"""Utility functions for two- and three-dimensional vectors."""

__all__ = [
    "get_norm",
    "quaternion_mult",
    "quaternion_from_angle_axis",
    "angle_axis_from_quaternion",
    "quaternion_conjugate",
    "rotate_vector",
    "thick_diagonal",
    "rotation_matrix",
    "rotation_about_z",
    "z_to_vector",
    "angle_between",
    "angle_of_vector",
    "angle_between_vectors",
    "project_along_vector",
    "normalize",
    "cross",
    "get_unit_normal",
    "compass_directions",
    "complex_to_R3",
    "R3_to_complex",
    "complex_func_to_R3_func",
    "center_of_mass",
    "midpoint",
    "find_intersection",
    "line_intersection",
    "get_winding_number",
    "cross2d",
    "earclip_triangulation",
]


import itertools as it
import math
from functools import reduce

import numpy as np
from mapbox_earcut import triangulate_float32 as earcut

from .. import config
from ..constants import DOWN, OUT, PI, RIGHT, TAU
from ..utils.iterables import adjacent_pairs
from ..utils.simple_functions import fdiv


def get_norm(vect):
    return sum([x ** 2 for x in vect]) ** 0.5


def norm_squared(v):
    return v[0] * v[0] + v[1] * v[1] + v[2] * v[2]


# Quaternions
# TODO, implement quaternion type


def quaternion_mult(*quats):
    if config.renderer == "opengl":
        if len(quats) == 0:
            return [1, 0, 0, 0]
        result = quats[0]
        for next_quat in quats[1:]:
            w1, x1, y1, z1 = result
            w2, x2, y2, z2 = next_quat
            result = [
                w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2,
                w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2,
                w1 * y2 + y1 * w2 + z1 * x2 - x1 * z2,
                w1 * z2 + z1 * w2 + x1 * y2 - y1 * x2,
            ]
        return result
    else:
        q1 = quats[0]
        q2 = quats[1]

        w1, x1, y1, z1 = q1
        w2, x2, y2, z2 = q2
        return np.array(
            [
                w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2,
                w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2,
                w1 * y2 + y1 * w2 + z1 * x2 - x1 * z2,
                w1 * z2 + z1 * w2 + x1 * y2 - y1 * x2,
            ]
        )


def quaternion_from_angle_axis(angle, axis, axis_normalized=False):
    if config.renderer == "opengl":
        if not axis_normalized:
            axis = normalize(axis)
        return [math.cos(angle / 2), *(math.sin(angle / 2) * axis)]
    else:
        return np.append(np.cos(angle / 2), np.sin(angle / 2) * normalize(axis))


def angle_axis_from_quaternion(quaternion):
    axis = normalize(quaternion[1:], fall_back=np.array([1, 0, 0]))
    angle = 2 * np.arccos(quaternion[0])
    if angle > TAU / 2:
        angle = TAU - angle
    return angle, axis


def quaternion_conjugate(quaternion):
    result = np.array(quaternion)
    result[1:] *= -1
    return result


def rotate_vector(vector, angle, axis=OUT):
    if len(vector) == 2:
        # Use complex numbers...because why not
        z = complex(*vector) * np.exp(complex(0, angle))
        return np.array([z.real, z.imag])
    elif len(vector) == 3:
        # Use quaternions...because why not
        quat = quaternion_from_angle_axis(angle, axis)
        quat_inv = quaternion_conjugate(quat)
        product = reduce(quaternion_mult, [quat, np.append(0, vector), quat_inv])
        return product[1:]
    else:
        raise ValueError("vector must be of dimension 2 or 3")


def thick_diagonal(dim, thickness=2):
    row_indices = np.arange(dim).repeat(dim).reshape((dim, dim))
    col_indices = np.transpose(row_indices)
    return (np.abs(row_indices - col_indices) < thickness).astype("uint8")


def rotation_matrix_transpose_from_quaternion(quat):
    quat_inv = quaternion_conjugate(quat)
    return [
        quaternion_mult(quat, [0, *basis], quat_inv)[1:]
        for basis in [
            [1, 0, 0],
            [0, 1, 0],
            [0, 0, 1],
        ]
    ]


def rotation_matrix_from_quaternion(quat):
    return np.transpose(rotation_matrix_transpose_from_quaternion(quat))


def rotation_matrix_transpose(angle, axis):
    if axis[0] == 0 and axis[1] == 0:
        # axis = [0, 0, z] case is common enough it's worth
        # having a shortcut
        sgn = 1 if axis[2] > 0 else -1
        cos_a = math.cos(angle)
        sin_a = math.sin(angle) * sgn
        return [
            [cos_a, sin_a, 0],
            [-sin_a, cos_a, 0],
            [0, 0, 1],
        ]
    quat = quaternion_from_angle_axis(angle, axis)
    return rotation_matrix_transpose_from_quaternion(quat)


