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Diff-TTSG
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"""
Tools for Manipulating and Converting 3D Rotations

By Omid Alemi
Created: June 12, 2017

Adapted from that matlab file...
"""

import math

import numpy as np
import transforms3d as t3d

from pymo.Quaternions import Quaternions


def deg2rad(x):
    return x / 180 * math.pi


def rad2deg(x):
    return x / math.pi * 180


def unroll(rots):
    new_rot = rots.copy()
    ang0 = np.linalg.norm(rots, axis=1) + 1e-8
    idx = np.where(ang0 > np.pi)[0]
    ax = rots / np.tile(ang0[:, None], (1, 3))
    ang1 = ang0 - 2 * np.pi
    alt_rot = ax * np.tile(ang1[:, None], (1, 3))
    new_rot[idx] = alt_rot[idx]
    return new_rot


def unroll_1(rots):
    new_rots = rots.copy()

    # Compute angles and alternative rotation angles
    angs = np.linalg.norm(rots, axis=1)
    alt_angs = 2 * np.pi - angs

    # find discontinuities
    d_angs = np.diff(angs, axis=0)
    d_angs2 = alt_angs[1:] - angs[:-1]

    swps = np.where(np.abs(d_angs2) < np.abs(d_angs))[0]

    # reshape into intervals where we should unroll the rotations
    isodd = swps.shape[0] % 2 == 1
    if isodd:
        swps = np.append(swps, rots.shape[0] - 1)
    intv = 1 + swps.reshape((swps.shape[0] // 2, 2))
    for ii in range(intv.shape[0]):
        new_ax = -rots[intv[ii, 0] : intv[ii, 1], :] / np.tile(angs[intv[ii, 0] : intv[ii, 1], None], (1, 3))
        new_angs = alt_angs[intv[ii, 0] : intv[ii, 1]]
        new_rots[intv[ii, 0] : intv[ii, 1], :] = new_ax * np.tile(new_angs[:, None], (1, 3))

    return new_rots


def unroll_2(rots):
    new_rots = rots.copy()

    # Compute angles and alternative rotation angles
    angs = np.linalg.norm(rots, axis=1)
    dotprod = np.einsum("ij,ij->i", rots[:-1, :], rots[1:, :])
    # ax = rots/np.tile(angs[:, None], (1,3))
    # d_ax = np.linalg.norm(np.diff(ax, axis=0), axis=1)
    alt_angs = 2 * np.pi - angs

    # find discontinuities
    d_angs = np.diff(angs, axis=0)
    d_angs2 = alt_angs[1:] - angs[:-1]

    # FIXME should check if dot product is <0 not norm d_ax
    swps = np.where(dotprod < -1)[0]
    # swps = np.where((np.abs(d_ax)>0.5))[0]
    # swps = np.where(np.abs(d_angs2)<np.abs(d_angs))[0]

    # reshape into intervals where we should unroll the rotations
    isodd = swps.shape[0] % 2 == 1
    if isodd:
        swps = swps[:-1]
        # swps = np.append(swps, rots.shape[0]-1)
    intv = 1 + swps.reshape((swps.shape[0] // 2, 2))
    for ii in range(intv.shape[0]):
        new_ax = -rots[intv[ii, 0] : intv[ii, 1], :] / np.tile(angs[intv[ii, 0] : intv[ii, 1], None], (1, 3))
        new_angs = alt_angs[intv[ii, 0] : intv[ii, 1]]
        new_rots[intv[ii, 0] : intv[ii, 1], :] = new_ax * np.tile(new_angs[:, None], (1, 3))

    return new_rots


def euler_reorder2(rots, order="XYZ", new_order="XYZ", use_deg=False):
    if order == new_order:
        return rots

    if use_deg:
        rots = np.deg2rad(rots)

    quats = Quaternions.from_euler(rots, order=order.lower())
    eul = quats.euler(order=new_order.lower())

    if use_deg:
        eul = np.rad2deg(eul)

    return eul


def euler_reorder(rot, order="XYZ", new_order="XYZ", use_deg=False):
    if order == new_order:
        return rot

    if use_deg:
        rot = np.deg2rad(rot)
    print("order:" + order)
    print("new_order:" + new_order)

    rotmat = t3d.euler.euler2mat(rot[0], rot[1], rot[2], "r" + order.lower())
    eul = t3d.euler.mat2euler(rotmat, "r" + new_order.lower())

