Given two triangle I have the transformation (three rotation followed by three translation)of both the triangles. How can I calculate the transformation between two triangles? A numerical example will help. Thanks in advance!
How can I calculate the transformation of two 3D triangles?
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geometry
transformation
triangles
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0@Irina: please do not use answers to make comments. I have merged your accounts so you should be able to edit your question now; please register so that you won't have to keep starting new accounts. – 2011-05-02
1 Answers
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When rotating a rigid body into standard position, the three rotations are not one around each spatial axis. One approach is Euler angles. In any case, you would hope to have three single-axis rotation matrices that, when multiplied, give the whole rotation.
Given that this is true, if the matrices for triangle $ABC$ are $R_1,R_2,R_3$ and the translation is $T_1$, and for $DEF$ are $R_4,R_5,R_6,T_2$, and A'B'C' is triangle $ABC$ in standard position (after the rotation/translation) you have A'B'C'=T_1+R_3R_2R_1ABC=D'E'F'=T_2+R_6R_5R_4DEF. Then $DEF=R_4^{-1}R_5^{-1}R_6^{-1}(T_1+R_3R_2R_1ABC-T_2)$
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0If you translate it along $x$, you don't need radians-that is an angle. If you do your rotations around fixed space directions, I believe there are positions you cannot achieve, but am not sure. – 2011-05-03