Inferring CAD Modeling Sequences Using Zone Graphs

1. Introduction

• Recovering parametric programs for everyday objects could support editing and repurposing in mechanical and industrial design.The paper frames the task as inferring the operations that construct a B-rep, distinct from converting input geometry into a B-rep.Source: §1 · pp. 1–2
• Feature-based modeling with B-reps is more expressive than parametric primitive CSG, but its program space is much larger.CAD practitioners use surface-based operations such as sketching a slot profile and specifying its depth.Source: §1 · pp. 1–2
• The zone graph turns feature-based program inference from an infinite search space into a finite search over operation sequences that fill interior zones.It is constructed by extending the input B-rep’s faces and partitioning space with them.Source: §1 · p. 2
• The method searches sketch + extrude + Boolean operations, which create solid masses or cut holes and slots.A graph neural network trained on CAD sequences scores candidate operations so search can prioritize learned design patterns without human guidance.Source: §1 · p. 2
• In experiments on real-world CAD shapes, the zone graph method outperforms a recent CSG inference method in reconstruction accuracy and produces more plausible programs using industry-standard operations.The stated comparison is with a recent CSG inference method.Source: §1 · p. 2

2. Related Work

• Zone graphs differ from prior space-partitioning work by representing incidence among parametric surfaces, including curved surfaces, for modeling-sequence inference.Prior work includes point-cloud surface reconstruction and binary space partitioning for compact CSG mesh generation.Source: §2 · p. 2
• Commercial rule-based feature recognition can recover some operations but may fail to rebuild the full parametric history from the first step.The paper focuses on automatically recovering the entire construction sequence in a manner consistent with human designs.Source: §2 · p. 2
• CSG reconstruction methods infer programs using simple primitives, whereas professional design tools commonly build from sketches using operations such as extrude, revolve, and sweep.InverseCSG uses constraint-based synthesis; CSGNet uses a neural network to infer CSG operation sequences.Source: §2 · p. 3
• The paper also uses neurally guided search, with learned proposals and ranking algorithms for zone graphs.Neurally guided search prioritizes options during visual program induction.Source: §2 · p. 3

3. Task & Approach

• The task is to find a sequence of modeling operations that reproduces a shape specified as a B-rep.Source: §3 · p. 3
• The target operation family sketches closed profiles on a plane, extrudes them into solid regions, and applies them by union or difference.Source: §3 · p. 3
• The approach converts the input B-rep into a zone graph and searches for graph-consistent operations that reproduce it.A learned guidance network prioritizes candidate operations according to patterns in a dataset of example CAD programs.Source: §3 · p. 3

• A zone graph partitions the input B-rep’s axis-aligned bounding box into solid regions, with edges representing the surface patches connecting adjacent regions.Source: §4 · p. 3
• Face extensions are clipped to the B-rep’s bounding box; planar, generalized cylindrical, and spherical faces use different extensions, while free-form faces are not extended.Source: §4 · p. 3
• Zone count grows superlinearly with face count, so the method extends faces in selected four-edged face loops only along their shared-edge direction.The loops form cycles whose consecutive faces share parallel edges.Source: §4 · pp. 3–4
• Zone graph construction time increases linearly with zone count, and most graphs take under a minute.Source: §4 · p. 4
• The method reconstructs 6,900 of 8,625 dataset models, while the zone graph represents the ground-truth sequence for 5,175 of those reconstructions.Reported failure causes include GFA numerical robustness issues, unsupported tapered extrude and revolve operations, and sequences not captured by extrusion proposals or not expressible by the zone graph.Source: §4 · p. 4

5. Searching for Modeling Sequences

• The search guarantees each intermediate shape is a combination of zones, but exact reconstruction is guaranteed only when the target is expressible by the supported operations and search time is unbounded.Source: §5 · p. 4
• Search keeps the top five proposals, explores the highest-scoring first, and backtracks when a terminal canvas does not match the target.It stops when the canvas matches the target or the time budget expires; if time expires, it returns the canvas with the highest reconstruction IoU.Source: §5 · p. 4

5.1. Generating Candidate Modeling Operations

• Candidate extrusions begin with parallel start and end planes; adjacent zones guide which connected face groups can form sketches for union or subtraction.Each sketch is extruded along the plane-to-plane direction to form a generalized cylinder; proposals that reverse an earlier operation are discarded to prevent cycles.Source: §5.1 · pp. 4–5

5.2. Ranking Candidate Modeling Operations

• The scoring network predicts how likely an operation is to be next from the zone graph, current canvas, target, and proposed extrusion.Zone point clouds are encoded with PointNet, processed by a graph convolutional network, then pooled and passed through an MLP.Source: §5.2 · p. 5, Figure 5 · p. 6
• Training labels non-ground-truth extrusions as neutral or negative using random sequence completions, rather than treating every alternative as negative.The method uses 3,000 sequences for training and holds out 440 for testing.Source: §5.2 · pp. 5–6
• Ours Net performs about 2x better than Ours Heur when ranking ground-truth extrusions by average candidate count.Lower is better; evaluation uses held-out Fusion 360 test sequences.Source: §5.2 · p. 6, Figure 6 · p. 6

