MediumCalculusca-262

Geodesic Distance on a Sphere

Problem

The geodesic or great-circle distance between two points on a sphere of radius R with unit position vectors u and v is R * arccos(u dot v).

Given the two unit vectors as lists and the radius, return the distance. Clamp the dot product to the interval [-1, 1] to guard against rounding.

Hint

The central angle is the arccosine of the dot product of unit vectors.

case 1

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

expected: 1.5707963267948966

case 2

in: [[1,0,0],[1,0,0],5]

expected: 0

case 3

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

expected: 6.283185307179586

case 4

in: [[0.6,0.8,0],[1,0,0],2]

expected: 1.8545904360032246

Starter codePython

def geodesic_sphere_distance(u, v, radius):
    # Your code here
    pass

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