#!/usr/bin/env python3

from math import floor, isqrt, sqrt
from lib import draw_circle, mirror_points_4, mirror_points_8


def get_circle_points_naive_4(r):
    """ Draw a circle by pairing up each Y value with an X value that lie on a
    circle with radius 'r'. This has a bug because some Y values get skipped.
    Can you see why?
    """
    points = []
    for x in range(r + 1):
        # isqrt() gets the integer square root.
        y = isqrt((r * r) - (x * x))
        points.extend(mirror_points_4(x, y))
    return points


def get_circle_points_naive_8(r):
    """ Better than get_circle_points_naive_4, but wastes CPU cycles because
    the 8-way symmetry overcorrects and we draw some pixels more than once.
    """
    points = []
    for x in range(r + 1):
        y = isqrt((r * r) - (x * x))
        points.extend(mirror_points_8(x, y))
    return points


def get_circle_points_naive_8_faster(r):
    """ Slightly faster than get_circle_points_naive_8, because of the break
    condition at the middle of the arc. However this is still inefficient due
    to the square root calculation with `isqrt()`.
    """
    points = []
    for x in range(r + 1):
        y = isqrt((r * r) - (x * x))
        # When we cross the middle of the arc, stop, because we're already
        # invoking 8-way symmetry.
        if x > y:
            break
        points.extend(mirror_points_8(x, y))
    return points


def get_circle_points_naive_8_faster_tweaked_radius(r):
    """ This is much closer to Bresenham's algorithm aesthetically, by simply
    using 'r + 0.5' for the square root calculation instead of 'r' directly.
    """
    points = []
    # In the square root calculation, we just use (r + 0.5) instead of just r.
    # This is more pleasing to the eye and makes the lines a bit smoother.
    r_tweaked = r + 0.5
    for x in range(r + 1):
        y = sqrt((r_tweaked * r_tweaked) - (x * x))
        if x > y:
            break
        points.extend(mirror_points_8(x, floor(y)))
    return points


if __name__ == "__main__":
    draw_circle(get_circle_points_naive_4, 17)
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    #   ╰───────────────────────────────────╯
    #    11111111987654321012345678911111111
    #    76543210                   01234567

    #   Signature: b6f7a9ebafd39870c7cf16be29208ad3

    # These two draw the same circle.
    draw_circle(get_circle_points_naive_8, 17)
    draw_circle(get_circle_points_naive_8_faster, 17)
    #    11111111                   11111111
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    #   Signature: f6c20c82b8bcef31fc4b43dd42316140

    # Some edge-cases.
    draw_circle(get_circle_points_naive_8_faster, 0)
    #   0
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    #  Signature: 4ba6b15b13cd6adb310eeab8ee1adfd0

    draw_circle(get_circle_points_naive_8_faster, 1)
    #   101
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    #  Signature: 625c57cb30c48aeb33b48bebea893e83

    draw_circle(get_circle_points_naive_8_faster, 2)
    #   21012
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    #  ╰─────╯
    #   21012

    #  Signature: ed32e3d382baa7d5014bd00caa17c708

    draw_circle(get_circle_points_naive_8_faster, 3)
    #   3210123
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    #  Signature: 53f14d3462c32d694aa688d8685b50d7

    draw_circle(get_circle_points_naive_8_faster_tweaked_radius, 0)
    #    0
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    #   Signature: 4ba6b15b13cd6adb310eeab8ee1adfd0

    draw_circle(get_circle_points_naive_8_faster_tweaked_radius, 1)
    #
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    #   Signature: 879ffc6eb52acdea4996c531bb3e2663

    draw_circle(get_circle_points_naive_8_faster_tweaked_radius, 2)
    #    21012
    #   ╭─────╮
    #  2│·███·│2
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    #    21012
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    #   Signature: e6539d664b9120b376d1d4cda8574b6d

    draw_circle(get_circle_points_naive_8_faster_tweaked_radius, 3)
    #    3210123
    #   ╭───────╮
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    #   Signature: 463d7ac7210badfbb18c47a313cd16aa

    draw_circle(get_circle_points_naive_8_faster_tweaked_radius, 17)
    #     11111111                   11111111
    #     76543210987654321012345678901234567
    #    ╭───────────────────────────────────╮
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    #
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