Analemma

A little weekend diversion…drawing and analemma the hard way. Changing the radii of the circles changes the drawn shape in interesting ways.

from math import cos, sin, pi, sqrt
speed(100)
size(800, 800)
from nodebox.graphics import BezierPath
import numpy as _N
 
class circle(BezierPath):
    def __init__(self, x, y, radius, draw=True, **kwargs):
        BezierPath.__init__(self, _ctx, **kwargs)
        self._nsBezierPath.appendBezierPathWithOvalInRect_( ((x-radius, y-radius), (radius*2.0, radius*2.0)) )
        self.center = _N.array([x, y], _N.float)
        self.radius = float(radius)
        self.diameter = radius*2.0
        self.inheritFromContext(kwargs.keys())    
        if draw: self.draw()
    def pointAtBearing(self,rad):
        ''' returns a point at the angle given in radians 0 radian is the left of the cirle increasing counterclockwise'''
        x = self.center[0] - sin(rad-pi/2) * self.radius
        y = self.center[1] + cos(rad-pi/2) * self.radius
        return _N.array([x, y])
    def externalTangentCircleAtBearing(self, radian, radius, draw=True):
        point = self.pointAtBearing(radian)
        x = point[0] + radius*cos(radian)
        y = point[1] + radius*sin(radian)
        return circle(x, y, radius, draw)
    def tangentCircleWith(self,circ2, radius, draw=True):
        ''' Returns a circle of given radius tangent with both this and circ2 
            Returns None if circle doesnt exist'''
        r1 = self.radius + radius
        r2 = circ2.radius + radius
        d = distance(self.center, circ2.center)
        if  r1+r2 < d:
            # the circles are too far apart to make a connection with the given radius
            return None
        x1, y1 = self.center
        x2, y2 = circ2.center
        
        A = sqrt((d+r1+r2) * (d+r1-r2) * (d-r1+r2) * (-d+r1+r2))/4.0
        x = ((x1+x2)/2.0) - ((x1-x2)*(r1**2-r2**2))/(2.0*d**2) + 2.0*((y1-y2)/d**2)*A
        y = ((y1+y2)/2.0) - ((y1-y2)*(r1**2-r2**2))/(2.0*d**2) - 2.0*((x1-x2)/d**2)*A
        return circle(x, y, radius, draw=draw)        
 
 
########### UTILITY FUNCTIONS
 
def distance(p1, p2):
    '''p1 and p2 are numeric arrays'''
    return sqrt(_N.add.reduce((p1-p2)**2))    
def radians(degrees):
    return degrees *pi/180
def marker(point):
    oval(point[0]-2, point[1]-2, 4, 4, stroke=(.2, .2, .4))
def trailer(point, tran):
    oval(point[0]-2, point[1]-2, 4, 4, stroke=(None), fill=(.2, .2, .4, tran))    
def link(p1, p2, p3):
    marker(p1)
    marker(p2)
    marker(p3)
    line(p1[0], p1[1], p3[0], p3[1])
    line(p2[0], p2[1], p3[0], p3[1])
 
theta = -pi/2
y = 300
r = 50
trails = []
dy = .07
def draw():
    global theta, r, trails, y, dy
    autoclosepath(False)
 
    background(1)
    nofill()
    stroke(.2, .2, .5)
    strokewidth(.25)
    theta += dy
    y += dy
    a1 = circle(200, 221, 80)
    a2 = circle(600, 221, 80)
    
    b = a1.externalTangentCircleAtBearing(theta, 23)
    b2 = a2.externalTangentCircleAtBearing(theta+(pi/2), 23)
 
    c = b.tangentCircleWith(b2, 255)
    link(b2.center, b.center, c.center)
    line(a1.center[0], a1.center[1],  b.center[0], b.center[1])
    line(a2.center[0], a2.center[1],  b2.center[0], b2.center[1])
 
 
    trails.append(c.center)
 
    trails= trails[-92:]
    for i, p in enumerate(trails):
        trailer(p, i/92.)

It looks like an apostrophe in one of the comments messed up the syntax coloring here. Sorry about that--the code should run fine with a copy and paste regardless.

i removed the apostrophe leaving a spelling error..
a dilemma.