def GetBezierPoint(points, t):
"""EXPLANATION:
The formula for a point on the bezier curve defined by four points (points[0:3]) at a given value of t is as follows:
B(t) = ((1-t)^3 * points[0]) + (3 * (1-t)^2 * t * points[1]) + (3 * (1-t) * t^2 * points[2]) + (t^3 * points[3])
(Where 0 <= t <= 1.)
Here, the formula has been split into the four component parts, each returning a vactor:
-part1 = (1-t)^3 * points[0]
-part2 = 3 * (1-t)^2 * t * points[1]
-part3 = 3 * (1-t) * t^2 * points[2]
-part4 = t^3 * points[3]
These vectors are then added using the function fourpointsum() to give the final value for B(t).
"""
part1 = VectMath.vectmult(cube(1.0 - t), points[0])
part2 = VectMath.vectmult((3 * sqr(1.0 - t) * t), points[1])
part3 = VectMath.vectmult((3 * (1.0 - t) * sqr(t)), points[2])
part4 = VectMath.vectmult(cube(t), points[3])
return VectMath.fourpointsum(part1, part2, part3, part4)
