# Copyright (c) 2021-2022, Manfred Moitzi
# License: MIT License
from __future__ import annotations
from typing import Optional
import math
from ezdxf.math import (
    cubic_bezier_arc_parameters,
    Matrix44,
    UVec,
    basic_transformation,
    Vec3,
)
from ezdxf.render import forms
from .path import Path
from . import converter

__all__ = [
    "unit_circle",
    "elliptic_transformation",
    "rect",
    "ngon",
    "wedge",
    "star",
    "gear",
    "helix",
]


def unit_circle(
    start_angle: float = 0,
    end_angle: float = math.tau,
    segments: int = 1,
    transform: Matrix44 = None,
) -> Path:
    """Returns a unit circle as a :class:`Path` object, with the center at
    (0, 0, 0) and the radius of 1 drawing unit.

    The arc spans from the start- to the end angle in counter-clockwise
    orientation. The end angle has to be greater than the start angle and the
    angle span has to be greater than 0.

    Args:
        start_angle: start angle in radians
        end_angle: end angle in radians (end_angle > start_angle!)
        segments: count of Bèzier-curve segments, default is one segment for
            each arc quarter (π/2)
        transform: transformation Matrix applied to the unit circle

    """
    path = Path()
    start_flag = True
    for start, ctrl1, ctrl2, end in cubic_bezier_arc_parameters(
        start_angle, end_angle, segments
    ):
        if start_flag:
            path.start = start
            start_flag = False
        path.curve4_to(end, ctrl1, ctrl2)
    if transform is None:
        return path
    else:
        return path.transform(transform)


def wedge(
    start_angle: float,
    end_angle: float,
    segments: int = 1,
    transform: Matrix44 = None,
) -> Path:
    """Returns a wedge as a :class:`Path` object, with the center at
    (0, 0, 0) and the radius of 1 drawing unit.

    The arc spans from the start- to the end angle in counter-clockwise
    orientation. The end angle has to be greater than the start angle and the
    angle span has to be greater than 0.

    Args:
        start_angle: start angle in radians
        end_angle: end angle in radians (end_angle > start_angle!)
        segments: count of Bèzier-curve segments, default is one segment for
            each arc quarter (π/2)
        transform: transformation Matrix applied to the wedge

    """
    path = Path()
    start_flag = True
    for start, ctrl1, ctrl2, end in cubic_bezier_arc_parameters(
        start_angle, end_angle, segments
    ):
        if start_flag:
            path.line_to(start)
            start_flag = False
        path.curve4_to(end, ctrl1, ctrl2)
    path.line_to((0, 0, 0))
    if transform is None:
        return path
    else:
        return path.transform(transform)


def elliptic_transformation(
    center: UVec = (0, 0, 0),
    radius: float = 1,
    ratio: float = 1,
    rotation: float = 0,
) -> Matrix44:
    """Returns the transformation matrix to transform a unit circle into
    an arbitrary circular- or elliptic arc.

    Example how to create an ellipse with a major axis length of 3, a minor
    axis length 1.5 and rotated about 90°::

        m = elliptic_transformation(radius=3, ratio=0.5, rotation=math.pi / 2)
        ellipse = shapes.unit_circle(transform=m)

    Args:
        center: curve center in WCS
        radius: radius of the major axis in drawing units
        ratio: ratio of minor axis to major axis
        rotation: rotation angle about the z-axis in radians

    """
    if radius < 1e-6:
        raise ValueError(f"invalid radius: {radius}")
    if ratio < 1e-6:
        raise ValueError(f"invalid ratio: {ratio}")
    scale_x = radius
    scale_y = radius * ratio
    return basic_transformation(center, (scale_x, scale_y, 1), rotation)


def rect(
    width: float = 1, height: float = 1, transform: Matrix44 = None
) -> Path:
    """Returns a closed rectangle as a :class:`Path` object, with the center at
    (0, 0, 0) and the given `width` and `height` in drawing units.

    Args:
        width: width of the rectangle in drawing units, width > 0
        height: height of the rectangle in drawing units, height > 0
        transform: transformation Matrix applied to the rectangle

    """
    if width < 1e-9:
        raise ValueError(f"invalid width: {width}")
    if height < 1e-9:
        raise ValueError(f"invalid height: {height}")

    w2 = float(width) / 2.0
    h2 = float(height) / 2.0
    path = converter.from_vertices(
        [(w2, h2), (-w2, h2), (-w2, -h2), (w2, h2)], close=True
    )
    if transform is None:
        return path
    else:
        return path.transform(transform)


def ngon(
    count: int,
    length: Optional[float] = None,
    radius: float = 1.0,
    transform: Optional[Matrix44] = None,
) -> Path:
    """Returns a `regular polygon <https://en.wikipedia.org/wiki/Regular_polygon>`_
    a :class:`Path` object, with the center at (0, 0, 0).
    The polygon size is determined by the edge `length` or the circum `radius`
    argument. If both are given `length` has higher priority. Default size is
    a `radius` of 1. The ngon starts with the first vertex is on the x-axis!
    The base geometry is created by function :func:`ezdxf.render.forms.ngon`.

