And while I was at it, I did a Python Mode version too:
“Knot3D.pyde”:
"""
* 3D Knot (2017/Dec)
* Daniel Shiffman
* https://YouTu.be/r6YMKr1X0VA
*
* Mod GoToLoop (v1.0.3) (2018/Oct/16)
* https://OpenProcessing.org/sketch/608725 (pjs)
* https://OpenProcessing.org/sketch/608726 (p5js)
*
* https://Discourse.Processing.org/t/
* vertex-loop-and-draw-along-a-vertex-path/4545/4
"""
"""
* http://PaulBourke.net/geometry/knots/
* Knot 4 (1992/Oct):
*
* r(beta) = 0.8 + 1.6 * sin(6 * beta)
* theta(beta) = 2 * beta
* phi(beta) = 0.6 * pi * sin(12 * beta)
*
* x = r * cos(phi) * cos(theta)
* y = r * cos(phi) * sin(theta)
* z = r * sin(phi)
"""
ANGLE_STEP, BETA_STEP = .02, .01
MAG, SEGS_LIMIT = 100.0, PI + BETA_STEP
PI_DOT_6 = PI * .6
angle = beta = 0.0
paused = False
knots = []
def setup():
size(600, 600, P3D)
smooth(8)
colorMode(HSB)
noFill()
strokeWeight(8.0)
def draw():
global angle, beta
background(0)
translate(width>>1, height>>1)
rotateY(angle)
angle += ANGLE_STEP
beta <= SEGS_LIMIT and addKnot()
beta += BETA_STEP
with beginShape():
for k in knots:
stroke(k.c)
vertex(k.v.x, k.v.y, k.v.z)
def mousePressed():
global paused
paused ^= True
noLoop() if paused else loop()
def keyPressed(): mousePressed()
def addKnot():
r = MAG * (.8 + 1.6 * sin(6 * beta))
theta = 2 * beta
phi = PI_DOT_6 * sin(12 * beta)
rCosPhi = r * cos(phi)
x = rCosPhi * cos(theta)
y = rCosPhi * sin(theta)
z = r * sin(phi)
knot = Knot(x, y, z)
knots.append(knot)
print '%d: %s' % (len(knots), knot)
class Knot:
def __init__(k, *vec):
k.v = vec[0] if len(vec) is 1 else PVector(*vec)
k.c = color(k.v.mag(), 255, 255)
def __str__(k): return 'Vec: %s \tHSB: %d' % (k.v, k.c)