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2013-03-07T17:09:10.967
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2017-04-13T12:18:41.790
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Body
Ok, I found the solution and I post it here for reference. I hope it can be useful to someone else as well. Actually ggael's answer triggered the right solution, so many thanks to him and +1 for him. <hr> <pre><code>#include <Eigen/Geometry> typedef Eigen::Affine3d Transformation; typedef Eigen::Vector3d Point; typedef Eigen::Vector3d Vector; typedef Eigen::Translation<double,3> Translation; Transformation findTransformBetween2CS(Point fr0,Point fr1,Point fr2,Point to0,Point to1,Point to2) { Transformation T, T2, T3 = Transformation::Identity(); Vector3d x1,y1,z1, x2,y2,z2; // Axes of the coordinate system "fr" x1 = (fr1 - fr0).normalized(); // the versor (unitary vector) of the (fr1-fr0) axis vector y1 = (fr2 - fr0).normalized(); // Axes of the coordinate system "to" x2 = (to1 - to0).normalized(); y2 = (to2 - to0).normalized(); // transform from CS1 to CS2 // Note: if fr0==(0,0,0) --> CS1==CS2 --> T2=Identity T2.linear() << x1, y1, x1.cross(y1); // transform from CS1 to CS3 T3.linear() << x2, y2, x2.cross(y2); // T = transform to CS2 to CS3 // Note: if CS1==CS2 --> T = T3 T.linear() = T3.linear() * T2.linear().inverse(); T.translation() = t0; return T; } </code></pre> <hr> Inspiration also came from this post: <a href="https://gamedev.stackexchange.com/questions/26084/transform-between-two-3d-cartesian-coordinate-systems">https://gamedev.stackexchange.com/questions/26084/transform-between-two-3d-cartesian-coordinate-systems</a>
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