    # quat = t3d.euler.euler2quat(rot[0], rot[1], rot[2], 'r' + order.lower())
    # eul = t3d.euler.quat2euler(quat, 'r' + new_order.lower())

    if use_deg:
        eul = np.rad2deg(eul)

    return eul


def offsets_inv(offset, rots, order="XYZ", use_deg=False):
    if use_deg:
        offset = np.deg2rad(offset)
        rots = np.deg2rad(rots)

    q0 = t3d.euler.euler2quat(rots[0], rots[1], rots[2], "r" + order.lower())
    q_off = t3d.euler.euler2quat(offset[0], offset[1], offset[2], "r" + order.lower())
    q2 = t3d.euler.quat2euler(t3d.quaternions.qmult(q0, t3d.quaternions.qinverse(q_off)), "r" + order.lower())
    # q0=Quaternions.from_euler(rots, order=order.lower())
    # q_off=Quaternions.from_euler(offset, order=order.lower())
    # q2=((-q_off)*q0).euler(order=order.lower())

    if use_deg:
        q2 = np.rad2deg(q2)

    return q2


def offsets(offset, rots, order="XYZ", use_deg=False):
    if use_deg:
        offset = np.deg2rad(offset)
        rots = np.deg2rad(rots)

    q0 = t3d.euler.euler2quat(rots[0], rots[1], rots[2], "r" + order.lower())
    q_off = t3d.euler.euler2quat(offset[0], offset[1], offset[2], "r" + order.lower())
    q2 = t3d.euler.quat2euler(t3d.quaternions.qmult(q0, q_off), "r" + order.lower())
    # q0=Quaternions.from_euler(rots, order=order.lower())
    # q_off=Quaternions.from_euler(offset, order=order.lower())
    # q2=(q_off*q0).euler(order=order.lower())

    if use_deg:
        q2 = np.rad2deg(q2)

    return q2


def euler2expmap2(rots, order="XYZ", use_deg=False):
    if use_deg:
        rots = np.deg2rad(rots)
    # print("rot:" + str(rot))
    quats = Quaternions.from_euler(rots, order=order.lower())
    theta, vec = quats.angle_axis()
    return unroll(vec * np.tile(theta[:, None], (1, 3)))


def euler2expmap(rot, order="XYZ", use_deg=False):
    if use_deg:
        rot = np.deg2rad(rot)
    # print("rot:" + str(rot))
    vec, theta = t3d.euler.euler2axangle(rot[0], rot[1], rot[2], "r" + order.lower())
    return vec * theta


def expmap2euler(rot, order="XYZ", use_deg=False):
    theta = np.linalg.norm(rot)
    if theta > 1.0e-10:
        vector = rot / theta
    else:
        vector = np.array([1.0, 0.0, 0.0])
        theta = 0.0
    eul = t3d.euler.axangle2euler(vector, theta, "r" + order.lower())
    if use_deg:
        return np.rad2deg(eul)
    else:
        return eul


def euler2vectors(rot, order="XYZ", use_deg=False):
    if use_deg:
        rot = np.deg2rad(rot)

    # order = "r" + (order.lower())[::-1] # try both r and s
    # rotation_matrix = np.transpose(t3d.euler.euler2mat(rot[0], rot[1], rot[2], axes=order))
    rotation_matrix = t3d.euler.euler2mat(rot[0], rot[1], rot[2], "r" + order.lower())

    y_vector_x_value = rotation_matrix[0][1]
    y_vector_y_value = rotation_matrix[1][1]
    y_vector_z_value = rotation_matrix[2][1]
    z_vector_x_value = rotation_matrix[0][2]
    z_vector_y_value = rotation_matrix[1][2]
    z_vector_z_value = rotation_matrix[2][2]

    return y_vector_x_value, y_vector_y_value, y_vector_z_value, z_vector_x_value, z_vector_y_value, z_vector_z_value


def vectors2euler(axises, order="XYZ", use_deg=False):
    # create rotation matrix
    y_vector = [axises[0], axises[1], axises[2]]
    z_vector = [axises[3], axises[4], axises[5]]
    x_vector = np.cross(y_vector, z_vector)

    R = np.column_stack((x_vector, y_vector, z_vector))

    # orthogonalize vectors
    u, s, vt = np.linalg.svd(R)
    R = np.matmul(u, vt)

    # to euler
    eul = t3d.euler.mat2euler(R, "r" + order.lower())

    if use_deg:
        return np.rad2deg(eul)
    else:
        return eul


class Rotation:
    def __init__(self, rot, param_type, **params):
        self.rotmat = []
        if param_type == "euler":
            self._from_euler(rot[0], rot[1], rot[2], params)
        elif param_type == "expmap":
            self._from_expmap(rot[0], rot[1], rot[2], params)

    def _from_euler(self, alpha, beta, gamma, params):
        """Expecting degress"""

        if params["from_deg"] == True:
            alpha = deg2rad(alpha)
            beta = deg2rad(beta)
            gamma = deg2rad(gamma)

        order = "s" + ((params["order"]).lower())[::-1]
        #        Quaternions.from_euler()
        self.rotmat = np.transpose(t3d.euler.euler2mat(gamma, beta, alpha, axes=order))

