A cube made of curves.
A twist made of rotations.

Try the deformation

Educational diagram using the equations below. This is not an intro frame or a recording.

1. Start with edges, not faces

A cube has eight corners and twelve edges. The important thing here is the edge path: a cubic curve is described by four 3D control points. With the two inner controls on the straight segment, it starts as an ordinary straight edge.

2. Evaluate points on each curve

Advance a parameter t from zero to one. Each evaluation produces a 3D point. More samples make the stamped edge continuous; fewer expose the individual dots.

B(t) = (1−t)³ P₀
 3(1−t)²t P₁
 3(1−t)t² P₂ + t³ P₃

The cube's inlined kernel at 0x15834 uses the cubic Bézier weights. The intro also has a separate uniform cubic spline helper; those bases should not be confused.

3. Rotate by position

An ordinary rotation uses one angle for the entire object. A twist makes the angle depend on the point's coordinate along an axis. For a vertical Y-axis twist:

θ = k · y
x′ = x cos θ − z sin θ
z′ = x sin θ + z cos θ
y′ = y

The middle barely turns, while the top and bottom turn in opposite directions. The original deformation routine at 0x16263–0x1641b supports coordinate-dependent rotations about X, Y and Z, with separate factors. Combining these operations and animating their factors gives the changing distortion.

The interactive diagram isolates a Y twist. Its speed, shape and controls are illustrative; they do not reproduce the intro's complete choreography.

4. Project, then stamp

After deformation and camera transformation, perspective turns a 3D point into a screen position. In the translated projection path:

screenX = trunc(128 · x / z) + 160
screenY = trunc(128 · y / z) + 100
sprite radius ≈ 128 / z

Nearby points become larger sprite stamps. Overlapping soft stamps accumulate intensity, so the edge looks like a glowing tube rather than a one-pixel wire. The shape is carried by sampled geometry; its material-like appearance comes from the sprite and indexed-color composition.

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