Fix 3D multi-robot safety metric, threshold display, and animation output path

[bardhh]

Summary

Three fixes to the 3D multi-robot visualization. The controller and the enforced constraints are untouched; this only changes what gets measured and drawn.

The distance metric was wrong

_compute_distance_metrics reshaped each robot's state block to its full width (6 columns here: x, y, z, vx, vy, vz) and took the norm across all of them, so the "min inter-robot distance" panel plotted sqrt(|dp|^2 + |dv|^2) instead of |dp|. The error grows with closing speed, which made the plot least accurate at the one moment it matters. On a captured trajectory it read 11.94 where the true separation was 0.65. Two robots sitting at the same point and closing at 3 m/s each get reported as 6.0 apart against a threshold of 0.5.

goal_dists and obs_dists in the same function already sliced positions correctly. This makes the third metric agree with them.

The threshold line was missing or clipped

The manim backend drew no threshold line at all, so its panel could not be read as satisfied or violated. All three backends also took the y limit from the data alone, which pushed the line off screen in the case you most need it: a run that violates the constraint throughout rendered as a clean plot. The limit now accounts for the threshold and handles non-finite data.

There is also a new safety_radius argument, so the per-robot bubbles are sized from the same constant the controller enforces rather than happening to match it.

Animations were written to the wrong path

render_multi_robot_3d handed manim a full filename, which manim appends its own extension to, and never set the format. Asking for anim.gif produced anim.gif.mp4 under <media_dir>/videos/<quality>/ and left whatever already sat at the requested path alone. Regenerating a showcase asset looked like it worked while the advertised file stayed months out of date. The renderer now honors the extension you ask for and copies the finished file there.

Two warnings are gone too. The manim path warned that include_min_distance_plot would be ignored, then forwarded the data and drew the panel anyway.

Checks

Removing the safety filter puts all four robots through the obstacle (closest approach 0.63 against a required 8.0), while the filtered run stays at 10.83. The CBF was doing its job the whole time; only the reporting was off. On the same simulation the reported metric went from 18.33x over-stated to exact.

The new tests/test_utils/test_visualization_helpers_3d.py covers the coincident-but-moving case, velocity independence, and an independent min-over-pairs check, plus pins for the sdim == 3 layout and the two metrics that were already right. Three of its six tests fail against the old code; the other three guard against breaking things in the other direction.

The manim dispatch tests were patching cbfkit.utils.animator's re-export of _HAS_MANIM, which _require_manim() never consults. They passed only because manim was absent and would have failed on any machine that had it. They now patch the real binding, and no longer skip, since nothing they test needs manim itself.

Full fast suite: 490 passed, 4 skipped. ruff check src and black are clean.

Tutorial

It now seeds the scenario, which previously drew new random initial conditions on every run. D_MIN_SQUARED is wired into the barrier constraint that used to hard-code the value; the enforced number stays 0.25, so the dynamics are identical. Initial velocities are drawn as three independent components instead of one scalar broadcast across all three. The tutorial passes the enforced constant as both threshold and bubble radius, and prints the path the backend actually returns.

The showcase animation is re-rendered from this tutorial, so its panel now shows true separation against a visible threshold.