find a point in a Bezier segment

find-bezier-point.py

'''find a point in a Bezier segment'''

# formulas converted from:
# http://13thparallel.com/archive/bezier-curves/

# run this script in DrawBot: http://drawbot.com/

def B1(t): return t*t*t
def B2(t): return 3*t*t*(1-t)
def B3(t): return 3*t*(1-t)*(1-t)
def B4(t): return (1-t)*(1-t)*(1-t)

def getPoint(t, p1, p2, p3, p4):
    x1, y1 = p1
    x2, y2 = p2
    x3, y3 = p3
    x4, y4 = p4
    x = x1*B1(t) + x2*B2(t) + x3*B3(t) + x4*B4(t)
    y = y1*B1(t) + y2*B2(t) + y3*B3(t) + y4*B4(t)
    return x, y

size(200, 200)
fill(None)
stroke(1, 0, 0)
strokeWidth(3)

B = BezierPath()
B.moveTo((38, 36))
B.curveTo((-18, 160), (168, 190), (150, 56))
drawPath(B)

p1, p4 = B.onCurvePoints
p2, p3 = B.offCurvePoints

Variable([dict(name='t', ui='Slider',
    args=dict(value=0.5, minValue=0.0, maxValue=1.0))],
    globals())

x, y = getPoint(t, p1, p2, p3, p4)

r = 10
oval(x-r, y-r, r*2, r*2)