feat(pedagogy): tangent-planes audit + capability additions (§11.4)

[bradleypmartin]

Sub-issue of #233.

Per-scene pedagogical coverage audit for tangent-planes against APPM 2350 §11.4, and the resulting capability additions. Sub-epic — audit-phase findings get broken out into real sub-sub-issues at plan-doc time. Pedagogically thinner per initial read; likely substantive new capability work, not just polish.

Starter audit findings (from initial planning pass)

Today: sphere + draggable / aim-pickable point + tangent plane work mechanically. What's missing: the math is invisible. The scene answers "what does a tangent plane look like" but is silent on "how do you compute one."

• Visible normal-vector derivation. Show the normal vector at the selected point, with some indication of how it's derived from the surface (gradient of the implicit form, or other geometric/algebraic construction).
• Visible tangent-plane equation construction. Show how the tangent plane's equation is constructed from the point + normal vector — point-normal form, displacement from origin, etc.
• General principle: make the math visible, not just operational.
• Additional gaps surfaced during full audit at plan-doc time.

Open questions (defer to plan doc)

• How much equation rendering surfaces in-world (overlay on the math object) vs. on the InfoPlinth narrative (feat(pedagogy): tangent-planes narrative (§11.4) #229)? Some belongs in-world to tie to the visual; some belongs in the narrative.
• Equation readout primitive: same EquationReadout candidate flagged in the quadrics audit — extract-on-second-consumer if both want it.
• Surface family: today's scene uses a sphere. Audit whether additional surfaces (graph of f(x, y), parametric, level surface) are in scope for v1.0 or deferred to v1.x.

Composition

Paired with the tangent-planes narrative (#229). These two should be planned together; the capability additions here are exactly what the narrative will reference.