import numpy as np

import gtsam
from gtsam import Values

def circlePose3(numPoses: int = 8, radius: float = 1.0, symbolChar: str = '\0') -> Values:
    """
    circlePose3 generates a set of poses in a circle. This function
    returns those poses inside a gtsam.Values object, with sequential
    keys starting from 0. An optional character may be provided, which
    will be stored in the msb of each key (i.e. gtsam.Symbol).

    We use aerospace/navlab convention, X forward, Y right, Z down
    First pose will be at (R,0,0)
    ^y   ^ X
    |    |
    z-->xZ--> Y  (z pointing towards viewer, Z pointing away from viewer)
    Vehicle at p0 is looking towards y axis (X-axis points towards world y)
    """

    values = gtsam.Values()
    theta = 0.0
    dtheta = 2 * np.pi / numPoses
    gRo = gtsam.Rot3(
        np.array(
            [
                [0., 1., 0.],
                [1., 0., 0.],
                [0., 0., -1.]
            ], order='F'
        )
    )
    for i in range(numPoses):
        key = gtsam.symbol(symbolChar, i)
        gti = gtsam.Point3(radius * np.cos(theta), radius * np.sin(theta), 0)
        # negative yaw goes counterclockwise, with Z down !
        oRi = gtsam.Rot3.Yaw(-theta)  
        gTi = gtsam.Pose3(gRo.compose(oRi), gti)
        values.insert(key, gTi)
        theta = theta + dtheta
    return values