import math
from polygon import *
from matrix import *


def polygon(edges, center, radius, phase=0, M=((1,0),(0,1)), color=(0,0,0)):
    """
    Return a regular polygon.

    edges (int) -- number of sides
    center (Vector) -- position of center
    radius (float) -- radius to vertex
    phase (float) -- rotates polygon 'phase' vertics
    M (Matrix) -- distortion matrix
    """

    poly = Polygon(color=color)
    for n in range(edges):
        x = radius * math.sin((n + phase) * math.tau / edges)
        y = radius * math.cos((n + phase) * math.tau / edges)
        poly.append(Vector(*center) + Matrix(*M).prod(Vector(x, y)))

    return poly


def star(edges, center, radius, ratio=0.5, phase=0, M=Matrix((1,0),(0,1)), color=(0,0,0)):
    """
    Return a regular star polygon.

    edges (int) -- number of convex vertices
    center (Vector) -- position of center
    radius (float) -- radius to vertex
    ratio (float) -- radius ratio to inner vertices
    phase (float) -- rotates polygon 'phase' vertics
    M (Matrix) -- distortion matrix
    """

    poly = Polygon(color=color)
    for n in range(edges):
        x = radius * math.sin((n + phase) * math.tau / edges)
        y = radius * math.cos((n + phase) * math.tau / edges)
        poly.append(Vector(*center) + M.prod(Vector(x, y)))

        x = ratio * radius * math.sin((n + 0.5 + phase) * math.tau / edges)
        y = ratio * radius * math.cos((n + 0.5 + phase) * math.tau / edges)
        poly.append(Vector(*center) + M.prod(Vector(x, y)))

    return poly


def border(polygon):
    """
    Turn a polygon into a border.
    (split it into its sides)
    """

    bor = []
    for i, _ in enumerate(polygon):
        bor.append(Polygon(polygon[i-1], polygon[i]))
    return bor


def door(start, end, part):
    """
    Turn a wall into a door.
    (make a hole in the middle with relative size 'part')
    """

    return (Polygon(start, start+(1-part)/2*(end-start)), Polygon(end+(1-part)/2*(start-end), end))