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Say I am given a point in an x1,y1,z1 coordinate system. I have a different coordinate system, x2,y2,z2 that has the same origin as the x1,y1,z1 system, but the axis are not aligned. I have roll, pitch, and yaw sensors fitted on the x2,y2,z2 coordinate system.

This picture may help:

How do I go about transforming the point in x1,y1,z1 coordinates to x2,y2,z2 coordinates? My original thought was that I simply just rotate by "head" degrees about y1 by the heading first, then rotate by "roll" degrees about z, then rotate by "pitch" degrees about x. This seems too easy and direct. Is this the correct approach?

linear-transformations coordinate-systems orientation

share|cite|improve this question

edited 20 hours ago

user2913869

asked 20 hours ago

user2913869user2913869

1628

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If by skewed you mean rotated then you simply need to have the transformation matrix from the first basis to the second basis (which is built by the basis vectors of the second system expressed in the first as column vectors in the matrix). Then multiplying your point coordinates by that matrix you get the corresponding coordinates in the second system.
  $endgroup$
  – lightxbulb
  20 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you describe this process in greater detail?
  $endgroup$
  – user2913869
  20 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  en.wikipedia.org/wiki/Transformation_matrix
  $endgroup$
  – lightxbulb
  20 hours ago
  

  
  
  
  

add a comment | 

0

$begingroup$

Say I am given a point in an x1,y1,z1 coordinate system. I have a different coordinate system, x2,y2,z2 that has the same origin as the x1,y1,z1 system, but the axis are not aligned. I have roll, pitch, and yaw sensors fitted on the x2,y2,z2 coordinate system.

This picture may help:

How do I go about transforming the point in x1,y1,z1 coordinates to x2,y2,z2 coordinates? My original thought was that I simply just rotate by "head" degrees about y1 by the heading first, then rotate by "roll" degrees about z, then rotate by "pitch" degrees about x. This seems too easy and direct. Is this the correct approach?

linear-transformations coordinate-systems orientation

share|cite|improve this question

edited 20 hours ago

user2913869

asked 20 hours ago

user2913869user2913869

1628

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If by skewed you mean rotated then you simply need to have the transformation matrix from the first basis to the second basis (which is built by the basis vectors of the second system expressed in the first as column vectors in the matrix). Then multiplying your point coordinates by that matrix you get the corresponding coordinates in the second system.
  $endgroup$
  – lightxbulb
  20 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you describe this process in greater detail?
  $endgroup$
  – user2913869
  20 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  en.wikipedia.org/wiki/Transformation_matrix
  $endgroup$
  – lightxbulb
  20 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Say I am given a point in an x1,y1,z1 coordinate system. I have a different coordinate system, x2,y2,z2 that has the same origin as the x1,y1,z1 system, but the axis are not aligned. I have roll, pitch, and yaw sensors fitted on the x2,y2,z2 coordinate system.

This picture may help:

How do I go about transforming the point in x1,y1,z1 coordinates to x2,y2,z2 coordinates? My original thought was that I simply just rotate by "head" degrees about y1 by the heading first, then rotate by "roll" degrees about z, then rotate by "pitch" degrees about x. This seems too easy and direct. Is this the correct approach?

linear-transformations coordinate-systems orientation

share|cite|improve this question

edited 20 hours ago

user2913869

asked 20 hours ago

user2913869user2913869

1628

$endgroup$

share|cite|improve this question

edited 20 hours ago

user2913869

asked 20 hours ago

user2913869user2913869

1628

share|cite|improve this question

edited 20 hours ago

user2913869

asked 20 hours ago

user2913869user2913869

1628

asked 20 hours ago

user2913869user2913869

1628

asked 20 hours ago

user2913869user2913869

1628