def rotation_matrix(angle, axis):
    """
    Rotation in R^3 about a specified axis of rotation.
    """
    about_z = rotation_about_z(angle)
    z_to_axis = z_to_vector(axis)
    axis_to_z = np.linalg.inv(z_to_axis)
    return reduce(np.dot, [z_to_axis, about_z, axis_to_z])


def rotation_about_z(angle):
    return [
        [np.cos(angle), -np.sin(angle), 0],
        [np.sin(angle), np.cos(angle), 0],
        [0, 0, 1],
    ]


def z_to_vector(vector):
    """
    Returns some matrix in SO(3) which takes the z-axis to the
    (normalized) vector provided as an argument
    """
    norm = get_norm(vector)
    if norm == 0:
        return np.identity(3)
    v = np.array(vector) / norm
    phi = np.arccos(v[2])
    if any(v[:2]):
        # projection of vector to unit circle
        axis_proj = v[:2] / get_norm(v[:2])
        theta = np.arccos(axis_proj[0])
        if axis_proj[1] < 0:
            theta = -theta
    else:
        theta = 0
    phi_down = np.array(
        [[np.cos(phi), 0, np.sin(phi)], [0, 1, 0], [-np.sin(phi), 0, np.cos(phi)]]
    )
    return np.dot(rotation_about_z(theta), phi_down)


def angle_between(v1, v2):
    return np.arccos(np.dot(v1 / get_norm(v1), v2 / get_norm(v2)))


def angle_of_vector(vector):
    """
    Returns polar coordinate theta when vector is project on xy plane
    """
    if config.renderer == "opengl":
        return np.angle(complex(*vector[:2]))
    else:
        z = complex(*vector[:2])
        if z == 0:
            return 0
        return np.angle(complex(*vector[:2]))


def angle_between_vectors(v1, v2):
    """
    Returns the angle between two 3D vectors.
    This angle will always be btw 0 and pi
    """
    if config["renderer"] == "opengl":
        diff = (angle_of_vector(v2) - angle_of_vector(v1)) % TAU
        return min(diff, TAU - diff)
    else:
        return np.arccos(fdiv(np.dot(v1, v2), get_norm(v1) * get_norm(v2)))


def project_along_vector(point, vector):
    matrix = np.identity(3) - np.outer(vector, vector)
    return np.dot(point, matrix.T)


def normalize(vect, fall_back=None):
    norm = get_norm(vect)
    if norm > 0:
        return np.array(vect) / norm
    else:
        if fall_back is not None:
            return fall_back
        else:
            return np.zeros(len(vect))


def normalize_along_axis(array, axis, fall_back=None):
    norms = np.sqrt((array * array).sum(axis))
    norms[norms == 0] = 1
    buffed_norms = np.repeat(norms, array.shape[axis]).reshape(array.shape)
    array /= buffed_norms
    return array


def cross(v1, v2):
    return np.array(
        [
            v1[1] * v2[2] - v1[2] * v2[1],
            v1[2] * v2[0] - v1[0] * v2[2],
            v1[0] * v2[1] - v1[1] * v2[0],
        ]
    )


def get_unit_normal(v1, v2, tol=1e-6):
    if config.renderer == "opengl":
        v1 = normalize(v1)
        v2 = normalize(v2)
        cp = cross(v1, v2)
        cp_norm = get_norm(cp)
        if cp_norm < tol:
            # Vectors align, so find a normal to them in the plane shared with the z-axis
            new_cp = cross(cross(v1, OUT), v1)
            new_cp_norm = get_norm(new_cp)
            if new_cp_norm < tol:
                return DOWN
            return new_cp / new_cp_norm
        return cp / cp_norm
    else:
        return normalize(cross(v1, v2))


###


def compass_directions(n=4, start_vect=RIGHT):
    angle = TAU / n
    return np.array([rotate_vector(start_vect, k * angle) for k in range(n)])


def complex_to_R3(complex_num):
    return np.array((complex_num.real, complex_num.imag, 0))


def R3_to_complex(point):
    return complex(*point[:2])


def complex_func_to_R3_func(complex_func):
    return lambda p: complex_to_R3(complex_func(R3_to_complex(p)))


def center_of_mass(points):
    points = [np.array(point).astype("float") for point in points]
    return sum(points) / len(points)


def midpoint(point1, point2):
    return center_of_mass([point1, point2])


def line_intersection(line1, line2):
    """
    Returns intersection point of two lines,
    each defined with a pair of vectors determining
    the end points
    """
    x_diff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])
    y_diff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1])

    def det(a, b):
        return a[0] * b[1] - a[1] * b[0]

    div = det(x_diff, y_diff)
    if div == 0:
        raise ValueError("Lines do not intersect")
    d = (det(*line1), det(*line2))
    x = det(d, x_diff) / div
    y = det(d, y_diff) / div
    return np.array([x, y, 0])


