MiCADangelo: Fine-Grained Reconstruction of Constrained CAD Models from 3D Scans
Authors: Ahmet Serdar Karadeniz
Dimitrios Mallis
Danila Rukhovich
Kseniya Cherenkova
Anis Kacem
Djamila Aouada
Venue: NeurIPS 2025 poster ()
Keywords: cad
3d
reverse engineering
sketch
constraint
reconstruction
cross section
Primary area: applications
TL;DR: We propose a novel CAD reverse engineering method that mimics human design workflows by using multi-plane 2D cross-sections to reconstruct detailed, editable, and fully parametric CAD models.

Abstract: Computer-Aided Design (CAD) plays a foundational role in modern manufacturing and product development, often requiring designers to modify or build upon existing models. Converting 3D scans into parametric CAD representations—a process known as CAD reverse engineering—remains a significant challenge due to the high precision and structural complexity of CAD models. Existing deep learning-based approaches typically fall into two categories: bottom-up, geometry-driven methods, which often fail to produce fully parametric outputs, and top-down strategies, which tend to overlook fine-grained geometric details. Moreover, current methods neglect an essential aspect of CAD modeling: sketch-level constraints. In this work, we introduce a novel approach to CAD reverse engineering inspired by how human designers manually perform the task. Our method leverages multi-plane cross-sections to extract 2D patterns and capture fine parametric details more effectively. It enables the reconstruction of detailed and editable CAD models, outperforming state-of-the-art methods and, for the first time, incorporating sketch constraints directly into the reconstruction process.

Mi CADangeel:: Fine-Grained Reconstruction of Constrained CAD Models from 3D Scans
Ahmet Serdar Karadeniz SnT. University of Luxembourg ahmet. karadenizeumi
Dimitrios Mallis
SnT, University of Luxembourg dimitrios wwtrriisssmaaaleee malmimmllnns.m.... lu
Danila Rukhovich
Kseniya Cherenkova
SnT, University of Luxembourg danila, rukhovi ch@uni lu
SnT, University of Luxembourg, Artec 3D
kseniya. wwwwehoovwwuuii......
Anis Kacem
Djamila Aouada
Sn', University of Luxembourg anis. kacem@uni...
SnT, University of Luxembourg dj amila. aouada@uni. ,lu
Abstract
Computer-Aided Design (CAD) plays foundational role in modern manufacturing and product development, often requiring designers to modify or build upon existing models. Converting 3D scans into parametric CAD representations-a process significant challenge due to the high
known as CAD reverse sesginering-remaaae precision and structural complexity of CAD models. Existing deep learning-based approaches typically fall into two categories: bottom-up, geometry- methods, which often fail produce fully parametric outputs, and top-down strategies, which tend to overlook fine-grained geometric details. Moreover, current methods neglect an essential aspect CAD modeling: sketch-level constraints. In this work, we introduce a novel approach to CAD reverse engineering inspired by how human designers manually perform the task. Our method leverages multi-plane cross- sections to extract 2D patterns and capture fine parametric details more effectively. It enables the reconstruction detailed and editable CAD models, outperforming state-of-thee -frt- methods and, for the first time, incorporating sketch constraints directly into reconstruction process.
Introduction
Computer-Aided Design (CAD) modeling, typically performed using specialized software 1 plays a critical role the development and manufacturing of real-world objects. In modern CAD workflows, designers begin by creating 2D sketches composed of parametric curves (e.g., lines, ares, circles), which are further constrained by geometric relationships (c.g.. coincident, tangent, parallel) [4. These sketches are then transformed into 3D geometry using operations such as extrusion, revolution, and cutting. By following this sequential process, designers can construct 3D parametric solids that accurately represent the intended object. A common and practical approach in CAD workflows is to begin with a template of an existing object and adapt it to new design requirements. However, existing real-world objects commonly do not have publicly available CAD models. In such cases, a digital representation can be obtained through 3D scanning, which usually produces a mesh. While meshes capture the surface geometry of an object, they are unstructured and lack the parametric information needed for further design and modification in CAD software. Consequently,
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

