If you try to make the next Ecstatica sequel

    • Center is c and radius is r.

    • Surface Area S = 4πr2

    • Volume V = (4/3)*2πr3

Closest point on a sphere

    • q is the point.

    • d is the vector between c and q.

    • q' = q + (||d|| - r / ||d||)*d

    • If ||d|| < r then point q is inside the circle.

Intersection of two spheres.

    • d is the vector between spheres centers.

    • If ||d|| < r1 +r2 then spheres intersect.

A Sphere-Sphere Sweep Test - 1999

Uniform points in sphere and capped cone

Evenly distributing points on a sphere - 2018