    Args:
        count: count of polygon corners >= 3
        length: length of polygon side
        radius: circum radius, default is 1
        transform: transformation Matrix applied to the ngon

    """
    vertices = forms.ngon(count, length=length, radius=radius)
    if transform is not None:
        vertices = transform.transform_vertices(vertices)
    return converter.from_vertices(vertices, close=True)


def star(count: int, r1: float, r2: float, transform: Matrix44 = None) -> Path:
    """Returns a `star shape <https://en.wikipedia.org/wiki/Star_polygon>`_ as
    a :class:`Path` object, with the center at (0, 0, 0).

    Argument `count` defines the count of star spikes, `r1` defines the radius
    of the "outer" vertices and `r2` defines the radius of the "inner" vertices,
    but this does not mean that `r1` has to be greater than `r2`.
    The star shape starts with the first vertex is on the x-axis!
    The base geometry is created by function :func:`ezdxf.render.forms.star`.

    Args:
        count: spike count >= 3
        r1: radius 1
        r2: radius 2
        transform: transformation Matrix applied to the star

    """
    vertices = forms.star(count, r1=r1, r2=r2)
    if transform is not None:
        vertices = transform.transform_vertices(vertices)
    return converter.from_vertices(vertices, close=True)


def gear(
    count: int,
    top_width: float,
    bottom_width: float,
    height: float,
    outside_radius: float,
    transform: Matrix44 = None,
) -> Path:
    """
    Returns a `gear <https://en.wikipedia.org/wiki/Gear>`_ (cogwheel) shape as
    a :class:`Path` object, with the center at (0, 0, 0).
    The base geometry is created by function :func:`ezdxf.render.forms.gear`.

    .. warning::

        This function does not create correct gears for mechanical engineering!

    Args:
        count: teeth count >= 3
        top_width: teeth width at outside radius
        bottom_width: teeth width at base radius
        height: teeth height; base radius = outside radius - height
        outside_radius: outside radius
        transform: transformation Matrix applied to the gear shape

    """
    vertices = forms.gear(
        count, top_width, bottom_width, height, outside_radius
    )
    if transform is not None:
        vertices = transform.transform_vertices(vertices)
    return converter.from_vertices(vertices, close=True)


def helix(
    radius: float,
    pitch: float,
    turns: float,
    ccw=True,
    segments: int = 4,
) -> Path:
    """
    Returns a `helix <https://en.wikipedia.org/wiki/Helix>`_ as
    a :class:`Path` object.
    The center of the helix is always (0, 0, 0), a positive `pitch` value
    creates a helix along the +z-axis, a negative value along the -z-axis.

    Args:
        radius: helix radius
        pitch: the height of one complete helix turn
        turns: count of turns
        ccw: creates a counter-clockwise turning (right-handed) helix if ``True``
        segments: cubic Bezier segments per turn

    """
    # Source of algorithm: https://www.arc.id.au/HelixDrawing.html
    def bezier_ctrl_points(b, angle, segments):
        zz = 0.0
        z_step = angle / segments * p
        z_step_2 = z_step * 0.5
        for _, v1, v2, v3 in cubic_bezier_arc_parameters(0, angle, segments):
            yield (
                Vec3(v1.x * rx, v1.y * ry, zz + z_step_2 - b),
                Vec3(v2.x * rx, v2.y * ry, zz + z_step_2 + b),
                Vec3(v3.x * rx, v3.y * ry, zz + z_step),
            )
            zz += z_step

    def param_b(alpha: float) -> float:
        cos_a = math.cos(alpha)
        b_1 = (1.0 - cos_a) * (3.0 - cos_a) * alpha * p
        b_2 = math.sin(alpha) * (4.0 - cos_a) * math.tan(alpha)
        return b_1 / b_2
    rx = radius
    ry = radius
    if not ccw:
        ry = -ry
    path = Path(start=(radius, 0, 0))

    p = pitch / math.tau
    b = param_b(math.pi / segments)
    full_turns = int(math.floor(turns))
    if full_turns > 0:
        curve_params = list(bezier_ctrl_points(b, math.tau, segments))
        for _ in range(full_turns):
            z = Vec3(0, 0, path.end.z)
            for v1, v2, v3 in curve_params:
                path.curve4_to(z + v3, z + v1, z + v2)

    reminder = turns - full_turns
    if reminder > 1e-6:
        segments = math.ceil(reminder * 4)
        b = param_b(reminder * math.pi / segments)
        z = Vec3(0, 0, path.end.z)
        for v1, v2, v3 in bezier_ctrl_points(b, math.tau * reminder, segments):
            path.curve4_to(z + v3, z + v1, z + v2)

    return path
