

Alright, basically what you're looking for, is a way to determine the [affine transformation matrix] (an affine transformation, is a transformation that essentially fits the same constraints that this simplified case of elastic stretching has) corresponding to known distortion of 4 known points. From that matrix one can easily determine the distorted location of any other point. I'll work up a nice solution to the 2-dimensional (I assume 2-dimensional is what you're wanting) form of the problem, which should be understandable without needing a background with linear algebra, tomorrow. Tonight I am tired :) -- Rednaxela