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SubDGuide: A Modeler-Inspired Agentic Workflow for Mesh-to-SubD Reconstruction
Mengnan Jiang, Christian Franke, Michele Franco Adesso, Antonio Haas, Grace Li Zhang
TL;DR
Recovering a subdivision cage from a dense mesh requires inferring its control structure and features, not merely fitting its surface. SubDGuide uses multiview planning with deterministic geometry tools and stateful feedback; it improves all five reported metrics over automatic remeshing across six planner models.
Problem
A dense mesh does not reveal the unique control cage, yet reconstruction must produce a compact cage whose broad form and salient features agree with the observed object.
Source: §1 · p. 1, §3.1 · p. 3Method
SubDGuide combines multiview pre-build planning, deterministic cage construction and fitting, stateful refinement, and verification without planner-generated geometry.
Source: §1 · pp. 2–3Results
SubDGuide improves all five reported metrics over automatic remeshing across six planner models.
Source: §6 · p. 9Takeaways & Limitations
The workflow supports semantic planning for mesh-to-SubD reconstruction while keeping geometry generation outside the planner.
Source: §6 · p. 9Evaluation uses a curated 20-mesh cohort without source control cages, so it measures agreement with targets rather than recovery of an artist’s unique topology.
Source: §5 · p. 8
Abstract
from arXiv · showhide
Subdivision surfaces represent free-form geometry through a sparse control cage, but recovering that cage from a dense mesh is not merely a fitting problem: the system must infer where control is needed, which curves encode design features, and when an initial result should be revised. We present SubDGuide, a modeler-inspired agentic workflow for this task. Stage A reads aligned multiview geometric evidence and produces a compact plan for cage resolution, feature mapping, and broad-form fitting. Stage B inspects the resulting surface, requests targeted diagnostics, and chooses repair, rollback, or stopping actions. Geometry tools execute and verify every change; the planner never generates vertices or connectivity. On a fixed evaluation cohort, SubDGuide improves all five reported metrics over automatic remeshing: median Chamfer-L1 decreases from 0.641% to 0.443% of the target bounding-box diagonal, and F-score at a 1% tolerance increases from 82.00% to 92.78%. Stateful feedback improves four of five reported median metrics over one-shot planning, while verification retains the earlier checkpoint when a proposal is unhelpful. The same interface supports six multimodal planners, showing how semantic judgment can guide a practical, inspectable mesh-to-SubD workflow.
1. Introduction
Recovering a subdivision cage requires inferring control structure and feature flow, not just fitting the dense mesh. SubDGuide separates semantic planning from deterministic construction and verification, then uses feedback to revise or retain a result.
1. Introduction
- A dense mesh does not specify its design structure: many cages can fit the same samples, but only some preserve defining features such as a raised ridge.Automatic remeshing may recover broad form while smoothing away a narrow ridge after subdivision.Source: §1 · p. 1, Figure 1 · p. 1
- Fixed-topology fitting can improve a suitable initial cage but cannot invent a missing loop or rescue a fundamentally unsuitable initialization.Source: §1 · p. 2
- The planner chooses what to attempt, while geometry tools determine how it is constructed and whether it works; the workflow connects multiview interpretation, feature-aware fitting, and feedback-driven repair.The planner does not generate vertices or connectivity.Source: §1 · pp. 2–3
- Stage A plans cage resolution and feature roles from multiview evidence, while deterministic tools construct, fit, and verify the cage before Stage B requests diagnostics, repairs, or revisits a checkpoint.Verification returns the best verified result.Source: §1 · p. 2, Figure 2 · p. 2
- The complete workflow improves every reported reconstruction metric over automatic remeshing; feedback improves both directional distances in six cases and preserves the earlier result in the other 14.Across five alternative multimodal planners, geometry is closely clustered even though search behavior differs.Source: §1 · p. 3
2. Related Work
Prior work supplies geometry representations, fitting methods, and semantic planning interfaces, but these strands do not by themselves address recovery of an editable Catmull–Clark cage from a dense free-form mesh. SubDGuide targets that intersection through deterministic cage tools guided by visual evidence.
