Research: prior art on inverse procedural modelling from messy meshes

Eyes pass, 2026-10-10: inverse CSG and shape-program synthesis, primitive
fitting front ends, differentiable SDF/CSG fitting, measured LLM spatial
reasoning with a target, hard-surface detail, and the VibeGeometry record.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/research/inverse-procedural-modelling-prior-art.md

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+# Inverse procedural modelling: describing messy meshes as programs
+
+Eyes pass, 2026-10-10. Operator: "What if the model had some trash geo and its goal is to describe it parametrically?" Context: Tripo hard-surface hulls; CultMath intervals and affine forms on main, tape/brush grammar parked (docs/cultmath-tape-target.md); the earlier GameCult/VibeGeometry attempt (2026-05). Facts only; tags mark FETCHED, SEARCH (search summary only) and KNOWLEDGE (unverified).
+
+# Eyes facts: inverse procedural modelling (mesh -> parametric program)
+Date 2026-10-10. Tags: FETCHED (page/file read this session), SEARCH (search-result digest only), KNOWLEDGE (unverified recall).
+Search digests come from a small model; SEARCH numbers are not paper-verified.
+
+## 0. What exists in GameCult
+- FETCHED F:\Projects\CultLib\docs\cultmath-tape-target.md: steps 2-5 (tape, pruning, HLSL interpreter, meshing) PARKED (2026-10-02,
+  ruling tape-target-unparks-when-asura-stable). Step 1 intervals + affine forms are on main (docs/cultmath-interval-ground-cut.md).
+  The "grammar of nested brushes" is operator intent only (quote 2026-10-02: space station from "a grammar of nested brushes");
+  doc says the station project is "a separate project with its own target". Chosen shape (c): port Fidget ideas into CultLib (Fidget =
+  MPL-2.0 Rust, v0.5.1). Meshing plan: surface nets + Asura tile pass (Newton refinement onto f=0, crease snapping from field gradients);
+  "Thin authored bevels can be shaded by their analytic normals". Tape gradients "reuse CultMath's analytic-gradient primitives".
+- FETCHED grep CultLib\docs for brush/tape: "brush" hits in cultmath-interval-ground-cut.md are Aetheria noise/gravity-well field brushes
+  (PowerBrush (1-x^2)^16 etc.), not CSG brushes. No CSG brush grammar or tape code exists in CultLib; only the parked doc.
+- FETCHED (voidbot) separate repo GameCult/GameCult.Geometry.Csg ("CultGeometry CSG", Rust; local F:\Projects\GameCult.Geometry.Csg).
+  Mesh-based convex plane-splitting CSG (not SDF), RealtimeCSG-shaped API: ordered Additive/Subtractive/Intersecting brush streams, boxes,
+  oriented boxes, CylinderZ/DomeCapZ/FloretArm, dirty-frontier, OBJ output, plus domain-tree/selected-cut LOD schemas (src/cult_geometry).
+  Doc text: "agents should revise intent by moving, adding, or renaming brushes, not by poking triangles"; "brush list is the durable
+  design surface. The mesh is a cache."
+
+## 0b. The earlier "vibe geometry" attempt
+- FETCHED voidbot gamecult-site GameCult/Projects/VibeGeometry.md: repo GameCult/VibeGeometry, started 2026-05-04, last public push
+  2026-05-07; "agent-authored Blender scene generation: geometry nodes, Python builders, semantic graph contracts, render evidence, and
+  the ongoing war against decorative node spaghetti". Org ledger: "Started as architecture and persistence scaffolding, then dived almost
+  immediately into CSG grammar, parity fixtures, native bridge probing, mesh generation, and performance work."
+- FETCHED local git F:\Projects\VibeGeometry-cultgeometry-rename (93 commits). Commit 09bff8c (2026-05-29, "Focus VibeGeometry on vg-csg")
+  deleted the scene-generation tree; recoverable at 09bff8c^: docs/research/procedural-doctrine.md (~1000-line "spatial reasoning
+  playbook"), dream-machine-grammar.md, geonodes-translation-corpus.md, ircss-french-houses-* (translations of Blender node graphs into
+  Geometry Script Python), builds/{aetheria-bloom-habitat, lucent-tether-habitat, dream-machine-level, industrial-maintenance-loop}.md,
+  notes/architecture-rationale.md, a "reusable procedural helper library" (aa4d49d). The DSL was Blender Python via Geometry Script
+  (fork F:\Projects\geometry-script; upstream PR carson-katri/geometry-script#69 linked by Metacrat 2026-05-04) emitting geometry-node
+  graphs, plus the Rust brush DSL (LevelDsl: solid_box, cut_box, solid_oriented_box, dome_cap_z, floret_arm).
