[ https://issues.apache.org/jira/browse/MATH-639?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13073554#comment-13073554 ]
Luc Maisonobe commented on MATH-639:
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The expected result quaternion computed to high precision manually and checked afterwards is:
q0 = 0.62283703596082005783621150
q1 = 0.02577076214564987845778149
q2 = -0.00000000025030122695149900
q3 = -0.78192703908611094998656730
> numerical problems in rotation creation
> ---------------------------------------
>
> Key: MATH-639
> URL: https://issues.apache.org/jira/browse/MATH-639
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.2
> Environment: Linux
> Reporter: Luc Maisonobe
> Assignee: Luc Maisonobe
> Fix For: 3.0
>
>
> building a rotation from the following vector pairs leads to NaN:
> u1 = -4921140.837095533, -2.1512094250440013E7, -890093.279426377
> u2 = -2.7238580938724895E9, -2.169664921341876E9, 6.749688708885301E10
> v1 = 1, 0, 0
> v2 = 0, 0, 1
> The constructor first changes the (v1, v2) pair into (v1', v2') ensuring the following scalar products hold:
> ==
> ==
> ==
> Once the (v1', v2') pair has been computed, we compute the cross product:
> k = (v1' - u1)^(v2' - u2)
> and the scalar product:
> c =
> By construction, c is positive or null and the quaternion axis we want to build is q = k/[2*sqrt(c)].
> c should be null only if some of the vectors are aligned, and this is dealt with later in the algorithm.
> However, there are numerical problems with the vector above with the way these computations are done, as shown
> by the following comparisons, showing the result we get from our Java code and the result we get from manual
> computation with the same formulas but with enhanced precision:
> commons math: k = 38514476.5, -84., -1168590144
> high precision: k = 38514410.36093388..., -0.374075245201180409222711..., -1168590152.10599715208...
> and it becomes worse when computing c because the vectors are almost orthogonal to each other, hence inducing additional cancellations. We get:
> commons math c = -1.2397173627587605E20
> high precision: c = 558382746168463196.7079627...
> We have lost ALL significant digits in cancellations, and even the sign is wrong!
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