CAD Designer Reverse Engineering workflow
OU
Constrained CAD Sketch Parameterization
Reverse Engineered CAD Model
Scan
Plane Selection
Applying CAD Operations
Reverse Engineered
3D Scan
Stetch Plane Detection
Constrained
Extrusion Optimization
Parametorization
Mi CADangell
Figure MiCADangelo is novel framework for CAD reverse-engineering that mimics human design workflows. It analyzes 3D scans via 2D cross-sections to detect sketch planes, predict constrained parametric sketches and optimize extrusions.
converting a 3D mesh into parametric CAD model-an operation commonly referred to as CAD reverse engineering- is a crucial step for enabling efficient design iteration and customization.
Today, CAD reverse engineering is typically carried out manually by designers using specialized software [5]. As illustrated in the top part of Figure [] the process generally involves the following steps: (i) extracting a 2D cross-section of specific part from the imported 3D scan; (ii) reconstructing the contour of the section using parametric 2D curves and placing the CAD constraints to restrict the modification; and (iii) applying CAD operations (e.g., extrusion) to the parametric sketch to create 3D solid model of the part. These steps are repeated for the remaining parts until the entire 3D scan is reconstructed as complete parametric CAD model within the software. While this process allows for faster CAD modeling compared to creating models from scratch, remains tedious and demands CAD expertise. As a result, automating this process became an active research area
Automated 3D CAD reverse engineering has advanced from identifying parts in 3D scans 13 14, to fitting parametrie primitives scanned geometry [15 [6]. and more recently, to predicting sequential design step directly from point clouds 17 9] The latter approach is particularly valuable, as supports parametric reconstruction while preserving an editable design history. This advancement has been enabled by the emergence of datasets such as DeepCAD G and Fusion 360 [18], which provide sequences of 2D sketches and extrusion operations-commonlly referred as sketch-extrude sequences. Several recent methods have explored learning the mapping from point clouds to sketch- extrude sequences, which can be broadly categorized into: (i) top-down approaches [17 19, which directly predict the parameters of the sketch-extrude sequence as series of parametric values from the input point cloud; and (ii) bottom-up approaches [ 20 77 which attempt to predict individual extrusion cylinders that, when combined, closely approximate the target geometry. While top-down approaches offer the advantage of producing fully parametric outputs that approximate fround-truth sketch- sketch-extrude sequences, they often struggle to capture fine-grained details of the input geometry frequently dominated by larger structures. contrast, bottom-up approaches can better preserve local geometrical details, but they lack full parametrization and do not integrate seamlessly into standard CAD workflows [17). Furthermore, to the best of our knowledge, none of these approaches consider CAD sketch constraints which are critical component of CAD modeling 211.
In this work, we propose MiCADangelo, solution for automating CAD reverse engineering by emulating the way human designers approach the task. As illustrated in the bottom part of Figure MiCADangelo begins by analyzing the input sean through series of 2D cross-sectional slices and predicting key slices to serve as sketch planes. For each selected plane, closed loops are extracted from the cross-section and converted into raster images, which are used to predict both the 2D parametric curves and associated CAD sketch constraints. These constrained sketches are then extruded via an optimization process that leverages the local mesh geometry around each loop. The resulting extruded parts ultimately merged to produce structured, fully parametric CAD model.