2. Related Work
- Triangle-mesh reconstruction and generation can improve geometric or visual fidelity, but their outputs do not reveal sparse control structure for editing or reproduction.The paper treats scanned, modeled, or generated triangle meshes as possible inputs to inverse reconstruction.Source: §2 · p. 3
- Reverse-engineering methods recover structured CAD or fit analytic, spline, B-Rep, or NURBS surfaces, whereas this work targets a sparse Catmull–Clark cage for free-form features.Source: §2 · p. 3
- Subdivision fitting and quadrangulation provide essential components, but do not decide how ambiguous views should guide control density, feature semantics, or cage revision.The cited prior methods include inverse subdivision [14, 33, 41, 42, 47, 51, 53, 76] and quadrangulation [38].Source: §2 · p. 3
- Agentic 3D systems demonstrate semantic planning for executable operations, but do not directly recover an explicit Catmull–Clark cage from a dense mesh.A visually plausible suggestion can still produce poor edge flow or an invalid subdivided surface.Source: §2 · p. 3
- Language-conditioned CAD typically targets parametric CAD, solids, assemblies, or scripts; SubDGuide instead limits planner influence to deterministic cage construction, mapping, fitting, and repair tools.Source: §2 · p. 3
3. Method
The workflow constructs a compact quadrilateral cage whose subdivided surface follows the target while preserving its components, boundaries, apertures, and salient curves. A planner selects typed operations, while deterministic geometry tools construct, fit, repair, and verify the resulting candidates.
3.1. Problem and Workflow
- The goal is a compact quadrilateral cage whose subdivided surface follows the target while preserving components, open boundaries, apertures, and salient curves.The workflow does not seek an unknowable unique source cage, but a valid control representation that agrees with the observed object.Source: §3.1 · p. 3
3.2. Stage A: Pre-Build Planning
- Stage A uses aligned multiview evidence and candidate descriptors to select a resolution tier, initialization policy, and semantic treatment for each feature.Feature decisions distinguish creases, smooth features, open boundaries, and candidates to ignore.Source: §3.2 · p. 4
3.3. Deterministic Geometry Workspace
- The geometry workspace maps selected curves to executable cage-edge paths, fits the surface and features, then assigns crease attributes to hard-line paths.The planner identifies features and intended treatment; the mapper and fitter turn those decisions into traceable geometric constraints.Source: §3.3 · p. 5
3.4. Stage B: Stateful Agentic Refinement
- Stage B reviews the current surface and diagnostics, then may refit a region, insert a support loop, roll back, or stop.Proposed repairs are checked before replacing the current best state, so an unhelpful proposal leaves the earlier result in place.Source: §3.4 · p. 5
3.5. Deterministic Verification and Output
- Deterministic verification independently rebuilds candidate cages, checks geometric and structural criteria, and returns the best passing result or no geometry.The output includes the control cage, its boundary and crease attributes, the evaluated CC-L3 surface, and a verification report.Source: §3.5 · p. 5
4. Experiments
The experiments test whether planning and the geometry workspace improve reconstruction, what stateful feedback changes, and how planner choice affects geometry and search. On a fixed 20-shape cohort, the comparisons cover reconstruction quality, feedback behavior, and six planners using a shared workflow.
4.1. Setup
- The fixed cohort contains 20 single-component meshes, and the five configurations vary the source of the pre-build plan and availability of post-build feedback.The configurations share the target, cage-budget policy, fitter, and CC-L3 evaluator; the cohort comprises 16 Thingi10K meshes and four anonymous reference shapes.Source: §4.1 · pp. 5–6
4.2. Metrics
- Evaluation uses 20,000 area-weighted samples per target and output, with distances reported as percentages of the target bounding-box diagonal D.The case-wise medians cover the same 20 meshes; Chamfer-L1 summarizes two-way distance, F-score uses a 1% of D tolerance, and six-view silhouette IoU measures outline agreement.Source: §4.2 · p. 6
4.3. Reconstruction Quality
- Deterministic Fitting reduces median Dev. P95 from 1.242% to 1.037% of D and Chamfer-L1 from 0.641% to 0.462% of D versus Automatic Remeshing.Rule-based control further reduces the distance tail; Stage A improves normal, F-score, and silhouette metrics through changes to resolution, initialization, and feature treatment.Source: §4.3 · p. 6, Table 1 · p. 7
- Ours records the lowest Dev. P95 (0.970% of D) and normal P95 (29.34°), highest F-score (92.78%) and silhouette IoU (93.13%), and ties One-shot AI Planning on Chamfer-L1.Relative to Automatic Remeshing, median Dev. P95 decreases by 21.9% and Chamfer-L1 by 30.9%, while F-score increases from 82.00% to 92.78%.Source: §4.3 · p. 6, Table 1 · p. 7
