If you're trying to distinguish between a "classic" torus (volume of revolution created by sweeping a circle around an axis coplanar with said circle) and a sph

If you're trying to distinguish between a "classic" torus (volume of revolution created by sweeping a circle around an axis coplanar with said circle) and a sphere, there's a fairly easy way. Measure the curvature at your current point. (Say, by drawing a triangle and measuring angles). Walk in an arbitrary direction in a straight line until you come back to your starting point, measuring curvature at at least two points along the way. Then do the same at 90 degrees from your previous walk. If you're on a torus, at least one of your measurements of the curvature will be different. If you're on a sphere, the curvature will be constant and positive.