from __future__ import annotations

import numpy as np
from numpy import ndarray

import gdsfactory as gf
from gdsfactory.component import Component
from gdsfactory.config import ErrorType
from gdsfactory.geometry.functions import angles_deg, curvature, path_length, snap_angle
from gdsfactory.typings import (
    Coordinate,
    Coordinates,
    CrossSectionSpec,
)


def bezier_curve(t: ndarray, control_points: Coordinates) -> ndarray:
    """Returns bezier coordinates.

    Args:
        t: 1D array of points varying between 0 and 1.
        control_points: for the bezier curve.
    """
    from scipy.special import binom

    xs = 0.0
    ys = 0.0
    n = len(control_points) - 1
    for k in range(n + 1):
        ank = binom(n, k) * (1 - t) ** (n - k) * t**k
        xs += ank * control_points[k][0]
        ys += ank * control_points[k][1]

    return np.column_stack([xs, ys])



[docs]
@gf.cell
def bezier(
    control_points: Coordinates = ((0.0, 0.0), (5.0, 0.0), (5.0, 1.8), (10.0, 1.8)),
    npoints: int = 201,
    with_manhattan_facing_angles: bool = True,
    start_angle: int | None = None,
    end_angle: int | None = None,
    cross_section: CrossSectionSpec = "xs_sc",
    bend_radius_error_type: ErrorType | None = None,
) -> Component:
    """Returns Bezier bend.

    Args:
        control_points: list of points.
        npoints: number of points varying between 0 and 1.
        with_manhattan_facing_angles: bool.
        start_angle: optional start angle in deg.
        end_angle: optional end angle in deg.
        cross_section: spec.
    """
    xs = gf.get_cross_section(cross_section)
    t = np.linspace(0, 1, npoints)
    path_points = bezier_curve(t, control_points)
    path = gf.Path(path_points)

    if with_manhattan_facing_angles:
        path.start_angle = start_angle or snap_angle(path.start_angle)
        path.end_angle = end_angle or snap_angle(path.end_angle)

    c = Component()
    bend = path.extrude(xs)
    bend_ref = c << bend
    c.add_ports(bend_ref.ports)
    c.absorb(bend_ref)
    curv = curvature(path_points, t)
    length = gf.snap.snap_to_grid(path_length(path_points))
    if max(np.abs(curv)) == 0:
        min_bend_radius = np.inf
    else:
        min_bend_radius = gf.snap.snap_to_grid(1 / max(np.abs(curv)))

    c.info["length"] = float(length)
    c.info["min_bend_radius"] = min_bend_radius
    c.info["start_angle"] = path.start_angle
    c.info["end_angle"] = path.end_angle

    xs.validate_radius(min_bend_radius, bend_radius_error_type)

    return c



def find_min_curv_bezier_control_points(
    start_point: ndarray,
    end_point: Coordinate,
    start_angle: float,
    end_angle: float,
    npoints: int = 201,
    alpha: float = 0.05,
    nb_pts: int = 2,
) -> Coordinates:
    """Returns bezier control points that minimize curvature.

    Args:
        start_point: start point.
        end_point: end point.
        start_angle: start angle in deg.
        end_angle: end angle in deg.
        npoints: number of points varying between 0 and 1.
        alpha: weight for angle mismatch.
        nb_pts: number of control points.
    """
    from scipy.optimize import minimize

    t = np.linspace(0, 1, npoints)

    def array_1d_to_cpts(a):
        xs = a[::2]
        ys = a[1::2]
        return list(zip(xs, ys))

    def objective_func(p):
        """minimize  max curvaturea and negligible start angle and end angle mismatch"""
        ps = array_1d_to_cpts(p)
        control_points = [start_point] + ps + [end_point]
        path_points = bezier_curve(t, control_points)

        max_curv = max(np.abs(curvature(path_points, t)))

        angles = angles_deg(path_points)
        dstart_angle = abs(angles[0] - start_angle)
        dend_angle = abs(angles[-2] - end_angle)
        angle_mismatch = dstart_angle + dend_angle
        return angle_mismatch * alpha + max_curv

    x0, y0 = start_point[0], start_point[1]
    xn, yn = end_point[0], end_point[1]

    initial_guess = []
    for i in range(nb_pts):
        x = (i + 1) * (x0 + xn) / nb_pts
        y = (i + 1) * (y0 + yn) / nb_pts
        initial_guess += [x, y]

    # initial_guess = [(x0 + xn) / 2, y0, (x0 + xn) / 2, yn]
    res = minimize(objective_func, initial_guess, method="Nelder-Mead")
    p = res.x
    return [tuple(start_point)] + array_1d_to_cpts(p) + [tuple(end_point)]


if __name__ == "__main__":
    control_points = ((0.0, 0.0), (5.0, 0.0), (5.0, 5.0), (10.0, 5.0))
    c = bezier(control_points=control_points)
    c.show(show_ports=True)