def makeCubicBezier(A, P, Q, B, divisions=100):
return Curve(
lambda t: [(1 - t) * (1 - t) * (1 - t) * A[0] + 3 * (1 - t) *
(1 - t) * t * P[0] + 3 *
(1 - t) * t * t * Q[0] + t * t * t * B[0], (1 - t) *
(1 - t) * (1 - t) * A[1] + 3 * (1 - t) *
(1 - t) * t * P[1] + 3 *
(1 - t) * t * t * Q[1] + t * t * t * B[1], (1 - t) *
(1 - t) * (1 - t) * A[2] + 3 * (1 - t) *
(1 - t) * t * P[2] + 3 *
(1 - t) * t * t * Q[2] + t * t * t * B[2]], 0, 1,
divisions)
def makeLineSegment(startPoint, endPoint, divisions=2):
return Curve(
lambda t: [(1 - t) * startPoint[0] + t * endPoint[0],
(1 - t) * startPoint[1] + t * endPoint[1],
(1 - t) * startPoint[2] + t * endPoint[2]], 0, 1,
divisions)
def makeFigureEightKnot(divisions=100):
return Curve(
lambda t: [
0.5 * (t**3 - 3 * t), 0.2 * t * (t**2 - 1) * (t**2 - 4), 0.02 *
(t**7 - 42 * t)
], -2.1, 2.1, divisions)
def makeTrefoilKnot(divisions=100):
return Curve(
lambda t: [
0.5 * (t**3 - 3 * t), 0.5 * (t**4 - 4 * t**2 + 2), 0.1 *
(t**5 - 10 * t)
], -2, 2, divisions)
def makeTorusKnot(p=2, q=3, divisions=128):
return Curve(
lambda t: [
0.5 * (2 + cos(q * t)) * cos(p * t), 0.5 *
(2 + cos(q * t)) * sin(p * t), 0.5 * sin(q * t)
], 0, 2 * pi, divisions)
def makeHelix(radius=1, height=2, revolutions=3, divisions=128):
return Curve(
lambda t: [
radius * cos(t), height * t /
(2 * pi * revolutions) - height / 2, radius * sin(t)
], 0, 2 * pi * revolutions, divisions)
def makePolygon(sides=6, radius=1):
return Curve(lambda t: [radius * cos(t), radius * sin(t), 0], 0,
2 * pi, sides + 1)
def makeCircle(radius=1, divisions=64):
return Curve(lambda t: [radius * cos(t), radius * sin(t), 0], 0,
2 * pi, divisions)