---

MiCADangelo offers the advantage of preserving fine- the-ggained geometric details of the imput scan while generating fully parametric sketch-extrude sequences, including CAD constraints an aspect largely unexplored in 3D CAD reverse engineering.
Contributions
The main contributions of this work can be summarized follows:
1. We introduce a real-world CAD reverse ungineering-isppine approach that can effectively reconstruct fully parametric CAD models from 3D scans while preserving fine-grained geometric details.
2. To the best of our knowledge, this is the first approach capable of reconstructing CAD models from 3D scans while incorporating sketch constraints.
3. We conduct comprehensive experiments on publicly available benchmarks and demonstrate that our method outperforms existing sfate-of-the-ard techniques in CAD reverse engineering.
2 Related Work
3D CAD Reverse Engineering. Early approaches to CAD reconstruction rely on Constructive 23
26 27 28), , using Boolean operations over primitives, but these are limited in capturing complex, real world CAD structures. Other works target Boundary Representation (BRep) reconstruction 29 30
Solid Geometry (CSG) representations (22
24
25|
31. focusing on high-precision surface and topology modeling. More recent efforts adopt sketch-extrude paradigms, which better reflect the way CAD models are constructed in practice. Within this direction, geometry-groundee bottom-up methods 7 estimate sketches and extrusion parameters from input scans, leveraging structural cues from the geometry but often lacking full parametric editability and seamless integration in CAD software 177. Alternatively, language- based top-down methods [17 19 9 learn to generate construction sequences, capturing design intent but struggling to preserve fine- mne-grained geometric fidelity. We propose practical reverse engineering inspired approach that reconstructs detailed and editable CAD models with explicit sketch primitives and constraints, directly compatible with standard CAD software.
Constrained Sketches in CAD. In CAD modeling, sketch primitives and their associated constraints form the foundation of design intent [32 33). as they govern how a design adapts when modified. Parametric CAD sketch primitives (e.g.. lines, ares, circles) provide a flexible 2D interface for defining shapes, while constraints (e.g., perpendicular, parallel, tangent) preserve geometric relationships, allowing controlled variation without compromising the overall structure. When designers apply constraints (e.g., orthogonality) to sketch primitives (e.g., two lines), any changes made to one primitive are automatically adjusted to preserve these relationships. For example, if the parameters of one line are modified, the other will update accordingly to maintain orthogonality. In reverse engineering context, it is highly desirable not only to infer accurate CAD geometry from input scans but also to recover the underlying design intent, ensuring that the reconstructed model responds to modifications in a manner consistent with how a designer would have originally constrained it. The availability of large-scale CAD sketch datasets (34] has facilitated research in this area, with recent work focusing on generative CAD sketch modeling [21 35), sketch image parameterization [36] 37 [38], , and design intent inference [39 40). While these methods have achieved promising results for 2D sketches, their effectiveness in 3D CAD modeling remains underexplored.
3 Preliminaries and Problem Statement
In this section, we provide the problem statement along with the preliminary definitions. Definition 1 (Sketch Primitive). A sketch primitive p is 2D entity uniquely defined by geomet- ric parameters. We define the following 2D sketch primitives: Line: Defined by its start point (NayWa) E IR² and end point (Ke, We) E IR?. Circle: Represented by its center (Xg, Uc) E R² and radius r E R. Arc: A segment of a circle, specified by its start point (Le.ys) E R2, mid mii-pointt (I.m Vm) E R and end point (Ze.ye)= E RR? all lying the same circle.
Definition 2 (Sketch Constraint). A sketch constraint = (P:. ct) is defined by constraint type a. that specifies the relationship between two primitives p. and Pj- The types of constraints considered in this work are: coincident, concentric, equal, fix, horizontal, midpoint, normal, offset, parallel, perpendicular, quadrant, tangent and vertical. Note that some constraints are defined on a single primitive such vertical and horizontal.
3

---

100
feuc
plaaxe
Xx
rept moton M. (ni)
[<)1]
(hi)
[
Sketthh Plane Detection
Key Slice Skey
Input Mesh M
fycte
S:
fese
fiwp
Optimization
fe
{(Kg.
S:) E Swy
Sketch Parameterization
CAD Model
Figure 2: Overview of the method. Mi MiCADaneelo comprises three main components: Sketch Plane Detection, Sketch Parameterization, and Differentiable Extrusion. The generated constrained sketches, together with the optimized extrusion parameters, are assembled into the final parametric CAD model.
Definition 3 (Constrained Sketch). A constrained sketch K. = C) is defined by set of ny 2D sketch primitives P { and set of n. sketch constraints C = |-
Definition 4 (Sketch Plane). A sketch plane π is defined by an origin point o E IR'S and a normal vector E S which sketch is defined and centered at
Definition 5 (3D Mesh). A 3D mesh is defined as M = -V,F) where V C RR3 are vertices and F v are triangles forugleesforeed by 3 vertices.
Definition (Cross-section Slice). Given 3D mesh M and a slicing plane cross-section slice formed by sets of line segments resulting from the intersection of the mesh triangles with This slicing process naturally yields multiple connected components, each corresponding to a distinct set of connected line segments. Formally, the cross-section slice can represented as a collection of L line sets (=1 where each line set composed of successive points {q) Ln E IR is defined Ljj {(q,, 9++1) i 1....,... 1}.
Definition (Closed Loop). A closed loop L is a set of line segments connecting succes- sive points 1 RR3 forming non-self-interseciing and enclosed region. It is defined as: n 13 U {(gm, }. It is important to note that, in the context of CAD models, the line sets forming the cross-section slice S defined in the above definition are usually closed loops.
L = {(g,
Definition 8 (Extrusion). An extrusion e (T, v, h) defined by a sketch plane æ, an extrusion type and extrusion parameters h), where IR3 is the extrusion direction vector and h E R is the extrusion length. The extrusion operation extends a sketch K. along v for a distance h, forming 3D solid. The extrusion type specifies whether the operation creates material (new) removes material (cut).
Detinition 9 (CAD Model Representation). CAD model C is defined as the sequential combination of n, sketch-extrude steps {(C,, H
Problem Statement. Given an input 3D mesh M, the goal n,
recover the sequence of steps reconstructing the CAD model C (KK,,e))) Each extrusion ej (my, lj, yj, hy) is defined by sketch plane nj, an extrusion type Lj. and extrusion pa- rameters (Vj, hy). Each constrained sketch KC = (Pj,C) consists of 2D parametric primitives P, along with their associated CAD constraints Cj-
4 Proposed Method
4.1 Method Overview
As illustrated in Figure reverse engineering. Given an input mesh M obtained from a 3D sean, the key idea idea-mirroring human intuition- is to identify the most relevant cross-section slices that enable accurate reconstruction of
Mi CiCDnngool is inspired by the way human designers approach CAD