6.1. Search Proposal Ranking

• The network and heuristic both significantly outperform random in ground-truth extrusion ranking, and the network dominates the heuristic by a factor of two.The evaluation uses held-out test sequences from the Fusion 360 Gallery reconstruction dataset.Source: §6.1 · p. 6
• For the same input shape, the heuristic produces the shortest sequence, while the network produces a more intuitive one.Figure 7 illustrates sequences inferred under random, heuristic, and network guidance.Source: §6.1 · p. 6, Figure 7 · p. 7

6.2. Reconstruction Performance Ablation Study

• Network and heuristic guidance reach 100% reconstruction accuracy after about 20 seconds, whereas random guidance does not converge.Heuristic guidance is faster because it avoids network-evaluation cost and seeks fewer operations, but shorter sequences are not always better.Source: §6.2 · p. 7, Figure 8 · p. 7

6.3. Comparison to InverseCSG

• Our method has lower median reconstruction error and search time in all cases, with 13 of 33 exact reconstructions versus 1 for InverseCSG.The comparison uses the InverseCSG test set and its sketch + extrude subset; 27 of the 33 test shapes are expressible by our supported operations.Source: §6.3 · p. 7, Table 1 · p. 7
• The qualitative comparison includes a case where our method reconstructs perfectly but InverseCSG approximates, a case where both perform well, and a failure requiring revolve.The failure illustrates a boundary of the sketch + extrude + Boolean operation set.Source: §6.3 · p. 8, Figure 9 · p. 8

6.4. Expert Perceptual Evaluation

• Participants preferred Our Net sequences to InverseCSG’s and judged them better than ground truth about a third of the time.Exploratory-design participants preferred Our Net over Our Heur at a significantly higher rate than reconstruction-focused participants; the authors suggest network-guided sequences support exploratory modification, while heuristic sequences may suit direct reconstruction.Source: §6.4 · p. 8, Table 2 · p. 8

7. Conclusion

• The zone graph reduces the search space to finite size, and learned scoring prioritizes CAD operations based on design patterns in example sequences.The search targets sketch + extrude + Boolean modeling sequences.Source: §7 · p. 8
• Sequences containing steps that leave no trace in the output B-rep may not be recoverable, although alternative, potentially equally good reconstruction sequences can still be inferred.Source: §7 · p. 8
• Training the proposal-scoring network uses a large CAD dataset, which is not widely available beyond the Fusion 360 Gallery reconstruction dataset.The paper identifies weakly supervised approaches requiring little human input as a direction to investigate.Source: §7 · p. 8

A.1. Simplification by face loop

• Figure 10 demonstrates finding face loops in the target geometry for zone-graph simplification.Source: §A.1 · p. 10

A.2. Search

• The procedure takes a zone graph as input and returns a proposed extrusion list.Source: §A.2 · p. 10
• It iterates over parallel plane pairs and computes an extrusion vector from the planes’ normal and distance.Source: §A.2 · p. 10
• For each candidate, it groups faces to form sketches and extrusions, finds and labels inside zones, and assigns a Boolean type.Source: §A.2 · p. 10

A.3. Network Architecture

• The network architecture is documented in four tables, while ablations compare message-passing rounds and geometry information.The geometry comparison includes variants with and without point clouds.Source: §A.3 · p. 10, Table 3 · p. 10, Table 4 · p. 12

A.4. Fusion 360 Gallery Success/Fail Case Summary

• 80% of Fusion 360 Gallery shapes are reconstructed by the method, with Tables 7–9 breaking down successes and failures.The tables categorize why shapes can or cannot be reconstructed.Source: §A.4 · p. 10
• Increasing the extrusion proposal level from 1 to 3 raises captured ground-truth extrusion sequences from 60% to 63%, at the cost of a larger search space and more computation.Higher levels add candidate subsets of face groups beyond individual components and their full union.Source: §A.4 · pp. 10, 12

A.5.1 Ours vs. random and heuristics

• Figures 18–19 provide qualitative comparisons of Network-inferred programs with Random and Heuristics.Source: §A.5.1 · p. 12, Figure 18 · p. 14, Figure 19 · p. 15

A.5.2 Ours vs. InverseCSG

• Figure 17 compares per-model reconstruction error and search time for InverseCSG and the heuristic method on 33 of 50 test models; Figures 20–23 show further qualitative and reconstruction comparisons.Reconstruction error uses 1-IoU; InverseCSG search times come from its paper, and its errors use author-released reconstructions.Source: Figure 17 · p. 13, §A.5.2 · p. 13, Figure 20 · p. 16