# Geometric accuracy analysis of 2d rectangular models

I have reconstructed set of rectangular objects lie on a 2D plane (for ex. ABCD). All these objects are in a one coordinate system. On the other hand, I have reference models for all of them (for ex. A’B’C’D’). But reference models are in another coordinate system. Here, I must say that although these two models are in two different coordinate systems, there scale is same but only different is their origin.

Now, I want to analyze the geometric accuracy of my reconstruction. I need to do some sort of RMSE analysis of vertices. But the problem is as these two systems have two different origins; actually, I cannot find an exactly corresponding point to overlap one another. Because my original data set is point data. Therefore, I cannot find an exact vertex even by manually. To solve this, I was thinking to shift one system and overlap from a certain corner from the other model. But then, I found the RMSE are not the same as when they would be in same origin.

(I was created two artificial rectangles which are in a same coordinate system with same origin. And get the RMSE and then overlap one corner and then again get the RMSE of the rectangle. These two are not the same).

So, I want your assistant to solve this.

I have uploaded a sample figure of my rectangles for your reference.

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