import math

from OpenGL.GL import *

from OpenGL.GLUT import *

from OpenGL.GLU import *

"""

Rosette

Introduction

A rosette appears when the points of an n-gon (regular polygon with points

P_i = (R cos(2*pi*i/n),R sin(2*pi*i/n)) ) are connected to all other points of

the n-gon. E.g. when n=5, the result is an outer pentagon and an inner pentagram.

In the code below, first all points of the n-gon are calculated, then a double for

loop connect points i to points i+1,...,n-1,n.

http://www.de-brauwer.be/wiki/wikka.php?wakka=PyOpenGLRosette

"""

N = 25

RADIUS = 95

def init_fun():

glClearColor(1.0, 1.0, 1.0, 0.0)

glColor3f(0.0, 0.0, 0.0)

glMatrixMode(GL_PROJECTION)

glLoadIdentity()

gluOrtho2D(-100, 100, -100, 100)

def reshape_fun(w, h):

glViewport(0, 0, w, h)

# if w > h:

# glViewport((w - h) / 2, 0, h, h)

# else:

# glViewport(0, (h - w) / 2, w, w)

def display_fun():

glClear(GL_COLOR_BUFFER_BIT)

glColor3f(0.0, 0.0, 1.0)

xpts = []

ypts = []

for i in range(0, N):

xpts.append(RADIUS * math.sin(2.0 * math.pi * i / N))

ypts.append(RADIUS * math.cos(2.0 * math.pi * i / N))

glBegin(GL_LINE_STRIP)

for i in range(0, N):

for j in range(i, N):

glVertex2f(xpts[i], ypts[i])

glVertex2f(xpts[j], ypts[j])

glEnd()

glFlush()

if __name__ == "__main__":

glutInit()

glutInitWindowSize(400, 400)

glutCreateWindow(b"Rosette")

glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB)

glutDisplayFunc(display_fun)

glutReshapeFunc(reshape_fun)

init_fun()

glutMainLoop()