Re: [eigen] geometry module

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

On Tue, Sep 7, 2010 at 12:57 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
> Here, "most efficiently" depends on what you're doing. If you want to
> apply this transformation to a vector, it's going to be faster if you
> have a matrix representation of your transform, as the Transform class
> does. This is one of the most performance-critical use cases...

some numbers to transform N 3D vectors stored into a 3xN column major
matrix and transformed using a 3x3 matrix, a quaternion using the
quaternion x a single vector product, and a quaternion converted on
the fly to a 3x3 matrix. The times are in second for 100000 runs (in
the last case the quaternion is converted 100000 times to a matrix).

N                  1         2         3         4         5         6
        7         8
matrix 3x3 0.0007521 0.0008807  0.001357  0.002339  0.002869  0.003583
 0.004301   0.02684
quaternion  0.001332  0.002183  0.003098  0.004002  0.004913  0.005945
 0.007081  0.007997
quat-mat    0.001165   0.00152  0.001822  0.002925  0.003396  0.003964
 0.004615   0.02727

as expected the matrix product is significantly faster, but what is
surprising is that even for transforming a single vector (N=1), it is
faster to convert the quaternion to a matrix and then perform the
matrix product rather than directly using the optimized
quaternion-vector product since the costs are respectively:

3x3 matrix : 9 mul + 6 add = 15 ops
quaternion : 15 mul + 15 add = 30 ops
quat-mat   : 18 mul + 21 add = 39 ops

These numbers directly come from the assembly where we can see gcc
optimized the "2 * v" by "v+v".

also Daniel you might be interested to know that this benchmark is in
bench/quaternion.cpp (in trunk).


gael