Bezier Curve Point

Problem

Evaluate a Bezier curve at parameter t in [0, 1] with de Casteljau's algorithm.

points is a list of 2D control points; repeatedly replace each consecutive pair by its linear interpolation at t until one point remains, and return that point as [x, y].

Hint

de Casteljau builds the point from repeated linear interpolations, which is numerically stable.

Test cases

case 1

in: [[[0,0],[1,2],[2,0]],0.5]

expected: [1,1]

case 2

in: [[[0,0],[1,2],[2,0]],0]

expected: [0,0]

case 3

in: [[[0,0],[1,2],[2,0]],1]

expected: [2,0]

case 4

in: [[[0,0],[0,1],[1,1],[1,0]],0.5]

expected: [0.5,0.75]

case 5

in: [[[1,2],[3,6]],0.25]

expected: [1.5,3]

Starter codePython

def bezier_point(points, t):
    # Your code here
    pass

5 test cases · run your code against them in the editor