---

the original CAD model. To achieve this, MiCanngoo samples N gqually-spaced slicing planes { 1 along the I-, yr, and 2-axes, producing a set of 2D cross-section slices {S, These slices are then converted into raster images and supplied with contextual embeddings before being passed into a sketch plane detection network that identifies the most relevant slices Skey (S. " (Section 4.2) Once the key cross-section slices are identified-agee again following the logic used by human designers- the next step is to predict the sketch primitives and their associated constraints from these slices to obtain the corresponding constrained sketches. To achieve this, each key cross- section slice is decomposed into separate closed loops { Each loop is converted into a raster image and passed to network for constrained sketch parameterization with the goal of inferring the corresponding sketch primitives and constraints {1, 7-1 (Section 4.3 After obtaining the constrained sketches, differentiable extrusion optimization is performed for each sketch XC w.Et the input geometry of the mesh M to find out the corresponding extrusion parameters ej (Section (4.4). Finally, the obtained extruded elements assembled together obtain the final CAD model. An overview of the proposed method is illustrated in Figure
4.2 Sketch Plane Detection Network
Given set of cross-section slices { extracted from the input mesh M, our goal is identify subset of these as key sketch plane slices. Each slice S; is projected onto a 2D plane and normalized to fit within unit bounding box, which is subsequently rendered as a binary image X; E [0. [0,1] The slice image X; is passed through convolutional ResNet34 encoder Senc {0, 1 ]] Re to produce a d-dimensional latent vector f; = (X;). In order to contextualize the embedding of the different slices and maintain their spatial relationships, each slice is associated with slice index o, E (O....,.. .N- - 1}. axis identifier ag E {0, 1, 2 for I-, y-, or 2-axis, normalization parameters ni = (17 f 8&) I that correspond to the translation and the scale parameters of the normalization process. These inputs are embedded into the latent space Rdd
w W Yo,
W axis W axisya; W parm
W norm??
where Yo, E 10,1)N and Ya, E 1)3 are one-hot vectors for slice index and axis identifier, Wpos E RRdx and axis E Rdx3 are the corresponding learnable matrices, and W norm E Rdx3 is a linear projection of normalization parameters. The final embedding z; E Hd is obtained as
z, + W/:
(2)
where the contextual embedding defined as W, = w.th + wixt + w, Next, the of embedding {2:) fed into a multi-layer multi-head transformer encoder fplane : 12d - IRd to obtain set of richer embedding (h:)a Id follows,
(hi...., hN) fplane (Z1, ZN)-
Each encoded slice embedding h, is passed through a binary classifier fley : IRd [0, 1] composed of linear layer and sigmoid to predict the probability of being key sketch plane as follows,
= fiey (h.)
Note that the sketch plane detection network is trained by binary cross-entropy loss using supervised key sketch plane labels from the DeepCAD dataset [6]. The process of obtaining these labels is explained in the supplementary. Finally, the subset Skey = {S. g! 2 7 is determined to be the set of key slices with the corresponding planes R,, where 7 a fixed threshold 0.5.
4.3 Constrained Sketch Parameterization Network
Once the key cross-section slices Skey are obtained by the sketch plane detection network, the goal of the constrained sketch parameterization network is to infer the constrained parametric sketches (K,) from the individual closed loops (L, of each key cross-section slice. For each S E Skey, the set of resulting closed loops {L,}}=1 are projected to 2D and rendered as binary images (x The constrained sketch parameterization network operates directly on these rasterized loop images to infer the corresponding sketch primitives and geometric constraints. This
5