- Figure 5 shows errors concentrated in smaller regions for feature-aware configurations, with cleaner boundary and ridge behavior; Ours is never worse than One-shot AI Planning in the displayed cases.Each panel shows the retained CC-L3 surface and control cage, with output-to-target deviation colored on a shared scale from 0 to 2% of D.Source: §4.3 · p. 6, Figure 5 · p. 7
4.4. What Feedback Changes
- Stage B performs 123 reviews and evaluates 47 repair candidates; verified updates improve both directional P95 distances in six cases, while the earlier result is retained in 14.The workflow requests additional evidence 26 times in 13 cases, and verification admits 12 geometry updates across the six improved cases.Source: §4.4 · p. 7, Figure 6 · p. 8
4.5. Planner Choice and Efficiency
- Final geometry remains tightly clustered across planners, with no planner dominating every metric, while their search behavior differs more substantially.Claude Opus 5 selects verified improvements in the most runs, GPT-5.6 Luna is fastest, and Gemini uses the fewest reported tokens per valid reply; more reviews or tokens do not automatically mean better geometry.Source: §4.5 · p. 8, Table 2 · p. 8, Table 3 · p. 8
5. Limitations and Outlook
SubDGuide’s initial cage is its main geometric bottleneck, and the evaluation’s curated scope limits what its results establish. The paper also cautions that cross-model token counts are operational, not hardware-independent, efficiency measures.
5. Limitations and Outlook
- The initial cage cannot generally recover missing components or redesign arbitrary edge flow, despite supported local refinement and loop insertion.Broader part decomposition, alternative cage constructors, and pole-aware local relayout are proposed as extensions.Source: §5 · p. 8
- The curated 20-mesh cohort has no source cages, so evaluation measures agreement with observable targets rather than recovery of an artist’s unique topology.Interactive editing performance is unmeasured, and each configuration was evaluated once per case.Source: §5 · p. 8
- Cross-model token counts use provider-specific accounting and are operational efficiency measures, not hardware-independent costs.Source: §5 · p. 9
6. Conclusion
SubDGuide combines multiview planning, cage construction, stateful feedback, and verification. It improves all five reported metrics over automatic remeshing across six planner models, without direct geometry generation.
6. Conclusion
- SubDGuide improves all five reported metrics over automatic remeshing across six planner models.Source: §6 · p. 9
- The workflow combines multiview planning, cage construction, stateful feedback, and verification.Source: §6 · p. 9
- The workflow achieves these results without direct geometry generation.Source: §6 · p. 9
Reconstruction
The supplement documents the evidence and settings used to interpret and reproduce the experiments. Its fixed comparison cohort contains 20 meshes and provides a common denominator for the reported metrics.
A. Evaluation Protocol
- The supplement provides evidence for interpreting and reproducing the experiments, focusing on the common cohort, semantic-to-geometry interface, additional results, and fixed settings.It excludes development logs and superseded pipeline variants; D denotes the target axis-aligned bounding-box diagonal.Source: A. Evaluation Protocol · p. 13
A.1. Targets and Comparison Cohort
- The fixed cohort contains 20 single-component meshes: 16 Thingi10K targets and four pre-existing anonymous reference shapes, with no source SubD cages or design labels.The meshes span shells, elongated parts, enclosures, ergonomic forms, boundaries, apertures, and quadrangulation challenges.Source: §A.1 · p. 13
- All five configurations produce comparable outputs on the same 20 targets, giving geometry, normal, and silhouette metrics an identical denominator.Source: §A.1 · p. 13
A.2. Aligned Evidence and Fixed Evaluation
Each target is presented through aligned multiview evidence, while the evaluation fixes shared settings for the main comparison. The cross-model study changes only the planner.
A.2. Aligned Evidence and Fixed Evaluation
- Each target is observed from six canonical cameras with five spatially aligned modalities, including clay appearance, silhouette, normals, dihedral variation, and candidate feature curves.The planner also receives normalized curve descriptors and topology summaries; candidate curves are not a privileged extra channel.Source: §A.2 · p. 13
- One-shot AI Planning and Ours use GPT-5.6 Sol at high reasoning effort in the main comparison.Source: §A.2 · p. 13
- The cross-model study changes only the planner.Source: §A.2 · p. 13
A.3. Metrics
The evaluation reports normalized surface-distance, coverage, normal, and silhouette metrics, while separating geometric validity from structural-quality diagnostics.
