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Fix bug #609: avoid if statement and improve consistency of eulerAngles method

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This commit is contained in:
Gael Guennebaud
2013-06-09 23:14:45 +02:00
parent e04b59929e
commit c98fd7a6ca
2 changed files with 85 additions and 31 deletions
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58
Eigen/src/Geometry/EulerAngles.h
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@@ -27,12 +27,18 @@ namespace Eigen {
* * AngleAxisf(ea[1], Vector3f::UnitX())
* * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
* This corresponds to the right-multiply conventions (with right hand side frames).
*
* The returned angles are in the ranges [0:pi]x[0:pi]x[-pi:pi].
*
* \sa class AngleAxis
*/
template<typename Derived>
inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
using std::atan2;
using std::sin;
using std::cos;
/* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
@@ -44,39 +50,53 @@ MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
const Index i = a0;
const Index j = (a0 + 1 + odd)%3;
const Index k = (a0 + 2 - odd)%3;
if (a0==a2)
{
Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
res[1] = atan2(s, coeff(i,i));
if (s > epsilon)
res[0] = atan2(coeff(j,i), coeff(k,i));
if((odd && res[0]<0) || ((!odd) && res[0]>0))
{
res[0] = atan2(coeff(j,i), coeff(k,i));
res[2] = atan2(coeff(i,j),-coeff(i,k));
res[0] = (res[0] > 0) ? res[0] - M_PI : res[0] + M_PI;
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = -atan2(s2, coeff(i,i));
}
else
{
res[0] = Scalar(0);
res[2] = (coeff(i,i)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = atan2(s2, coeff(i,i));
}
}
// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
// we can compute their respective rotation, and apply its inverse to M. Since the result must
// be a rotation around x, we have:
//
// c2 s1.s2 c1.s2 1 0 0
// 0 c1 -s1 * M = 0 c3 s3
// -s2 s1.c2 c1.c2 0 -s3 c3
//
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
}
else
{
Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
res[1] = atan2(-coeff(i,k), c);
if (c > epsilon)
{
res[0] = atan2(coeff(j,k), coeff(k,k));
res[2] = atan2(coeff(i,j), coeff(i,i));
res[0] = atan2(coeff(j,k), coeff(k,k));
Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
if((odd && res[0]<0) || ((!odd) && res[0]>0)) {
res[0] = (res[0] > 0) ? res[0] - M_PI : res[0] + M_PI;
res[1] = atan2(-coeff(i,k), -c2);
}
else
{
res[0] = Scalar(0);
res[2] = (coeff(i,k)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
}
res[1] = atan2(-coeff(i,k), c2);
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
}
if (!odd)
res = -res;
return res;
}