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4442785
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2010-12-14T18:29:46.450
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2010-12-15T23:41:42.253
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2010-12-15T23:41:42.253
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Here you have your problem modeled and running with Mathematica. I used the "Levenberg-Marquardt" method. This is why I asked for your data. With MY data, YOUR problems are always going to be easier:) <pre><code>xnew[x_, y_, z_] := RotationMatrix[rx, {1, 0, 0}].RotationMatrix[ ry, {0, 1, 0}].RotationMatrix[rz, {0, 0, 1}].{x, y, z} + {tx, ty, tz}; (* Generate Sample Data*) (* Angles 1/2,1/3,1/5 *) (* traslation -> {1,2,3} *) (* Minimum mean Noise 5% *) data = Table[{{x, y, z}, RotationMatrix[1/2, {1, 0, 0}]. RotationMatrix[1/3, {0, 1, 0}]. RotationMatrix[1/5, {0, 0, 1}].{x, y, z} +{1, 2, 3} +RandomReal[{-.05, .05}, 3]}, {x, 0, 1, .1}, {y, 0, 1, .1}, {z, 0, 1, .1}]; data = Flatten[data, 2]; (* Now find the parameters*) FindMinimum[ Sum[SquaredEuclideanDistance[xnew[i[[1]] /. List -> Sequence], i[[2]]], {i, data}] , {rx, ry, rz, tx, ty, tz}, Method -> "LevenbergMarquardt"] </code></pre> Out: <pre><code>{3.2423, {rx -> 0.500566, ry -> 0.334012, rz -> 0.199902, tx -> 0.99985, ty -> 1.99939, tz -> 3.00021}} </code></pre> (Within 1/1000 of the real values) Edit I worked a little with your data. The problem is that your system is very bad conditioned. You need much more data to effectively calculate such small rotations. These are the results I got: Rotations in degrees: <pre><code>rx = 179.99999999999999999999984968493536659553226696793 ry = 180.00000000000000000000006934755799995159952661222 rz = 180.0006286861217378980724139120849587855611645627 </code></pre> Traslations <pre><code>tx = 48.503663696727576867196234527227830090575281353092 ty = 63.974139455057300403798198525151849767949596684232 tz = -0.99999999999999999999997957276716543927459921348549 </code></pre> I should calculate the errors, but I've no time right now. BTW, rz = Pi + 0.000011 (in radians) HTH!
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singulars
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1. This table or related slice is empty.
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1. POLimitations of the Levenberg-Marquardt algorithm
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1. PTAnswer
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1. USDr. belisarius
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1. USDr. belisarius
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