A.3. Metrics
- Chamfer-L1 averages the two directional mean surface distances and normalizes them by the target bounding-box diagonal D.Surface distances use fixed area-weighted samples measured to the opposite triangle surface.Source: §A.3 · p. 13
- Dev. P95 is the 95th percentile of reconstruction-to-target distances, while Surface F-score uses precision and recall within 1%D.Source: §A.3 · p. 13
- Normal P95 measures the 95th percentile of oriented normal disagreement, and Silhouette IoU averages results over six canonical views.Source: §A.3 · p. 13
- A verified checkpoint must pass evaluated-surface validity and preserve target topology and apertures; structural warnings do not make it a topological failure.The structural-quality profile reports distance, normal, feature flow, and pole placement; feature flow and pole placement are not measures of user editing performance.Source: §A.3 · p. 13
B.1. Additional Method Comparisons
The supplementary comparisons expose cages alongside their evaluated surfaces and show how bounded planner choices affect geometry. The following sections describe multiview planning and the mapping of selected features onto cage edges.
B.1. Additional Method Comparisons
- Figure 7 presents six additional cohort targets with control cages, evaluated CC surfaces, and deviations on a shared scale for direct fitting comparisons.Its deviation panels show reconstruction-to-target Dev. P95, the 95th percentile of the same directional distance used in the main table.Source: §B.1 · p. 13, Figure 7 · p. 15
B.2. Cross-Model Geometry
- Figure 8 shows identical final cages across all six planners in four representative targets and distinct checkpoints in two, where planner choices visibly affect geometry.Targets, observations, tools, budgets, and verification are held fixed; the figure attributes the stabilizing effect to the bounded tool interface.Source: §B.2 · p. 13, Figure 8 · p. 16
C.1. A Bounded Modeling Plan
- Stage A assigns a control-density tier, feature-preservation policy, and semantic action to each candidate using aligned views and normalized curve descriptors.Candidate identifiers and colors remain consistent across six projections, allowing curves to be checked against corresponding clay, silhouette, normal, and dihedral evidence; the Mouse example is outside the quantitative cohort.Source: §C.1 · p. 17
C.2. Ordered Feature-to-Cage Mapping
- Feature mapping selects a continuous ordered path on existing cage edges, then remaps after broad fitting before applying crease weights to confirmed hard lines.Soft ridges retain positional and tangent objectives without hardening the surface; unmappable curves are reported and omitted rather than replaced by disconnected paths.Source: §C.2 · p. 17
D. Stateful Feedback and Implementation Details
Stateful refinement offers bounded post-build actions and can switch construction programs in a controlled example. Deterministic construction and verification constrain what the workflow can repair and the scope of its claims.
D.1. Post-Build Actions
- After reconstruction, the Agent reviews the surface, cage, aligned evidence, metrics, checkpoints, and prior outcome, then selects an available action from the current-state menu.The menu excludes unavailable tools and actions whose budget is exhausted.Source: §D.1 · p. 17, Table 7 · p. 18
D.3. Deterministic Construction and Verification
- Initialization scales a base cage budget by the selected low, medium, or high tier, with one predefined lower-tier fallback rather than a parameter sweep.The budget depends on candidate-curve complexity; the tiers multiply it by 0.75, 1.0, and 1.5, respectively.Source: §D.3 · p. 17
- Broad fitting combines surface, coverage, normal, silhouette, feature-anchor, displacement, and Laplacian terms, then reconstructs final surfaces independently with recorded crease and boundary attributes.Source: §D.3 · pp. 17–18
D.2. Complementary Controlled Program Switch
- The controlled program switch changes a geometrically valid but target-inaccurate paired-wall cage into one that passes the target-quality criterion.This single example is separate from the 20-case evaluation and does not establish broad program-selection superiority.Source: §D.2 · p. 17, Table 8 · p. 18
D.3. Deterministic Construction and Verification
- Repairs commit only after verification and score improvement; otherwise the previous checkpoint remains authoritative.Hard rejection covers evaluated-surface self-intersection, fold or orientation/Jacobian failure, degeneracy, and target topology or aperture corruption.Source: §D.3 · p. 18
D.4. Scope
- The generic initializer requires a usable starting cage; the Agent cannot invent unrestricted topology or decompose objects into independently joined parts.The study also does not measure professional editing time or compare against commercial retopology workflows.Source: §D.4 · p. 18