---

approach enables to preserve fine- lne-grained geometric details of the input mesh, which are essential for accurate CAD reconstruction.
The design of the constrained sketch parameterization network is similar to the one introduced in [3
Each image X, E (0, 1) 1) is then encoded by convolutional encoder Senc {0, 1 - T (same as the one used to encode the cross-section slices in Section 4.22, producing a latent feature
vector f E Rd The latent vector then passed to a transformer encoder-decoder froop R Rd.xx obtain a set of embedding for ny sketch primitives Sj E Rd as follows,
CJ = (f,)
(5)
As in (37], the set of embedding is passed to two separate heads; parameterization head Spim xnp + Q"r and a constraint prediction head far : Rd. + Q" where Q"r and Q denote the quantized space of "e primitive values and ne constraint values, respectively. These heads result in the parametric sketch primitives and their constraints as follows,
Pj = Sprim(()))
C -ar(GC
For further details on the quantization spaces of primitives and constraints, the design of the con- strained sketch parameterization network, and the loss functions employed during training, readers are referred to (37] as well as the supplementary materials for additional explanations, Due to the lack of CAD constraint annotations in the DeepCAD dataset (6) and other 3D CAD modeling datasets, the constrained sketch parameterization network is initially trained on the SketchGraphs dataset [4]. It is then fine-tuned on an augmented version of SketchGraphs that includes added noise and synthetically generated closed-loop images, enabling better adaptation to the characteristics of cross-sections slices. Note that both the sketch parameterization network and the sketch plane detection network share the same encoder fene- The encoder is initially trained as part of the sketch parameterization network and then kept frozen during parameterization, while is fine-tuned during the training of the sketch plane detection network.
4.4 Differentiable Extrusion Optimization
For each constrained sketch K; corresponding to a loop L, within a key cross-section slice S,, the goal of differentiable extrusion optimization is to recover the parameters of the extrusion e; that best fits the resulting extruded solid the 3D input mesh. As mentioned in Definition oof Section 3 the extrusion is defined by e, (TT, tg. Vj, h2), with πy denotes the sketch plane from which the extrusion originates, ty E [new, cut) specifies the extrusion type, and (V,, kt)) represent the extrusion direction and length, respectively.
The plane ny is determined by the key cross-section slice associated with the input sketch K,, and its normal vector is used to define the direction of the extrusion Vy. The extrusion type t, is assigned based on the nesting hierarchy of the loop L, within its corresponding cross-section slice S, The outermost loops are labeled as new extrusions, and the label alternates with each subsequent level of nesting: a loop contained within a new extrusion loop is labeled as cur extrusion, a loop within a cut extrusion loop is labeled as new extrusion, and this alternating pattern continues with increasing depth. For loops labeled as new, the corresponding length hy is determined through an extrusion optimization process. Loops labeled as cut are interpreted as infinite cuts.
Extrusion Length Optimization. To optimize over the extrusion length h,, we define a set of extrusion vectors over the sketch K, by sampling a set of n, 3D anchor points {rx hr E R along the loop boundary. Each anchor point is associated with a learnable scalar extrusion length h, E R, shared across the anchor points of the same loop. Each anchor point r& is mapped to an extrusion vector Pk E IR33 along the direction of the extrusion vj with length h; using the following function,
F F:R
x R +R3 IR3,
F(IK.))V,)) = ra + + Pk
This results in set of extrusion vectors (px ] each of them has its corresponding anchor point rk as starting point and all of them sharing the same length and direction hy and vj. Next, a set of nM points @ = {q)) E R are sampled on the input mesh M and the set of extrusion vectors tn + from each loop and each key cross-section slice are considered. The point-to-vector { Just

---

DeepCAD Dataset
Fusion360 Dataset
Input Mesh
CAD-SIGNET
Ours
Ground Truth
Input Mesh
CAD-SIGNET
Ours
Ground Truth
Figure 3: Qualitative comparison of of method and that of
DeepCAD and Fusion360.
NON NON
Input Mesh
CAD-SIGNET
Ours
Ground Truth
Input Mesh
CAD-SIGNET
Ours
Ground Truth
Figure 4: Qualitative comparison between our method and that of 17 on complex models containing
fine-grained geometric details.
distance d(q; Pa) is then computed between each point qi and extrusion vector Pu. to identify the closest extrusion vector Pmin := arg ming d(qr,Pa)
The total loss is defined as the mean squared distance over all sampled points, regularized by the squared sum of extrusion lengths to avoid trivial solution. is given by,
Lextr
d(qi, Prmin) )
Σ h3 4
(8)
TLM
where \ denotes scaling factor for the regularization term, refers the detected key slice plane and j refers to the individual sketch loop. The extrusion lengths h, are optimized jointly for all the sketch loops over the detected key slice planes via gradient descent to minimize Coxtr thereby adjusting the extrusion vectors Pa to best fit to the input mesh geometry.
5 Experiments
In this section, we detail the experimental setup and report results to evaluate the effectiveness the proposed MiCADangelo.
Datasets.
We evaluate our method on the test sets of DeepCAD 66 and Fusion360 (18) datasets.
The sketch plane detection is trained on the train set of DeepCAD 6), while the constrained sketch parameterization network is trained on the train set of the SketchGraphs (35) dataset and finetuned on an augmented version of the dataset. Details on the processing the datasets in the supplementary.
Metrics. For 3D CAD reconstruction, median Chamfer Distance, Intersection over Union (loU), dian Edge Chamfer Distance (ECD) and Invalidity Ratio (IR) are used. For 2D sketches, image-level sketch chamfer distance (SCD) is used. Additional metric details provided in the supplementary.
7

