Perspective Geometry & Ambiguous Shape Lab

Observer Vector

Azimuth: 0°

Elevation: 45°

Apparent Silhouette: Square

Saddle Non-Planar: True (Z-wave)

Aspect Ratio: 1.00

Sugihara Wave Tuner Calibrated 45°

Wave Amplitude (h) 0.35

Wave Frequency (k) 2

Observer Pitch Offset 45°

Orthogonal Projections

X-Y (Front)

Y-Z (Side)

Z-X (Top)

Analysis Visualizers

Slicing Plane (Horiz. Cut)

Camera Sightline Frustum

Simulate Mirror Reflection

Projective Geometry Proof

Kokichi Sugihara's ambiguous cylinders exploit human vision's planar bias. The top rim is not planar: its height varies sinusoidally z(θ) = A·cos(2θ). Under a 45° oblique projection, the convex crests and concave dips cancel perspective distortion, collapsing into an apparent square from azimuth 0° and a rounded circle from 180°.