def find_intersection(p0, v0, p1, v1, threshold=1e-5):
    """
    Return the intersection of a line passing through p0 in direction v0
    with one passing through p1 in direction v1.  (Or array of intersections
    from arrays of such points/directions).
    For 3d values, it returns the point on the ray p0 + v0 * t closest to the
    ray p1 + v1 * t
    """
    p0 = np.array(p0, ndmin=2)
    v0 = np.array(v0, ndmin=2)
    p1 = np.array(p1, ndmin=2)
    v1 = np.array(v1, ndmin=2)
    m, n = np.shape(p0)
    assert n in [2, 3]

    numer = np.cross(v1, p1 - p0)
    denom = np.cross(v1, v0)
    if n == 3:
        d = len(np.shape(numer))
        new_numer = np.multiply(numer, numer).sum(d - 1)
        new_denom = np.multiply(denom, numer).sum(d - 1)
        numer, denom = new_numer, new_denom

    denom[abs(denom) < threshold] = np.inf  # So that ratio goes to 0 there
    ratio = numer / denom
    ratio = np.repeat(ratio, n).reshape((m, n))
    return p0 + ratio * v0


def get_winding_number(points):
    total_angle = 0
    for p1, p2 in adjacent_pairs(points):
        d_angle = angle_of_vector(p2) - angle_of_vector(p1)
        d_angle = ((d_angle + PI) % TAU) - PI
        total_angle += d_angle
    return total_angle / TAU


def shoelace(x_y):
    """2D implementation of the shoelace formula.

    Returns
    -------
    :class:`float`
        Returns signed area.
    """
    x = x_y[:, 0]
    y = x_y[:, 1]
    area = 0.5 * np.array(np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1)))
    return area


def shoelace_direction(x_y):
    """
    Uses the area determined by the shoelace method to determine whether
    the input set of points is directed clockwise or counterclockwise.

    Returns
    -------
    :class:`str`
        Either ``"CW"`` or ``"CCW"``.
    """
    area = shoelace(x_y)
    return "CW" if area > 0 else "CCW"


def cross2d(a, b):
    if len(a.shape) == 2:
        return a[:, 0] * b[:, 1] - a[:, 1] * b[:, 0]
    else:
        return a[0] * b[1] - b[0] * a[1]


def earclip_triangulation(verts, ring_ends):
    """
    Returns a list of indices giving a triangulation
    of a polygon, potentially with holes

    - verts is a numpy array of points

    - ring_ends is a list of indices indicating where
    the ends of new paths are
    """

    # First, connect all the rings so that the polygon
    # with holes is instead treated as a (very convex)
    # polygon with one edge.  Do this by drawing connections
    # between rings close to each other
    rings = [list(range(e0, e1)) for e0, e1 in zip([0, *ring_ends], ring_ends)]
    attached_rings = rings[:1]
    detached_rings = rings[1:]
    loop_connections = {}

    while detached_rings:
        i_range, j_range = [
            list(
                filter(
                    # Ignore indices that are already being
                    # used to draw some connection
                    lambda i: i not in loop_connections,
                    it.chain(*ring_group),
                )
            )
            for ring_group in (attached_rings, detached_rings)
        ]

        # Closet point on the atttached rings to an estimated midpoint
        # of the detached rings
        tmp_j_vert = midpoint(verts[j_range[0]], verts[j_range[len(j_range) // 2]])
        i = min(i_range, key=lambda i: norm_squared(verts[i] - tmp_j_vert))
        # Closet point of the detached rings to the aforementioned
        # point of the attached rings
        j = min(j_range, key=lambda j: norm_squared(verts[i] - verts[j]))
        # Recalculate i based on new j
        i = min(i_range, key=lambda i: norm_squared(verts[i] - verts[j]))

        # Remember to connect the polygon at these points
        loop_connections[i] = j
        loop_connections[j] = i

        # Move the ring which j belongs to from the
        # attached list to the detached list
        new_ring = next(filter(lambda ring: ring[0] <= j < ring[-1], detached_rings))
        detached_rings.remove(new_ring)
        attached_rings.append(new_ring)

    # Setup linked list
    after = []
    end0 = 0
    for end1 in ring_ends:
        after.extend(range(end0 + 1, end1))
        after.append(end0)
        end0 = end1

    # Find an ordering of indices walking around the polygon
    indices = []
    i = 0
    for _ in range(len(verts) + len(ring_ends) - 1):
        # starting = False
        if i in loop_connections:
            j = loop_connections[i]
            indices.extend([i, j])
            i = after[j]
        else:
            indices.append(i)
            i = after[i]
        if i == 0:
            break

    meta_indices = earcut(verts[indices, :2], [len(indices)])
    return [indices[mi] for mi in meta_indices]

numpy.repeat numpy.append numpy.array numpy.dot numpy.arccos numpy.sin numpy.roll numpy.shape numpy.identity numpy.multiply numpy.transpose numpy.arange numpy.cos numpy.abs numpy.outer numpy.linalg.inv numpy.cross