3D Rotations and Quaternions vs CFOP Learning

3D Rotations and Quaternions is an interactive tool for users who work with 3D orientation math in graphics, roboticsor simulation. It provides precise computations, clean visualizations, and fast conversions between the standard rotation representations. Features include: • Conversion between Euler angles, axis–angle, quaternions, and rotation matrices • Interactive 3D visualization and rotation animation • Quaternion interpolation (LERP and SLERP) • Rotation of user-defined points by user-defined quaternions • Determination of a quaternion that rotates vector v into vector w • Composition of up to 10 sequential quaternion rotations • Quaternion generation from constant angular velocity and time • Reflection of a point across a plane Feedback and suggestions: graphmath@aol.com

CFOP Learning is a companion for learning the CFOP method and practising it every day: a case library, a spaced-repetition trainer, a speedcubing timer and your own progress, all in one app. SEE THE CUBE DIFFERENTLY • A glossy, rounded 3D cube you can turn and step through, move by move • A ring view where every layer is a ring and every piece a dot, so you can follow exactly where each piece goes • Clean 2D diagrams with arrows that match each algorithm SCAN & SOLVE • Point your camera at each face of your cube, tap to fix any sticker, and get a guided CFOP solve: cross, F2L, OLL and PLL • Follow every step on the 3D cube or a 2D map, and jump to the matching case in the library • Everything happens on your device: no photos are saved or uploaded LEARN • Notation guide: what every move means (faces, slices, wide moves, rotations, primes and double turns), played on a 3D cube • Full 41-case F2L library with side-view diagrams, plus OLL and PLL with every PLL side colour shown • Intuitive F2L basics: the six beginner inserts, kept as an easy first step • Quiz Me: hide the case or the solution to test recognition and recall • Mark each case Unseen, Learning or Mastered and watch your coverage grow TRAIN • Spaced-repetition reviews: grade each card Again, Hard, Good or Easy • Daily streak and a new-cases-per-day limit so you never overload • Choose 2D, 3D, rings or mixed card display • Real-cube drill: set a PLL, OLL or F2L case up on your own cube, then time how long you take to recognise it and to solve it TIME • Speedcubing timer with 15-second inspection, +2 and DNF penalties • A fresh, colour-coded scramble for every solve, with named sessions • Best, Ao5, Ao12 and solve history, with trend charts and session stats EXPLORE • 50+ cube patterns, from the Superflip to checkerboards, with step-by-step moves COACH • A personal coach that reads your own solves and reviews and suggests what to practise next. On devices with Apple Intelligence it can also answer questions; everywhere else you get built-in guidance. EVERYWHERE • Widgets, a Live Activity, Spotlight search and Shortcuts • Apple Watch companion with a complication • Your solves and progress sync through your own iCloud account • No ads, no account, no tracking • One-time purchase: no subscriptions and no in-app purchases