+- FETCHED notes/architecture-rationale.md @09bff8c^, section "Core Failure": "The central failure mode is local plausibility without global
+  coherence. An agent can write plausible Blender Python, create a large node graph, and still lose the visual machine ... the script
+  runs, the graph exists, the render has objects in it, and somehow the target has been replaced by decorative procedural fog".
+  "Seductive proxies": valid Python, non-empty renders, high node counts, pretty materials, parameter sliders.
+  procedural-doctrine.md: "Ornament in the wrong frame is not detail. It is a confident lie". Commit titles record frame errors:
+  "Correct Bloom terrace slum orientation", "Correct Lucent dome spin-gravity frame", "Move Lucent ray florets outside dome".
+- FETCHED VibeGeometry README: "failed experiments are useful without being allowed to hold a steering wheel"; old mission "deleted
+  from the live tree"; live mission narrowed to runtime CSG (domain tree -> LOD CSG -> selected cut -> triangles).
+- NOT FOUND: no indexed operator or agent statement that models "weren't good enough at spatial reasoning to use the DSL". voidbot
+  search_history (Discord) returned only unrelated hits. The repo docs above are the only failure statements in project words
+  (coherence and frame errors; the phrase "spatial reasoning" appears only in the playbook title and its body).
+
+## 1. Inverse CSG / shape-program synthesis
+Most train or test on DeepCAD / ShapeNet / ABC / Infinigen; none retrieved was evaluated on noisy AI-generated hard-surface meshes.
+- InverseCSG (Du et al., SIGGRAPH Asia 2018, MIT). SEARCH: mesh/point samples -> CSG program; geometric processing (RANSAC-style primitive
+  detection) turns the mixed discrete/continuous problem into a purely discrete one; careful point samples guide a discrete search;
+  divide-and-conquer segmentation; program synthesis (solver) per segment. Claims >100 primitive parts, compact programs, beats prior
+  methods on compactness/runtime. D2CSG authors (SEARCH) criticise it: RANSAC needs tuning, noisy initial primitives, long search.
+  Project page inversecsg.csail.mit.edu lists code; licence not checked.
+- CSGNet (Sharma 2018): KNOWLEDGE only; supervised, voxel/2D -> CSG sequence.
+- UCSG-Net (Kania, NeurIPS 2020). SEARCH: unsupervised; predicts box/sphere params; differentiable indicator on SDF; several CSG layers with
+  soft operator choice; structure and params learned jointly by gradient descent; autoencoding scope (2D/3D), no mesh-to-program at test
+  for unseen exotic shapes beyond the trained net.
+- CAPRI-Net (CVPR 2022). SEARCH: axis-aligned quadric primitives, fixed 3-layer assembly; ABC point-cloud Chamfer 0.09 vs UCSG 1.43; ~5.3 vs
+  12.92 convex shapes. D2CSG (2023), CSG-Stump (2021): SEARCH, unsupervised compact trees. SECAD-Net (CVPR 2023): SEARCH, sketch-extrude,
+  editable; CD 2.94/4.20 (ABC/Fusion) vs UCSG 3.14/4.45.
+- Point2CAD (Liu et al.): SEARCH only that a repo exists (jofcodeusal/point2cad mirror, Docker toshas/point2cad); method not retrieved.
+  Point2Cyl (CVPR 2022): SEARCH, supervised net to extrusion cylinders. DeepCAD (Wu 2021): KNOWLEDGE, ~178k sketch-extrude sequences.
+- ShapeAssembly (Jones 2020, TOG): SEARCH; programs of cuboid proxies attached to each other with free parameters; extraction from PartNet.
+  ShapeMOD (2021): SEARCH; discovers macros across a corpus minimising calls and free parameters. Repos/licences not found by search
+  (KNOWLEDGE: github rkjones4/ShapeAssembly exists; unverified).
+- CAD-Recode (Rukhovich et al., ICCV 2025, arXiv 2412.14042). FETCHED abstract: point cloud -> CadQuery Python (sketch-extrude); point-cloud
+  projector + small pretrained LLM decoder; trained on 1M procedurally generated CAD sequences; eval DeepCAD, Fusion360, CC3D (real scans);
+  output usable by off-the-shelf LLMs for editing and QA. SEARCH (unverified): Qwen 0.5B/1.5B decoders; DeepCAD mean CD 3.43 -> 0.30, IoU
+  77.6 -> 92.0 vs CAD-SIGNet; test time: 10 sampled candidates executed, min-Chamfer kept. Code github.com/filaPro/cad-recode (SEARCH);
+  HF dataset filapro/cad-recode is CC-BY-NC-4.0 (SEARCH); repo licence unchecked. Structure by autoregressive decoding, params as literal
+  tokens, re-ranking by Chamfer. Abstract says nothing on fillets/chamfers.
