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[37] | 1 | % By Philip Torr 2002
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| 2 | % copyright Microsoft Corp.
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| 3 | %%%%%%this is going to be my first try at some symbolic stuff
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| 4 |
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| 5 | %%%the purpose of this file is to set up an essential matrix that you can later do symbolic manipulation of,.
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| 6 |
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| 7 |
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| 8 | syms tx ty tz;
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| 9 |
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| 10 | Tx = [0 -tz ty; tz 0 -tx; -ty tx 0];
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| 11 |
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| 12 | %rodriggues formula a rotation angle l m n axis
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| 13 |
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| 14 | syms lx ly lz a
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| 15 |
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| 16 | Id = [1 0 0; 0 1 0; 0 0 1]
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| 17 | Ax = [0 -lz ly; lz 0 -lx; -ly lx 0];
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| 18 | rot_axT = [ lx ly lz]
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| 19 | rot_ax = [ lx; ly; lz]
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| 20 |
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| 21 | R = (cos(a) * Id + sin(a) * Ax + (1 - cos(a)) * rot_ax * rot_axT)
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| 22 |
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| 23 |
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| 24 | E = Tx * R
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| 25 |
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| 26 | syms foc
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| 27 |
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| 28 | Ca = [1 0 0; 0 1 0; 0 0 foc]
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| 29 |
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| 30 | G = Ca * E * Ca
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| 31 | %det(E)
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| 32 | %0.5 * (trace( E * E'))^2 - trace((E * E')^2)
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| 33 |
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| 34 | syms x1 x2 y1 y2
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| 35 |
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| 36 |
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| 37 |
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| 38 | r = [x2 y2 1] * G * [x1; y1; 1] |
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