    #        ca = math.cos(alpha)
    #        cb = math.cos(beta)
    #        cg = math.cos(gamma)
    #        sa = math.sin(alpha)
    #        sb = math.sin(beta)
    #        sg = math.sin(gamma)
    #
    #        Rx = np.asarray([[1, 0, 0],
    #              [0, ca, sa],
    #              [0, -sa, ca]
    #              ])
    #
    #        Ry = np.asarray([[cb, 0, -sb],
    #              [0, 1, 0],
    #              [sb, 0, cb]])
    #
    #        Rz = np.asarray([[cg, sg, 0],
    #              [-sg, cg, 0],
    #              [0, 0, 1]])
    #
    #        self.rotmat = np.eye(3)
    #
    #        order = params['order']
    #        for i in range(0,len(order)):
    #            if order[i]=='X':
    #                self.rotmat = np.matmul(Rx, self.rotmat)
    #            elif order[i]=='Y':
    #                self.rotmat = np.matmul(Ry, self.rotmat)
    #            elif order[i]=='Z':
    #                self.rotmat = np.matmul(Rz, self.rotmat)
    #            else:
    #                print('unknown rotation axis: ' + order[i])
    #
    #        # self.rotmat = np.matmul(np.matmul(Rz, Ry), Rx)
    #        print ("------" + "TRUE")
    #        print (self.rotmat)

    def _from_expmap(self, alpha, beta, gamma, params):
        if alpha == 0 and beta == 0 and gamma == 0:
            self.rotmat = np.eye(3)
            return

        # TODO: Check exp map params

        theta = np.linalg.norm([alpha, beta, gamma])

        expmap = [alpha, beta, gamma] / theta

        x = expmap[0]
        y = expmap[1]
        z = expmap[2]

        s = math.sin(theta / 2)
        c = math.cos(theta / 2)

        self.rotmat = np.asarray(
            [
                [2 * (x**2 - 1) * s**2 + 1, 2 * x * y * s**2 - 2 * z * c * s, 2 * x * z * s**2 + 2 * y * c * s],
                [2 * x * y * s**2 + 2 * z * c * s, 2 * (y**2 - 1) * s**2 + 1, 2 * y * z * s**2 - 2 * x * c * s],
                [2 * x * z * s**2 - 2 * y * c * s, 2 * y * z * s**2 + 2 * x * c * s, 2 * (z**2 - 1) * s**2 + 1],
            ]
        )

    def get_euler_axis(self):
        R = self.rotmat
        theta = math.acos((self.rotmat.trace() - 1) / 2)
        axis = np.asarray([R[2, 1] - R[1, 2], R[0, 2] - R[2, 0], R[1, 0] - R[0, 1]])
        axis = axis / (2 * math.sin(theta))
        return theta, axis

    def to_expmap(self):
        axis, theta = t3d.axangles.mat2axangle(self.rotmat, unit_thresh=1e-05)
        #        theta, axis = self.get_euler_axis()
        rot_arr = theta * axis
        if np.isnan(rot_arr).any():
            rot_arr = [0, 0, 0]
        return rot_arr

    def to_euler(self, use_deg=False, order="xyz"):
        order = "s" + order.lower()
        eulers = t3d.euler.mat2euler(np.transpose(self.rotmat), axes=order)
        return eulers[::-1]

        #        eulers = np.zeros((2, 3))
        #
        #        if np.absolute(np.absolute(self.rotmat[2, 0]) - 1) < 1e-12:
        #            #GIMBAL LOCK!
        #            print('Gimbal')
        #            if np.absolute(self.rotmat[2, 0]) - 1 < 1e-12:
        #                eulers[:,0] = math.atan2(-self.rotmat[0,1], -self.rotmat[0,2])
        #                eulers[:,1] = -math.pi/2
        #            else:
        #                eulers[:,0] = math.atan2(self.rotmat[0,1], -elf.rotmat[0,2])
        #                eulers[:,1] = math.pi/2
        #
        #            return eulers
        #
        #        theta = - math.asin(self.rotmat[2,0])
        #        theta2 = math.pi - theta
        #
        #        # psi1, psi2
        #        eulers[0,0] = math.atan2(self.rotmat[2,1]/math.cos(theta), self.rotmat[2,2]/math.cos(theta))
        #        eulers[1,0] = math.atan2(self.rotmat[2,1]/math.cos(theta2), self.rotmat[2,2]/math.cos(theta2))
        #
        #        # theta1, theta2
        #        eulers[0,1] = theta
        #        eulers[1,1] = theta2
        #
        #        # phi1, phi2
        #        eulers[0,2] = math.atan2(self.rotmat[1,0]/math.cos(theta), self.rotmat[0,0]/math.cos(theta))
        #        eulers[1,2] = math.atan2(self.rotmat[1,0]/math.cos(theta2), self.rotmat[0,0]/math.cos(theta2))
        #
        if use_deg:
            eulers = rad2deg(eulers)

        return eulers

    def to_quat(self):
        # TODO
        pass

    def __str__(self):
        return "Rotation Matrix: \n " + self.rotmat.__str__()