A walkthrough of three common 3D rotation systems used in interactive applications: turntable, tumbler, and trackball. Each system is evaluated on three criteria: ability to reach arbitrary rotation angles, path independence, and unlimited rotation range. Turntable locks the Z axis upright but is path-independent and unlimited; tumbler allows arbitrary angles but lacks path independence; trackball (using Holroyd's sphere-hyperbola blend) supports arbitrary angles and is path-independent but caps at 180°. The recommendation is to use turntable when a real-world axis exists, trackball otherwise, and to avoid tumbler. A real-world example from Formlabs' PreForm software shows how both systems can coexist in one application.
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