+- MeshCoder (Dai et al., NeurIPS 2025, arXiv 2508.14879). FETCHED: 16,384-point cloud -> triplane tokenizer -> Llama-3.2-1B (LoRA) ->
+  Blender Python. API: cube/cylinder/UV-sphere/cone/torus, Translation (sweep 2D section along 3D trajectory), Bridge Loop, Boolean
+  (union/intersect/diff), Array, Fill Grid, Spoon, Fork. Data: ~10M part-code pairs, ~1M object-code pairs, 41 categories (Infinigen
+  Indoor). Table 2 averages CD x1e-2 / IoU%: Shape2Prog 6.00/45.0, PLAD 1.87/67.6, MeshCoder 0.06/86.75. Worst: Fork 58.9 IoU, CeilingLight
+  65.8, Array parts 78.9. Limits: human-made objects only; geometry only; training objects kept only if every part CD < 5e-3. LLM does not
+  edit; edits are manual param changes; GPT-4o used only for QA on the code. Output is part-segmented. Licence not stated in paper.
+- CADCodeVerify (Alrashedy, ICLR 2025, arXiv 2410.05340). SEARCH: text prompt -> CadQuery (GPT-4); VLM writes/answers validation questions
+  about renders and refines; CADPrompt benchmark (200 objects); GPT-4 point-cloud distance -7.30%, compile rate +5.5% (v2; v1 said 5.0%
+  success). Target is a prompt, not a mesh.
+- Newer render-loop agents (SEARCH): SEIG "Thinking in Blender" (arXiv 2606.02580): single reference image -> staged Blender code (geometry,
+  materials, composition, lighting), VLM generator + verifier per stage; FETCHED abstract gives no numbers, no code link. LL3M (2508.08228):
+  text -> Blender with critic reading renders. ShapeCraft (2510.17603): renders bbox/part/global views as feedback. SceneCraft (2403.01248):
+  render-critique-revise. Not found by search: "3D-Premise", "LLMto3D", Img2CAD/Text2CAD specifics.
+
+## 2. Classical primitive fitting as a front end
+- Efficient RANSAC (Schnabel/Wahl/Klein, CGF 2007): SEARCH/FETCHED page text: planes, spheres, cylinders, cones, tori in unorganised clouds;
+  multi-million-point sets "within less than a minute". CGAL Shape Detection implements it plus Region Growing (Lafarge&Mallet). CGAL is
+  dual GPL/LGPL + commercial; the Shape Detection package's own licence NOT confirmed (digest guessed GPL).
+- GlobFit (Li/Wu/Chrysanthou/Sharf/Cohen-Or/Mitra, SIGGRAPH 2011): SEARCH; starts from RANSAC primitives, discovers global relations
+  (orientation, placement, equality; symmetry) and enforces them by constrained optimisation; assumes man-made, repeated, globally aligned
+  parts. Code: archived code.google.com/archive/p/globfit, "research use only" wording.
+- Mitra 2006 symmetry detection, SPFN (2019): KNOWLEDGE/SEARCH only. ParSeNet (2020): SEARCH; B-spline patch decomposition, beats RANSAC
+  and SPFN baselines. No repos/licences retrieved.
+- What fits supply as data: exact primitive parameters with inlier sets and residuals, segment labels, relation graph (GlobFit).
+  InverseCSG uses the primitives to make the problem discrete. Recorded weakness: noisy primitives, parameter tuning (SEARCH).
+
+## 3. Differentiable fitting of SDF/CSG programs
+- UCSG-Net (above): soft operator selection; structure learned jointly.
+- Fuzzy Boolean differentiable CSG (dgp.toronto.edu/~hsuehtil/pdf/fuzzyBoolean.pdf): SEARCH; gradient descent over boolean and primitive
+  parameters; notes prior work pre-fixes tree structure and operators and optimises only primitive params; replaces min/max with a unified
+  fuzzy operator so the operation type is optimised. Costs listed: analytic SDF per primitive type, per-iteration SDF evaluation, image
+  losses need differentiable sphere tracing.
+- DiffCSG (arXiv 2409.01421): SEARCH; differentiable rasterisation of mesh CSG, image-space gradients to primitive params; image-guided
+  editing, not mesh fitting.
+- ResFit, Residual Primitive Fitting with SuperFrusta (arXiv 2512.09201): SEARCH; one analytic SDF primitive with 8 params (dilation, taper,
+  bulge, onion hollowing, profile roundness, axial scaling); alternates global shape analysis and local primitive optimisation; code "to be
+  open-sourced upon acceptance".
+- Evolutionary mesh -> CSG abstraction (SEARCH; authors not retrieved): fast, coarse. Sigmoid-over-SDF soft occupancy with alternating
+  add-primitive / joint-refine loop (SEARCH, primitive-scene paper).
