MediumCalculusca-114

Curvature of a Curve

Problem

Compute the curvature of the parametric curve (x(t), y(t)) given by polynomial coefficient lists:

kappa = |x' * y'' - y' * x''| / (x'^2 + y'^2)^(3/2)

Evaluate all derivatives at the parameter t and return kappa.

Hint

The numerator is the 2D cross product of the velocity and acceleration.

case 1

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

expected: 2

case 2

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

expected: 0.17888543819998318

case 3

in: [[0,1],[0,3],2]

expected: 0

case 4

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

expected: 0.5

Starter codePython

def curvature(x_coeffs, y_coeffs, t):
    # Your code here
    pass

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