// rotate and derivatives
inline Point2 rotate_(const Rot2 & R, const Point2& p) {return R.rotate(p);}
int main() {
/**
* Step 1: Create a factor to express a unary constraint
* The "prior" in this case is the measurement from a sensor,
* with a model of the noise on the measurement.
*
* The "Key" created here is a label used to associate parts of the
* state (stored in "RotValues") with particular factors. They require
* an index to allow for lookup, and should be unique.
*
* In general, creating a factor requires:
* - A key or set of keys labeling the variables that are acted upon
* - A measurement value
* - A measurement model with the correct dimensionality for the factor
*/
Rot2 prior = Rot2::fromAngle(30 * degree);
prior.print("goal angle");
noiseModel::Isotropic::shared_ptr model = noiseModel::Isotropic::Sigma(1, 1 * degree);
Symbol key('x',1);
PriorFactor<Rot2> factor(key, prior, model);
/**
* Step 2: Create a graph container and add the factor to it
* Before optimizing, all factors need to be added to a Graph container,
* which provides the necessary top-level functionality for defining a
* system of constraints.
*
* In this case, there is only one factor, but in a practical scenario,
* many more factors would be added.
*/
NonlinearFactorGraph graph;
graph.add(factor);
graph.print("full graph");
/**
* Step 3: Create an initial estimate
* An initial estimate of the solution for the system is necessary to
* start optimization. This system state is the "RotValues" structure,
* which is similar in structure to a STL map, in that it maps
* keys (the label created in step 1) to specific values.
*
* The initial estimate provided to optimization will be used as
* a linearization point for optimization, so it is important that
* all of the variables in the graph have a corresponding value in
* this structure.
*
* The interface to all RotValues types is the same, it only depends
* on the type of key used to find the appropriate value map if there
* are multiple types of variables.
*/
Values initial;
initial.insert(key, Rot2::fromAngle(20 * degree));
initial.print("initial estimate");
/**
* Step 4: Optimize
* After formulating the problem with a graph of constraints
* and an initial estimate, executing optimization is as simple
* as calling a general optimization function with the graph and
* initial estimate. This will yield a new RotValues structure
* with the final state of the optimization.
*/
Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
result.print("final result");
return 0;
}
/* ************************************************************************* */
Rot2 Rot2betweenOptimized(const Rot2& r1, const Rot2& r2) {
// Same as compose but sign of sin for r1 is reversed
return Rot2::fromCosSin(r1.c() * r2.c() + r1.s() * r2.s(), -r1.s() * r2.c() + r1.c() * r2.s());
}
void go() {
typedef Vec4<T> Vec;
typedef Vec2<T> Vec2D;
std::cout << std::endl;
std::cout << sizeof(Vec) << std::endl;
std::vector<Vec> vec1; vec1.reserve(50);
std::vector<T> vect(23);
std::vector<Vec> vec2(53);
std::vector<Vec> vec3; vec3.reserve(50234);
Vec x(2.0,4.0,5.0);
Vec y(-3.0,2.0,-5.0);
std::cout << x << std::endl;
std::cout << Vec4<float>(x) << std::endl;
std::cout << Vec4<double>(x) << std::endl;
std::cout << -x << std::endl;
std::cout << x.template get1<2>() << std::endl;
std::cout << y << std::endl;
std::cout << T(3.)*x << std::endl;
std::cout << y*T(0.1) << std::endl;
std::cout << (Vec(1) - y*T(0.1)) << std::endl;
std::cout << mathSSE::sqrt(x) << std::endl;
std::cout << dot(x,y) << std::endl;
std::cout << dotSimple(x,y) << std::endl;
std::cout << "equal" << (x==x ? " " : " not ") << "ok" << std::endl;
std::cout << "not equal" << (x==y ? " not " : " ") << "ok" << std::endl;
Vec z = cross(x,y);
std::cout << z << std::endl;
std::cout << "rotations" << std::endl;
T a = 0.01;
T ca = std::cos(a);
T sa = std::sin(a);
Rot3<T> r1( ca, sa, 0,
-sa, ca, 0,
0, 0, 1);
Rot2<T> r21( ca, sa,
-sa, ca);
Rot3<T> r2(Vec( 0, 1 ,0), Vec( 0, 0, 1), Vec( 1, 0, 0));
Rot2<T> r22(Vec2D( 0, 1), Vec2D( 1, 0));
{
std::cout << "\n3D rot" << std::endl;
Vec xr = r1.rotate(x);
std::cout << x << std::endl;
std::cout << xr << std::endl;
std::cout << r1.rotateBack(xr) << std::endl;
Rot3<T> rt = r1.transpose();
Vec xt = rt.rotate(xr);
std::cout << x << std::endl;
std::cout << xt << std::endl;
std::cout << rt.rotateBack(xt) << std::endl;
std::cout << r1 << std::endl;
std::cout << rt << std::endl;
std::cout << r1*rt << std::endl;
std::cout << r2 << std::endl;
std::cout << r1*r2 << std::endl;
std::cout << r2*r1 << std::endl;
std::cout << r1*r2.transpose() << std::endl;
std::cout << r1.transpose()*r2 << std::endl;
}
{
std::cout << "\n2D rot" << std::endl;
Vec2D xr = r21.rotate(x.xy());
std::cout << x.xy() << std::endl;
std::cout << xr << std::endl;
std::cout << r21.rotateBack(xr) << std::endl;
Rot2<T> rt = r21.transpose();
Vec2D xt = rt.rotate(xr);
std::cout << x.xy() << std::endl;
std::cout << xt << std::endl;
std::cout << rt.rotateBack(xt) << std::endl;
std::cout << r21 << std::endl;
std::cout << rt << std::endl;
std::cout << r21*rt << std::endl;
std::cout << r22 << std::endl;
std::cout << r21*r22 << std::endl;
std::cout << r22*r21 << std::endl;
std::cout << r21*r22.transpose() << std::endl;
std::cout << r21.transpose()*r22 << std::endl;
}
}
/* ************************************************************************* */
Rot2 Rot2betweenDefault(const Rot2& r1, const Rot2& r2) {
return r1.inverse() * r2;
}