+- Not found: a published gradient fit of an SDF program with bevel/round parameters to a messy hard-surface mesh.
+- Handling of discrete structure across sources: soft selection (UCSG, CSG-Stump, fuzzy Boolean); pre-fixed structure (InverseCSG after
+  RANSAC; CAPRI-Net fixed layers); greedy add/prune (ResFit); neural token decoding (CAD-Recode, MeshCoder).
+
+## 4. LLM spatial reasoning in 3D code generation
+- BlenderGym (Gu et al., CVPR 2025, arXiv 2504.01786). FETCHED: 245 start-goal Blender scene pairs, five tasks (placement, lighting,
+  procedural material, blend shape, procedural geometry); the VLM sees start and goal and edits Blender code (target-matching setting).
+  Table 1 best-VLM vs human: geometry Chamfer 1.120 (GPT-4-Turbo) vs 0.334; geometry photometric loss 6.747 vs 1.269; placement CD 8.324 vs
+  1.532; blend shape CD 0.904 vs 0.399. Paper: VLMs "particularly poorly in procedural material and geometry editing"; all open-source
+  models except MiniCPM failed to produce executable code on >75% of geometry instances. Verifier agreement with humans: human 0.79,
+  Claude 3.5 Sonnet 0.66, random 0.5. Scaling a small verifier (InternVL2-8B, k 1 -> 64 over 32 candidates) beat unscaled GPT-4o and
+  Claude 3.5 on blend shape. Low compute: less verification share (0.33); high compute: more (0.62-0.73). Models are 2024-25 era. Code
+  licence not in retrieved text.
+- BenchCAD (arXiv 2605.10865): SEARCH; 17,900 CadQuery programs, 106 part families; frontier models recover coarse outer geometry but fail
+  faithful parametric programs; sweeps/lofts/twist-extrudes replaced by sketch-extrude; single-literal errors (5.6 vs 5.85) at IoU >= 0.9.
+  BenchCAD-Edit: text instruction sets the upper bound; the image is "at best a clarifier and at worst a distractor" for thinking models.
+- Text2CAD-Bench (2605.18430): SEARCH; execution failures even at easy level; sweep/loft/shell widely fail; executing != correct.
+- Text-to-B-Rep paper (2603.11831): SEARCH; spatial misalignment of primitives, omitted fillets, geometry contradicting described layout;
+  authors blame weak precise 3D spatial reasoning.
+- "Foundation Models for Automatic CAD Generation" (2607.05573): SEARCH, single source; numeric analytic feedback peaked at round 1; VLM
+  critique of renders kept improving in rounds 2-3 for DeepSeek/Qwen; VLM critics struggle on rotationally symmetric geometry.
+- Multi-view conditioning beat single-view and sketch on Chamfer/F-score in a B-Rep paper (SEARCH, not CadQuery).
+- Target vs description: BlenderGym gives a target and still shows a large human gap; CAD-Recode and MeshCoder avoid prompting by training
+  point-cloud encoders; no controlled prompted-LLM study of target-vs-description was found.
+- MindCube spatial study (SEARCH): errors 20% final reasoning step, 13% 3D reconstruction, 6% generated programs.
+
+## 5. Hard-surface specifics
+- SDF rounding (Quilez distfunctions, SEARCH): sdRoundBox = box SDF minus r, an iso-offset so the shape grows by r. Polynomial smin with k
+  as blend band; Quilez marks smin as "bound" not exact. Chamfer/fillet operators not retrieved; KNOWLEDGE: hg_sdf (Mercury) has
+  fOpUnionChamfer / fOpUnionRound / fOpUnionStairs (unverified here).
+- MeshCoder (FETCHED): no fillet/chamfer primitive; booleans, sweeps, bridge-loop, arrays only.
+- BenchCAD / text-to-B-Rep (SEARCH): omitted fillets/refinement features named as failure; sweeps/lofts degrade to extrudes.
+- CAD-Recode/DeepCAD data are sketch-extrude (SEARCH/KNOWLEDGE); fillet/chamfer not covered in what was retrieved.
+- InverseCSG output: boolean of primitives, no blends (KNOWLEDGE). CAPRI-Net quadrics: smooth surface in one primitive (SEARCH). ResFit
+  primitive has a profile-roundness parameter (SEARCH).
+
+## Gaps
+- Operator/agent words on why VibeGeometry failed: not indexed (see 0b).
+- Not read at body level: CAD-Recode fillet handling, InverseCSG experiments, GlobFit relation list, SEIG numbers, ResFit results.
+- Licences unverified: InverseCSG, ShapeAssembly, CAD-Recode repo, MeshCoder, GlobFit, CGAL Shape Detection, Point2CAD.