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faster implementation of SO3 random #105

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faster implementation of SO3 random #105

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48 changes: 31 additions & 17 deletions include/manif/impl/se3/SE3_base.h
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Original file line number Diff line number Diff line change
Expand Up @@ -374,28 +374,42 @@ struct RandomEvaluatorImpl<SE3Base<Derived>>
static void run(T& m)
{
// @note:
// We are using:
// http://mathworld.wolfram.com/HyperspherePointPicking.html
// which is faster than Quaternion::UnitRandom, and also,
// Quaternion::UnitRandom is not available in Eigen 3.3-beta1
// which is the default version in Ubuntu 16.04
// So we copy its implementation here.

using std::sqrt;
using std::sin;
using std::cos;

using Scalar = typename SE3Base<Derived>::Scalar;
using Scalar = typename SO3Base<Derived>::Scalar;
using Translation = typename SE3Base<Derived>::Translation;
using Quaternion = typename SE3Base<Derived>::QuaternionDataType;

const Scalar u1 = Eigen::internal::random<Scalar>(0, 1),
u2 = Eigen::internal::random<Scalar>(0, 2*EIGEN_PI),
u3 = Eigen::internal::random<Scalar>(0, 2*EIGEN_PI);
const Scalar a = sqrt(1. - u1),
b = sqrt(u1);

m = Derived(Translation::Random(),
Quaternion(a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3)));

//m = Derived(Translation::Random(), Quaternion::UnitRandom());
using Quaternion = typename SO3Base<Derived>::QuaternionDataType;

while (true)
{
const Scalar u1 = Eigen::internal::random<Scalar>(-1, 1),
u2 = Eigen::internal::random<Scalar>(-1, 1);
if (u1 * u1 + u2 * u2 > 1.0)
{
continue;
}

while (true)
{
const Scalar u3 = Eigen::internal::random<Scalar>(-1, 1),
u4 = Eigen::internal::random<Scalar>(-1, 1);
if (u3 * u3 + u4 * u4 > 1.0)
{
continue;
}
const Scalar zw_factor = sqrt((1 - u1 * u1 - u2 * u2) / (u3 * u3 + u4 * u4));
const Scalar z = u3 * zw_factor;
const Scalar w = u4 * zw_factor;
m = Derived(Translation::Random(), Quaternion(u1, u2, z, w));
break;
}
break;
}
}
};

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42 changes: 28 additions & 14 deletions include/manif/impl/so3/SO3_base.h
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Original file line number Diff line number Diff line change
Expand Up @@ -359,28 +359,42 @@ struct RandomEvaluatorImpl<SO3Base<Derived>>
template <typename T>
static void run(T& m)
{

// @note:
// We are using:
// http://mathworld.wolfram.com/HyperspherePointPicking.html
// which is faster than Quaternion::UnitRandom, and also,
// Quaternion::UnitRandom is not available in Eigen 3.3-beta1
// which is the default version in Ubuntu 16.04
// So we copy its implementation here.

using std::sqrt;
using std::sin;
using std::cos;

using Scalar = typename SO3Base<Derived>::Scalar;
using Quaternion = typename SO3Base<Derived>::QuaternionDataType;

const Scalar u1 = Eigen::internal::random<Scalar>(0, 1),
u2 = Eigen::internal::random<Scalar>(0, 2*EIGEN_PI),
u3 = Eigen::internal::random<Scalar>(0, 2*EIGEN_PI);
const Scalar a = sqrt(1. - u1),
b = sqrt(u1);
m = Derived(Quaternion(a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3)));


// m = Derived(Quaternion::UnitRandom());
while (true)
{
const Scalar u1 = Eigen::internal::random<Scalar>(-1, 1),
u2 = Eigen::internal::random<Scalar>(-1, 1);
if (u1 * u1 + u2 * u2 > 1.0)
{
continue;
}

while (true)
{
const Scalar u3 = Eigen::internal::random<Scalar>(-1, 1),
u4 = Eigen::internal::random<Scalar>(-1, 1);
if (u3 * u3 + u4 * u4 > 1.0)
{
continue;
}
const Scalar zw_factor = sqrt((1 - u1 * u1 - u2 * u2) / (u3 * u3 + u4 * u4));
const Scalar z = u3 * zw_factor;
const Scalar w = u4 * zw_factor;
m = Derived(Quaternion(u1, u2, z, w));
break;
}
break;
}
}
};

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