Added expmap coordinate mode option for Sphere2 retract and local coordinates, as well as unrotate for Sphere2.

release/4.3a0
Alex Trevor 2014-01-07 17:45:09 -05:00
parent bfd334dd0e
commit 401fede2e9
5 changed files with 104 additions and 26 deletions

View File

@ -81,6 +81,17 @@ Sphere2 Rot3::rotate(const Sphere2& p,
return q;
}
/* ************************************************************************* */
Sphere2 Rot3::unrotate(const Sphere2& p,
boost::optional<Matrix&> HR, boost::optional<Matrix&> Hp) const {
Sphere2 q = unrotate(p.point3(Hp));
if (Hp)
(*Hp) = q.basis().transpose() * matrix().transpose () * (*Hp);
if (HR)
(*HR) = q.basis().transpose() * q.skew();
return q;
}
/* ************************************************************************* */
Sphere2 Rot3::operator*(const Sphere2& p) const {
return rotate(p);

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@ -331,6 +331,10 @@ namespace gtsam {
Sphere2 rotate(const Sphere2& p, boost::optional<Matrix&> HR = boost::none,
boost::optional<Matrix&> Hp = boost::none) const;
/// unrotate 3D direction from world frame to rotated coordinate frame
Sphere2 unrotate(const Sphere2& p, boost::optional<Matrix&> HR = boost::none,
boost::optional<Matrix&> Hp = boost::none) const;
/// rotate 3D direction from rotated coordinate frame to world frame
Sphere2 operator*(const Sphere2& p) const;

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@ -98,7 +98,7 @@ double Sphere2::distance(const Sphere2& q, boost::optional<Matrix&> H) const {
}
/* ************************************************************************* */
Sphere2 Sphere2::retract(const Vector& v) const {
Sphere2 Sphere2::retract(const Vector& v, Sphere2::CoordinatesMode mode) const {
// Get the vector form of the point and the basis matrix
Vector p = Point3::Logmap(p_);
@ -106,35 +106,64 @@ Sphere2 Sphere2::retract(const Vector& v) const {
// Compute the 3D xi_hat vector
Vector xi_hat = v(0) * B.col(0) + v(1) * B.col(1);
Vector newPoint = p + xi_hat;
if (mode == Sphere2::EXPMAP) {
double xi_hat_norm = xi_hat.norm();
Vector exp_p_xi_hat = cos (xi_hat_norm) * p + sin(xi_hat_norm) * (xi_hat / xi_hat_norm);
return Sphere2(exp_p_xi_hat);
} else if (mode == Sphere2::RENORM) {
// Project onto the manifold, i.e. the closest point on the circle to the new location;
// same as putting it onto the unit circle
Vector newPoint = p + xi_hat;
Vector projected = newPoint / newPoint.norm();
// Project onto the manifold, i.e. the closest point on the circle to the new location;
// same as putting it onto the unit circle
Vector projected = newPoint / newPoint.norm();
return Sphere2(Point3::Expmap(projected));
return Sphere2(Point3::Expmap(projected));
} else {
assert (false);
exit (1);
}
}
/* ************************************************************************* */
Vector Sphere2::localCoordinates(const Sphere2& y) const {
Vector Sphere2::localCoordinates(const Sphere2& y, Sphere2::CoordinatesMode mode) const {
// Make sure that the angle different between x and y is less than 90. Otherwise,
// we can project x + xi_hat from the tangent space at x to y.
assert(y.p_.dot(p_) > 0.0 && "Can not retract from x to y.");
if (mode == Sphere2::EXPMAP) {
Matrix B = basis();
Vector p = Point3::Logmap(p_);
Vector q = Point3::Logmap(y.p_);
double theta = acos(p.transpose() * q);
// Get the basis matrix
Matrix B = basis();
// Create the vector forms of p and q (the Point3 of y).
Vector p = Point3::Logmap(p_);
Vector q = Point3::Logmap(y.p_);
// Compute the basis coefficients [v0,v1] = (B'q)/(p'q).
double alpha = p.transpose() * q;
assert(alpha != 0.0);
Matrix coeffs = (B.transpose() * q) / alpha;
Vector result = Vector_(2, coeffs(0, 0), coeffs(1, 0));
return result;
// the below will be nan if theta == 0.0
if (theta == 0.0)
return (Vector (2) << 0, 0);
Vector result_hat = (theta / sin(theta)) * (q - p * cos(theta));
Vector result = B.transpose() * result_hat;
return result;
} else if (mode == Sphere2::RENORM) {
// Make sure that the angle different between x and y is less than 90. Otherwise,
// we can project x + xi_hat from the tangent space at x to y.
assert(y.p_.dot(p_) > 0.0 && "Can not retract from x to y.");
// Get the basis matrix
Matrix B = basis();
// Create the vector forms of p and q (the Point3 of y).
Vector p = Point3::Logmap(p_);
Vector q = Point3::Logmap(y.p_);
// Compute the basis coefficients [v0,v1] = (B'q)/(p'q).
double alpha = p.transpose() * q;
assert(alpha != 0.0);
Matrix coeffs = (B.transpose() * q) / alpha;
Vector result = Vector_(2, coeffs(0, 0), coeffs(1, 0));
return result;
} else {
assert (false);
exit (1);
}
}
/* ************************************************************************* */

View File

@ -22,6 +22,10 @@
#include <gtsam/geometry/Point3.h>
#include <gtsam/base/DerivedValue.h>
#ifndef SPHERE2_DEFAULT_COORDINATES_MODE
#define SPHERE2_DEFAULT_COORDINATES_MODE Sphere2::EXPMAP
#endif
// (Cumbersome) forward declaration for random generator
namespace boost {
namespace random {
@ -121,11 +125,16 @@ public:
return 2;
}
enum CoordinatesMode {
EXPMAP, ///< Use the exponential map to retract
RENORM ///< Retract with vector addtion and renormalize.
};
/// The retract function
Sphere2 retract(const Vector& v) const;
Sphere2 retract(const Vector& v, Sphere2::CoordinatesMode mode = SPHERE2_DEFAULT_COORDINATES_MODE) const;
/// The local coordinates function
Vector localCoordinates(const Sphere2& s) const;
Vector localCoordinates(const Sphere2& s, Sphere2::CoordinatesMode mode = SPHERE2_DEFAULT_COORDINATES_MODE) const;
/// @}
};

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@ -75,6 +75,31 @@ TEST(Sphere2, rotate) {
}
}
//*******************************************************************************
static Sphere2 unrotate_(const Rot3& R, const Sphere2& p) {
return R.unrotate (p);
}
TEST(Sphere2, unrotate) {
Rot3 R = Rot3::yaw(-M_PI/2.0);
Sphere2 p(1, 0, 0);
Sphere2 expected = Sphere2(0, 1, 0);
Sphere2 actual = R.unrotate (p);
EXPECT(assert_equal(expected, actual, 1e-8));
Matrix actualH, expectedH;
// Use numerical derivatives to calculate the expected Jacobian
{
expectedH = numericalDerivative21(unrotate_, R, p);
R.unrotate(p, actualH, boost::none);
EXPECT(assert_equal(expectedH, actualH, 1e-9));
}
{
expectedH = numericalDerivative22(unrotate_, R, p);
R.unrotate(p, boost::none, actualH);
EXPECT(assert_equal(expectedH, actualH, 1e-9));
}
}
//*******************************************************************************
TEST(Sphere2, error) {
Sphere2 p(1, 0, 0), q = p.retract((Vector(2) << 0.5, 0)), //