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DrawBot: An Archimedean Spherical Spiral animation.
# This borrows heavily from:
# http://jsfiddle.net/Rebug/5uLr7s6o/
#
# Resulting gif:
# http://dailydrawbot.tumblr.com/post/134989689114/an-archimedean-spherical-spiral
import math
import colorsys
def circle(pt, radius):
x, y = pt
diameter = radius * 2
oval(x - radius, y - radius, diameter, diameter)
def rotatePointsX(points, angle):
for x, y, z in points:
y1 = y*cos(angle) - z*sin(angle)
z1 = y*sin(angle) + z*cos(angle)
x1 = x
yield x1, y1, z1
def rotatePointsY(points, angle):
for x, y, z in points:
z1 = z*cos(angle) - x*sin(angle)
x1 = z*sin(angle) + x*cos(angle)
y1 = y
yield x1, y1, z1
def rotatePointsZ(points, angle):
for x, y, z in points:
x1 = x*cos(angle) - y*sin(angle)
y1 = x*sin(angle) + y*cos(angle)
z1 = z
yield x1, y1, z1
# Create spherical spiral for given turns with almost same gap distance
# @see [Archimedean Spherical Spiral]{@link http://en.wikipedia.org/wiki/Spiral#Spherical_spiral}
# @param {number} turns - Times of turns around z-axis
# @param {number} [count=800] - Number of points on spiral
# @param {number} [radius=1] - Radius of sphere
# @returns {Point[]} - Points (r,θ,φ) of spiral in spherical coordinates
def createSphericalSpiral(turns, count=800, radius=1, startPhase=0):
# Spherical coordinate system in mathematics
# (radial distance r, azimuthal angle θ, polar angle φ)
# @see [Spherical coordinate system]{@link http://en.wikipedia.org/wiki/Spherical_coordinate_system}
step = 2 / count
i = -1
# for(var i = -1; i <= 1; i += step) {
while i <= 1.0:
phi = math.acos(i);
theta = (2 * turns * phi + startPhase) % (2 * math.pi)
yield (radius, phi, theta)
i += step
# Convert from spherical coordinates (r,θ,φ) to Cartesian coordinates (x,y,z)
# @see {@link http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates}
# @param {{radius:number,theta:number,phi:number}} point - Point in spherical coordinates
# @returns {{x:number,y:number,z:number}} - Point in Cartesian coordinates
def convert2xyz(points):
for radius, phi, theta in points:
phi += 0
theta += 0
x = radius * math.sin(phi) * math.sin(theta)
y = radius * math.sin(phi) * math.cos(theta)
z = radius * math.cos(phi)
yield (x, y, z)
canvasHeight = 500
canvasWidth = canvasHeight
sphereRadius = 0.363 * canvasHeight
circleRadius = 0.04 * canvasHeight
grayRange = 0.9
maxTurns = 9
nCircles = 1000
nFrames = 100
for frame in range(nFrames):
t = (frame/nFrames + 1/12) % 1.0
newPage(canvasWidth, canvasHeight)
frameDuration(1/12.5)
fill(0.0)
rect(0, 0, canvasWidth, canvasHeight)
translate(canvasWidth/2, canvasHeight/2)
points = convert2xyz(createSphericalSpiral(maxTurns * sin(t*2*pi), nCircles, 1.0, 0))
points = rotatePointsX(points, -t*2*pi + 0.0 * pi)
points = rotatePointsZ(points, -t*2*pi + 0.25 * pi)
points = rotatePointsY(points, -t*2*pi + 0.0 * pi)
for x, y, z in sorted(points, key=lambda pt: pt[1]):
gray = (y + 1) * 0.5
rgb = colorsys.hsv_to_rgb(0.15, 0.16, (1 - grayRange) + gray * grayRange)
fill(*rgb)
circle((x*sphereRadius, z*sphereRadius), circleRadius)
saveImage("SphericalSpiral.gif")
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