Drawing barycentric coordinates with Python. n-edge polyon and a point is describes by 0 <= v_i <= 1, sum(v_i) = 1, 0 < i <= n

barycentric_coordinates_drawer.py

#!/usr/bin/python

from PIL import Image, ImageDraw

from math import cos, sin, pi,log

class BarycentricImage(object):
    def __init__(self, n=3, size=(400,400)):
        self.dims = n
        self.size = size
        self.image = Image.new("RGB", size, (255,255,255))
        self.draw = ImageDraw.Draw(self.image)

        self.draw.setink(0)
        self.__draw_coordinates()

    def __draw_coordinates(self):
        self.coordinates = []

        centerX, centerY = self.size[0]/2, self.size[1]/2

        for alpha in range(self.dims):
            r = (2*pi/self.dims)*alpha;
            x = cos( r ) * self.size[0]/2.0 + centerX
            y = sin( r ) * self.size[1]/2.0 + centerY

            self.coordinates.append( (x,y) )

        #print(self.coordinates)

        self.draw.polygon(self.coordinates, (100,100,100), (50,50,50) )


    def add_point(self, vector):
#        assert len(vector) == self.dims
        assert all(map(lambda x: 0 <= x <= 1, vector))

        x,y = 0,0
        s = sum(vector)

        for v,(a,b) in zip(vector, self.coordinates):
            x += v * a / s
            y += v * b / s

        print(x,y)

        red = int(entropy(vector)/2.33*255)
        self.draw.point( (x,y), (red,0,0))


    def save(self, name):
        del self.draw
        self.image.save(name)


def entropy(seq):
    def log0(x):
        if x==0:
            return 0
        else:
            return log(x,2)

    return - sum(map(lambda p: p*log0(p), seq))

def prange(step=0.03):
    i = 0
    while i <= 1:
        yield i
        i += step
    yield 1

if __name__ == "__main__":
    I = BarycentricImage(5)

    #b.add_point((0.5, 1, 0.5, 0.3, 0.6))
    #b.add_point((0.2, 0.5, 0.5))
    #b.add_point((0.6, 0.20, 0.35))
    #b.add_point((0.7, 0.3, 0.35))

    step = 0.01
    for a in prange():
        for b in prange():
            for c in prange():
                for d in prange():
                    for e in prange():
                        x = (a,b,c,d,e)
                        if sum(x) == 1:
                            I.add_point(x)

    I.save("test.png")