Fix a bug in QuaternionRotatePoint.


the computation of the norm of a quaternion

scale = 1/sqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);

was replaced by

scale = 1/hypot(q[0], q[1], hypot(q[2], q[3]));

while this appear to be a more accurate computation because of the
use of hypot which can handle over and underflow it introduces a
bug for the case where q[2] = q[3] = 0.

While the hypot(q[2], q[3]) == 0 as scalars, if q[2] and q[3] are
jets, then the derivative will be NaN. Which means that even though
q[0] or q[1] is non-zero and the norm of the quaternion is non-zero,
and the resulting derivative is finite, this way of computing the
scale will produce nans in the derivative of scale.

The following quaternion will replicate the problem described above.

using Jet = ceres::Jet<double, 4>;
std::array<Jet, 4> quaternion = {Jet(1.0, 0), Jet(0.0, 1), Jet(0.0, 2), Jet(0.0, 3)};

This CL reverts the change to QuaternionRotatePoint and
adds a test for it.

Thanks to Jonathan Taylor for reproducing this bug.

Change-Id: I0fbbcc77d6945a38563d82efba4429f4b5278cd5
2 files changed
tree: 8f026bfcb7487d4e13d8b09ca69b576dcedae707
  1. .github/
  2. bazel/
  3. cmake/
  4. config/
  5. data/
  6. docs/
  7. examples/
  8. include/
  9. internal/
  10. scripts/
  11. .clang-format
  12. .gitignore
  13. BUILD
  14. CITATION.cff
  15. CMakeLists.txt
  18. package.xml

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Ceres Solver

Ceres Solver is an open source C++ library for modeling and solving large, complicated optimization problems. It is a feature rich, mature and performant library which has been used in production at Google since 2010. Ceres Solver can solve two kinds of problems.

  1. Non-linear Least Squares problems with bounds constraints.
  2. General unconstrained optimization problems.

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