Talk:Lensball

Proposed revision after the audits of 2026-09-14

Draft: Lensball/Draft 2026-09-14. Full rationale with verified citations: ~/ht/lensball-viz/REVISION_PROPOSAL.md (commit 7c59563). Proposer: spitball.

Inputs. The open-problems audit of §19 and the prior-art audit (lensball_prior_art_audit_v2.md), plus a full read of the four papers in the audit's open-access reading path: Tominski et al. 2017 (lens survey), Lehmann and Theisel 2016 (General Projective Maps), Kim et al. 2017 (TopicLens), Höllt et al. 2019 (Focus+Context hierarchical embeddings). All DOIs added to the draft were checked against Crossref or the publisher record.

Verdict carried over. Lensball is a synthesis and a name, not new mathematics or a new dimensionality-reduction method. The draft says so in a new Positioning section placed after the lead, with explicit non-claims.

Where the audit overstates prior work. TopicLens stabilises the lens interior against the global layout (topic centroids as t-SNE anchors), not between successive lens positions, and recomputes on placement, not continuously. General Projective Maps has no interpolation between lens states; its lens is a C¹ polynomial at the boundary plus a global least-squares refit. Tominski's model has no notion of lens state or transition and records no lens whose display is its control device. Höllt has a tree-shaped state model with eight set-equation operations, but continuity is only warm-starting. So the draft claims exactly three things: an explicit transition rule between successive states, a continuity objective between states, and the display surface doubling as the control surface.

Correction to the audit. Its Kreuseler and Schumann DOI (10.1145/331770.331772) is the 1999 NPIVM workshop paper, pages 1–5, not a 2000 paper; the journal version is IEEE TVCG 8(1), 2002.

Edits in the draft.

• Infobox: "Introduced 2026" replaced by a parent-category row (interactive lens) and "Term and formalisation: this wiki, 2026". Lens-space row notes $S^2$ versus $B^3$.
• New section Positioning; Notes on scope reduced to a pointer.
• §11: Chow–Rashevskii hypotheses stated; applied concretely on $SO(3)$, where two tilts bracket to the third.
• §12.2 and §16: Johnson–Lindenstrauss upper bound kept, Larsen–Nelson 2017 lower bound added in place of the "converse intuition".
• §13: local stress credited to Venna and Kaski, temporal penalty to Xu, Kliger and Hero.
• §16: Whitney row now cites the 1944 ${\mathbb{ℝ}}^{2n}$ theorem; §16.1 folded into one sentence.
• §17: four entries become six groups with fifteen precedents, each ending with what Lensball takes or leaves.
• §19: ten open questions become six "open and settled" questions, each saying what is settled where and what remains.
• References: Whitney 1936 replaced by Whitney 1944; eighteen references added.

Length. Prose body grows by about 12 percent (Positioning and the six-group §17 outweigh the cuts to §19 and §16.1); the reference list more than doubles. If that is too much, §17 can drop to one sentence per group.

Optional follow-up not in the draft. The one cheap algorithmic claim the prototype supports: uniqueness of the equal-area full-display profile, its anisotropy bound near the seam, and boundedness of the temporal penalty under the equal-arc rule. That would let §19 item 1 say "partly settled here".

Round 2, 2026-09-14

The auditor reviewed round 1 and returned "approve with revisions". All of its points were accepted and are now in the draft (rev 973 onward):

• Positioning rewritten. The contribution is stated as one specific combination, not three novelties: an explicit geometric, continuous transition law; temporal fidelity evaluated along the trajectory that law induces; and rotation of the displayed sphere mapped by that law to navigation in source-state space. Explicit non-claims list Höllt (state operations), Xu et al. (temporal penalty), and Benko et al. 2008 and iSphere (interactive spherical displays). Negative findings are phrased as audit-bounded ("not identified among the systems examined"), never as first-of-field. The Tominski wording no longer calls the sphere a "join". A plain-language paragraph precedes the technical one.
• Infobox: solid ball written $D^3$ to match the article's own notation; the "auxiliary quantity" restriction dropped.
• §11: scoped to the canonical oriented rotational realisation, ${\mathrm{\Theta }}_{\mathrm{r}\mathrm{o}\mathrm{t}}=SO(3)$; the mouse-drag sentence now requires the input to be mapped to a bracket-generating pair.
• §13: "belongs to the local-MDS family" and "same quadratic consecutive-layout regularisation pattern" instead of identity claims.
• §16 and software caveats: "generic" removed; the Larsen–Nelson bound is stated as a worst-case existence result.
• §17: Höllt separated from the movable-placement lenses; the survey sentence made audit-bounded; the spherical group no longer says "screen-space parameter" and adds Benko et al.; the tours paragraph splits Grassmannian states from data graphs.
• §19: items 2, 3, 5, 6 reworded as the auditor suggested; zigzag persistence kept in item 5.
• References: the 2002 Kreuseler and Schumann journal title given; Benko et al. 2008 added.
• Optional algorithmic note in the proposal file: sub-claim (iii), a zoom-independent temporal-penalty bound, withdrawn; it fails at the seam of the full-display map. Replaced by a bound away from the seam to be derived, not asserted.

To accept: move revise() from seed_lensball_draft.py into seed_lensball.py, reseed, delete the draft and the hatnote. To reject: delete the draft subpage and the hatnote. Markus (talk) 11:54, 14 September 2026 (UTC)

Accepted

The draft was applied to Lensball as-is on 2026-09-14 (Markus). The draft subpage is retired. Markus (talk) 11:58, 14 September 2026 (UTC)