ImpossibleMotions

Inspiration

CodeParade's Non-Euclidean Worlds Engine & M.C. Escher's Relativity: Proved that rendering impossible geometries in real-time is possible and visually striking.
Valve's Portal: Inspired our companion cube puzzles, tactile cause-and-effect mechanics, and environmental signposting.
Surreal Architecture: Artwork featuring impossible twisting corridors pushed us to turn visual illusions into physical, interactive puzzle mechanics.

Impossible Motions is a first-person puzzle-platformer built across three non-Euclidean chambers:

Room A (Distance Compression): A physical 20-meter chasm traversed via a long walkway, which is then unlocked as an impossible 4-step shortcut tunnel.
Room B (Gravity Shift): A 90° curved elbow conduit that smoothly rotates gravity onto vertical walls, requiring players to navigate sideways and place a cube on a wall-mounted magnetic plate.
Room C (Continuous Scaling): A 5-meter tapering tunnel that continuously scales the player down to 0.32x (while feeling completely static from the inside), allowing entry into miniature ducts to retrieve a tiny cube, grow it back, and unlock the exit.

Engine & Graphics: Unity 6 (6000.0.6f1) and Universal Render Pipeline (URP 17).
Oblique Portal Math: Dynamic virtual camera mapping using affine transform matrices paired with portalCamera.CalculateObliqueMatrix() to clip occluded geometry at doorway thresholds.
Conformal Metric Scaling: Real-time runtime driver synchronizing normalized tunnel depth $t \in [0, 1]$ with player scale ($1.0\times \leftrightarrow 0.32\times$), collider bounds, and camera near-clip planes.
Arbitrary Gravity Kinematics: Decoupled CharacterController from global $+Y$, implementing continuous $SO(3)$ gravity rotation and local-frame jumping.

Oblique Projection Artifacts: Skewing the near-clip plane to match portal quads altered depth buffer precision, requiring calibration to prevent z-fighting and shadow acne.
Continuous Scaling Invariance: Matching the rate of tunnel mesh taper precisely with eye-height decay so the corridor appeared static rather than warping.
Non-Vertical Physics: Rewriting character ground checks and jumping to operate along arbitrary -gravityDirection vectors without physics glitches or axis lock.

Seamless Visual Continuity: Zero screen-tearing, seam popping, or camera hitching across all portal transitions at 60+ FPS.
The "Static Tunnel" Illusion: Perfectly synchronizing scale decay so the player doesn't realize they've shrunk until stepping outside.
Unified Companion Cube: An interactive object that handles portals, dynamic scaling, throwing, and vertical magnetic locking without breaking physics.

Deriving custom projection frustums and homogeneous transformation matrices in URP.
Decoupling character kinematics and raycasts from global coordinate axes.
Designing spatial puzzles that visually prove their impossibility to the player before demanding a solution.

Reverse-Tapering Corridors: Hallways that expand into massive spaces while shrinking obstacles around you.
Compound Anomaly Stacking: Multi-mechanic puzzles combining scaling tunnels with shifting gravity spirals.
Momentum-Preserving Portals: Kinetic energy redirection for high-velocity traversal.