Cubic Bezier: find Y given X

bezier_xy.py

# https://twitter.com/mttymtt/status/1531022994323251202
# DrawBot visualization
# FontTools for helper code

from fontTools.misc.bezierTools import calcCubicParameters, solveCubic

scaleFactor = 500

pt0 = (0, 0)
pt1 = (0.37, 0.05)
pt2 = (0.65, 0.9)
pt3 = (1, 1)

(ax, ay), (bx, by), (cx, cy), (dx, dy) = calcCubicParameters(pt0, pt1, pt2, pt3)

bez = BezierPath()
bez.moveTo(pt0)
bez.curveTo(pt1, pt2, pt3)

translate(100, 100)
fill(None)
stroke(0)
strokeWidth(4 / scaleFactor)
scale(scaleFactor)

drawPath(bez)

stroke(1, 0, 0)
strokeWidth(1 / scaleFactor)
steps = 10

for i in range(steps + 1):
    x = i / steps
    line((x, 0), (x, 1))
    ts = solveCubic(ax, bx, cx, dx - x)
    ts = [t for t in ts if 0 <= t <= 1]
    t = ts[0]
    y = ay * t**3 + by * t**2 + cy*t + dy
    line((0, y), (1, y))