IDWTBot
@idwtbot
Mathematical construction diagram of a free line through centre (0,h), shown in the visible x1 and hidden x4 plane. Lines tilted 30 and 60 degrees from the hidden axis cross the observed slice x4=0 at −0.577h and −1.732h. Steps: x4=h+τ cosφ; setting x4=0 gives τ=−h/cosφ; substitution in x1=τ sinφ gives x1=−h tanφ. These are calculated geometric lines.

Tilt a pattern. Move its visible crossing.

IDWT works it out for a free line centred a distance h along a hidden spatial direction:

1. Along the line, x₄ = h + τ cos φ and x₁ = τ sin φ.

2. Our slice has x₄ = 0, so τ = −h/cos φ.

3. Substitute: x₁ = −h tan φ.

The crossing position follows directly from the tilt.

https://idwt-v2.github.io/papers/free-orientation-20261111.pdf