/* ************************************************************************* */
Pose2 Pose2betweenOptimized(const Pose2& r1, const Pose2& r2,
boost::optional<Matrix3&> H1, boost::optional<Matrix3&> H2)
{
// get cosines and sines from rotation matrices
const Rot2& R1 = r1.r(), R2 = r2.r();
double c1=R1.c(), s1=R1.s(), c2=R2.c(), s2=R2.s();
// Assert that R1 and R2 are normalized
assert(std::abs(c1*c1 + s1*s1 - 1.0) < 1e-5 && std::abs(c2*c2 + s2*s2 - 1.0) < 1e-5);
// Calculate delta rotation = between(R1,R2)
double c = c1 * c2 + s1 * s2, s = -s1 * c2 + c1 * s2;
Rot2 R(Rot2::atan2(s,c)); // normalizes
// Calculate delta translation = unrotate(R1, dt);
Point2 dt = r2.t() - r1.t();
double x = dt.x(), y = dt.y();
Point2 t(c1 * x + s1 * y, -s1 * x + c1 * y);
// FD: This is just -AdjointMap(between(p2,p1)) inlined and re-using above
if (H1) {
double dt1 = -s2 * x + c2 * y;
double dt2 = -c2 * x - s2 * y;
*H1 = Matrix3();
(*H1) <<
-c, -s, dt1,
s, -c, dt2,
0.0, 0.0,-1.0;
}
if (H2) *H2 = Matrix3::Identity();
return Pose2(R,t);
}
/* ************************************************************************* */
Rot2 Pose2::bearing(const Pose2& point,
boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
Rot2 result = bearing(point.t(), H1, H2);
if (H2) {
Matrix H2_ = *H2 * point.r().matrix();
*H2 = zeros(1, 3);
insertSub(*H2, H2_, 0, 0);
}
return result;
}
/* ************************************************************************* */
Vector Pose2::Logmap(const Pose2& p) {
const Rot2& R = p.r();
const Point2& t = p.t();
double w = R.theta();
if (std::abs(w) < 1e-10)
return (Vector(3) << t.x(), t.y(), w);
else {
double c_1 = R.c()-1.0, s = R.s();
double det = c_1*c_1 + s*s;
Point2 p = R_PI_2 * (R.unrotate(t) - t);
Point2 v = (w/det) * p;
return (Vector(3) << v.x(), v.y(), w);
}
}
/* ************************************************************************* */
double Pose2::range(const Pose2& pose2,
boost::optional<Matrix&> H1,
boost::optional<Matrix&> H2) const {
Point2 d = pose2.t() - t_;
if (!H1 && !H2) return d.norm();
Matrix H;
double r = d.norm(H);
if (H1) *H1 = H * (Matrix(2, 3) <<
-r_.c(), r_.s(), 0.0,
-r_.s(), -r_.c(), 0.0);
if (H2) *H2 = H * (Matrix(2, 3) <<
pose2.r_.c(), -pose2.r_.s(), 0.0,
pose2.r_.s(), pose2.r_.c(), 0.0);
return r;
}