from tkinter import *
import math
import dataclasses
size = 500
margin = 10
point_size = 8

@dataclasses.dataclass
class Point:
    x: float
    y: float
    def tuple(self): return (self.x, self.y)
    def __add__(self, p): return Point(self.x+p.x, self.y+p.y)
    def __truediv__(self, s): return self * (1/s)
    def __mul__(self, s): return Point(self.x*s, self.y*s)
    def __sub__(self, p): return self + (p*-1)

def midpoint(a,b):
    return (a+b) / 2

def lerp(a,b,t):
    """linear interpolation, AKA a linear bezier curve."""
    return (b-a)*t + a

def bezier(a,b,c):
    """yields coordinates for points on a quadratic bezier curve."""
    num_segments = 16
    for i in range(num_segments+1):
        t = i / num_segments
        yield lerp(lerp(a,b,t), lerp(b,c,t), t)

def create_smooth_poly(canvas, points, **kwargs):
    """
    emulates the behavior of tkinter's smooth-styled polygon.
    draws a series of quadratic bezier curves,
    using the polygon's vertices as control points,
    and the polygon's edge's midpoints as endpoints.
    """
    assert len(points) >= 3
    spline_points = []
    for i, p3 in enumerate(points):
        p2,p1 = points[i-1],points[i-2]
        spline_points.extend(list(bezier(midpoint(p1,p2), p2, midpoint(p2,p3))))
    return canvas.create_polygon([p.tuple() for p in spline_points], **kwargs)

def create_point(canvas, p, size, **kwargs):
    """Draw a point on the canvas. Why isn't this a native tkinter method?"""
    w = Point(size/2, size/2)
    canvas.create_arc((p-w).tuple() + (p+w).tuple(), start=0, extent=359, style=CHORD, **kwargs)
    #   is anyone else annoyed that you can't make a chord of extent 360?

def example_square():
    return [Point(margin, margin), Point(margin,size-margin), Point(size-margin,size-margin), Point(size-margin, margin)]

def example_triangle():
    p0 = Point(margin, margin)
    p1 = Point(size-margin, margin)
    side_length = size - margin/2
    p2 = p0 + Point(side_length*math.cos(math.radians(60)), side_length*math.sin(math.radians(60)))
    return [p0, p1, p2]

points = example_square()
rawpoly = [s for p in points for s in p.tuple()]

root = Tk()
canvas = Canvas(root, width=size, height=size)
canvas.pack()

#poly
canvas.create_polygon(rawpoly, fill="gray", smooth=False)
#native tkinter smooth poly
canvas.create_polygon(rawpoly, outline="red", fill="", smooth=True)
#custom smooth poly
create_smooth_poly(canvas, points, outline="blue", fill="")

#corners
for p in points:
    create_point(canvas, p, 8, fill="black")

#midpoints
w = Point(point_size/2, point_size/2)
for i, p1 in enumerate(points):
    p0 = points[i-1]
    create_point(canvas, midpoint(p0, p1), 8, fill="green", outline="green")

root.mainloop()