Intersection Lines

Where two SOs' faces cross each other, we draw dihedral intersection lines. Lives in Render.ts, phase 2c of the render pipeline.

Pipeline

1. Filter — shares_all_axes skips parent-child pairs where the child has identity orientation (no independent rotation = no crossing)
2. World-space faces — transform each face's corners through get_world_matrix, derive normal from world-space geometry via cross(e1, e2)
3. Plane-plane intersection — direction = cross(nA, nB), point on line via 2×2 system solve (set the coordinate along dir's largest component to 0)
4. Cyrus-Beck clip — clip the infinite line to both face quads. Inward edge normal = cross(face_normal, edge_vector)
5. Project + draw — surviving segments get projected through camera and stroked

Cyrus-Beck Convention

The entering/leaving classification:

• alignment = dot(inward_normal, line_direction)
• alignment > 0 → entering (line moving into inside half-plane) → raise t_min
• alignment < 0 → leaving (line moving out of inside half-plane) → lower t_max
• Getting this backwards clips everything (t_min > t_max always)

Test Scenario

From reset: add child, stretch it longer than parent, rotate it. The rotated child's faces cross the parent's faces, producing visible segments. A default child (identity orientation, contained inside parent) won't produce any — shares_all_axes skips it, and even without the filter, no faces geometrically cross.

Key methods

• render_intersections — builds world-space face data, iterates face pairs.
• intersect_face_pair — plane-plane math plus the double clip.
• clip_to_quad_with_edges — Cyrus-Beck against the convex quad's edges, returning which edge caused each clip boundary.

All three live in src/lib/ts/render/Render.ts. Line numbers shift as the file evolves; check the file directly.