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This is my problem (each landmark is a marker) :

Landmark multiple transforms

I need to express R1->R2. Aruco gives me transform between R1->RR and R2->RR. 

R1 = T1.RR (with T1 = transfo matrix containing rvec and tvec)  
R2 = T2.RR <=> RR = inv(T2).R2  
<=> R1 = T1.inv(T2).R2

The problem is that for me, I should have R1 = inv(T2).T1.R2 but I don't know where I'm wrong ...

Thanks, Alan

Nico Schertler
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Goren
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  • What are `R1` and `R2` in your formulas? Are the transforms model transforms or system transforms? If they are model transforms, your formula is correct. If they are system transforms, you need to swap the two transforms. How do you know that your results are wrong? – Nico Schertler Jul 27 '18 at 08:00
  • R1 ans R2 are two landmarks. I dont understand the difference between model or systems transform Can you explain please ? I think i'm wrong because in my studies I've always did R1 = inv(T2).T1 – Goren Jul 28 '18 at 09:31
  • I was more asking about their mathematical representation. What about the rest of my questions? – Nico Schertler Jul 28 '18 at 09:32
  • R1 = [Xr1; Yr1; Zr1] and same for R2=[Xr2;Yr2;Zr2] – Goren Jul 28 '18 at 09:47
  • So, those are points, represented in either of the coordinate systems? Or points represented in the global coordinate system? Can you explain what your `T1` does to a point when you transform it? In what coordinate systems are the untransformed and transformed points represented? – Nico Schertler Jul 28 '18 at 09:53
  • R1 and R2 are described by 3 points represented in the global coordinate system (RR). T1 is 4x4 transform matrix. So T1.P (with P a point in the R1 landmark) = P2 (the coordinate of P1 represented in the RR landmark). – Goren Aug 01 '18 at 07:01
  • Ok, so in this sense, `T1` is a system transform from `R1` to `RR`. Back to your question. What is `R1` in your last formula? You state that `R1 = T1 . RR`. what does that mean? If `T1` is the system transform from `R1` to `RR` that would mean that in your formula `RR` is a point in the coordinate system of `R1` and `R1` is a point in the coordinate system of `RR`? Sounds a bit weird. – Nico Schertler Aug 01 '18 at 11:11
  • Yes you're right I must be wrong. If I want to represent `R1` in the `RR` coordinate system it should be : `RR = T1.R1 <=> R1 = inv(T1) . RR` ? – Goren Aug 02 '18 at 12:14
  • Sounds correct. – Nico Schertler Aug 02 '18 at 15:35

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