MediumCalculusca-263

Arc Length Parametrization Check

Problem

A curve is parametrized by arc length when its speed ||dr/dt|| equals 1 everywhere.

Samples of the curve are given as 2D points with matching parameter values; estimate the speed on each segment by the secant length divided by the parameter gap. Given the points and parameters, return True when every speed is within tol (default 1e-6) of 1, and True vacuously for fewer than two points.

Hint

Arc length parametrization travels one unit of distance per unit of parameter.

Test cases

case 1

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

expected: true

case 2

in: [[[0,0],[2,0],[4,0]],[0,1,2]]

expected: false

case 3

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

expected: false

case 4

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

expected: false

case 5

in: [[[5,5]],[0]]

expected: true

Starter codePython

def is_unit_speed(points, params, tol=1e-6):
    # Your code here
    pass

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