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How to find the transformation matrix for a plat knowing the old and new coordinates of 3 points on it ?

Asked by farzad on 14 Jun 2019
Latest activity Commented on by farzad on 2 Jul 2019
Hi All
How do I define the transformation matrix of a plate that moves in space , knowing the old and new coordinates of 3 points on the plate ? (assume a circular plate and reference coordinate system in the center of the plate )

2 Answers

Answer by Matt J
on 14 Jun 2019
 Accepted Answer

  22 Comments

What is eulZYX?
>> which eulZYX
'eulZYX' not found.
@farzad: Do not assume, that the users of the forum have installed the same 3rd party tools or Matlab toolboxes as you have. Check the location of the functions by which . If it is not included in the standard toolboxes, post a link to the documentation or source of the function.
By the way: A simple test reveals, what the output is.

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Answer by Jan
on 27 Jun 2019

You can define the motion by a translation of the center of the 3 points and a rotation of the local coordinate system.
PointsA = [x1, y1, z1; ...
x2, y2, z2; ...
x3, y3, z3];
PointsB = ...
Translation = mean(PointsB, 1) - mean(PointsA, 1);
% For the local coordinate systems find an orthonormal tripod:
v1 = PointsA(1, :) - PointsA(2, :);
n1 = v1 ./ norm(v1);
v2 = PointsA(2, :) - PointsA(3, :);
n2 = v2 ./ norm(v2);
c2 = cross(n1, n2);
n12 = c2 ./ norm(c2);
CoorA = [n1, n12, cross(n1, n12)];
% The same for B...
Rotation = CoorA * CoorB'
Anotehr approach would be the "Helical Axis": Any motion can be defined by an axis and some rotation around it and translation along it. See http://www.kwon3d.com/theory/jkinem/helical.html

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so you are saying that using absor and rcParams.R is not a good idea ?
Jan's approach will be sub-optimal if you have non-neglible measurement errors in A and B. Also, if you decide to use more than 3 points (for data redundancy), absor will better accommodate that case.
@farzad: Of course I did not say that "using adsor is not a good idea". Especially if you have more than 3 points on a rigid body, an optimization appraoch is the correct approach.

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