Applying a rigid transformation matrix to a pair of coordinates?

[adrianom]

Not sure if this is the right place to ask this question. I am trying to apply a rigid transformation matrix generated from CloudCompare to a pair of coordinates, but my linear algebra skills are not the greatest. I attached a screenshot of the math I was doing. The 4x4 matrix you see is the transformation matrix generated from CC and the 4x1 matrix is a single point converted into a vector (-42788.463 is the x coordinate, 213124.639 is the y coordinate, 0 is the z coordinate, and 1 indicates I want to use the translation vector from the 4x4 matrix). The 4x4 matrix and the 4x1 matrix are both in a similar coordinate system (NAD_1983_CA_Teale_Albers). Is this the right way of doing this? I am making the assumption that the first column in the 4x4 matrix are x rotation values, the second column y rotation values, and the third column z rotation values.

[adrianom]

Disregard that last sentence about the assumption of x y and z. That is wrong.

[daniel]

Yes that's correct (apart, as you pointed out, that the 3x3 top-left part of the matrix is a 3D rotation matrix)

[adrianom]

Thanks for all the help recently, Daniel! Much appreciated.

[adrianom]

Got another question for you, Daniel. Does this math account for the rotation based on the origin point, as you told me in my previous question you answered (linked below)? I ask this because the shift I am seeing in the coordinates (due to the translation vector) is larger than I expected. If my math does not account for this, is there a method you know of that I can account for rotation based on the origin point when applying the matrix to a set of coordinates?

viewtopic.php?f=9&t=4504&sid=55fa217106 ... 41d488993d

[daniel]

Yes the rotation matrix implicitly rotates the points about the origin. And then the 'translation' part (the 4th columns) re-centers the cloud/entity.