how do I convert from one cartesian system to another

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how do I convert from one cartesian system to another

2D problem: I measure the position of the 3 ends of a triangle in a cartesian system. Now i move the system (triangle) to another cartesian system and measure the position of just two ends. How can I identify the location of the 3rd end based on this data?

thanks! (and sorry for the bad english as a second angle)

This is a pretty vague question, but if I'm reading it right, then you need even less information than that. If you have the transformation of the first coordinate system to the second, then apply that to each of the three points to find each of the 3 equivalent points.

Otherwise, if you don't have the transformation, I would think it's impossible. After all, an infinite number of possible transformations of a coordinate system can result in the same two locations of two points yet different locations of the third.

eruciform 2010-07-09 22:33:45

To try to clarify the problem, the way i see it could be solved is as follows. Since i do not have the transformation from the first to the second coordinate system i am to use the coordinates of the two points to actually determine the transfomration. Once i have it i can find the position of the third point.I am not sure how to put this into equations though - its been a while since I atttended the analytical geometry class...

Jon 2010-07-12 15:41:18

I don't think it's possible in the general case unless you know something about the general nature of the transformation. If you know it's a linear translation, then you can use the movement of one point to figure it out. If it's a rotation, you may need 2-3 (I'm rusty here, too). But if it's nonlinear, or more complex than the above, or a combination, then multiple transformations could result in the same displacement for the two points.

eruciform 2010-07-12 15:44:30

What i know is that the transformation involves a translation followed by a rotation. Also I can measure more than 2 points if that helps in identifying the details of the transformation.Thanks for taking the time to reply to my posting! Best regards,Jon

Jon 2010-07-13 21:43:03

no problem, good luck! if you find out, please post so I can know, too! oh, if the answer was helpful, a checkmark would be cool. ;-)

eruciform 2010-07-13 23:01:17

thank you! good luck!

eruciform 2010-07-14 17:15:05

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how do I convert from one cartesian system to another

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