---

Table 1: Quantitative Results on DeepCAD and Fusion360 Datasets.
DeepCAD Test Set
Fusion360 Test Set
Method
Med. CD1
loU1
IRC
ECD|
Med. CDL
IoUT
IRL
ECD
DeepCAD
9.64
46.7
7.1
89.2
39.9
25.2
Point2Cyl S
4.27
73.8
3.9
4.18
67.5
3.2
CAD-Diffuser
9
3.02
74.3
1.5
3.85
63.2
1.7
CAD-SIGNet
0,28
77.6
0.9
0.74
0.56
65.6
1.6
4.14
Ours
0.20
80.6
2.6
0.46
0.48
68.7
3.2
2.66
Implementation Details. Planes are preprocessed ensure consistent normal directions along the positive axes. The plane detection model is trained for 20 epochs on DeepCAD [ with 10-4 The constrained sketch parameterization model trained on SketchGraphs [35] as in [37 and finetuned for 50 epochs on synthetically generated,
augmented loops. We use 40 cross-sections per axis, each normalized to an image of size 128 128. Normalization is performed using 2D offsets and a scale factor corresponding to unit bounding box. The transformer encoder of sketch plane detection comprises layers and attention heads, with an embedding dimension of 256. The sketch parameterization network architecture is similar to (37]. For the extrusion optimization, we run 200 iterations with a learning rate of 2 x 10 Adam is used as an optimizer for all the experiments. More details are in the supplementary.
5.1 Comparison with state-of-the-art
The proposed method is compared with DeepCAD ( CAD-Diffuser [ Point2Cyl {8, and CAD- SIGNet [17] on the DeepCAD and Fusion360 test sets. A quantitative comparison with these methods provided Table [
Across datasets, MiCADAngelo achieves superior reconstruction performance. Note that low IR reported by the best performing [17] are enabled by test-time sampling, where multiple CAD reconstruction candidates are generated and the best is selected. Without test-time sampling, [17] yields an IR of 4.4 and 9.3 for DeepCAD and Fusion360, respectively. Figure provides a qualitative comparison with [17
Table 2: Quantitative results on complex models and on models with more than two extrusions.
Models with 2 4 Loops
Models with Extrusions
Method
Med. CD4
IoUt
IR4
ECD4
Med. CD4
IoUt
IR.
ECD
CAD-SIGNet 17
1.34
49.2
3,2
4.75
3.95
40.6
5.4
9.81
Ours
0.37
68.3
4.1
2.04
0.46
64.8
3.0
2.27
Our method consistently generates CAD models that closely resemble the ground-truth geometry across diverse range of samples. We also evaluate the performance of our method against [17] subset of complex models with fine-grained details (containing 4 or more loops) and models with more than 2 extrusions from DeepCAD. Results in Table demonstrate that methods significantly outperforms [17] in preserving fine-grained geometric details and handling complex geometries. More qualitative results on complex models are provided in Figure 4
5.2 Impact of Constraints in 3D Reverse Engineering
Mi MiCADAngelo is the first CAD reverse engineer-
ing method generate parametric constraints. The proposed explicit modeling of the reverse engineering pipeline enables sketch constraint inference directly from rasterized sketch im- ages, significantly reducing the solution space compared to predicting constraints from point clouds. To demonstrate the importance of con- straint modeling in 3D CAD reconstruction, we conduct an experiment analyzing how CAD re- constructions produced by Mi MiCAAAgeelo and [17 respond to sketch modifications similar to those typically performed by CAD designers. Specifically, we introduce a small random displacement to point in the recovered sketch geometry and evaluate how this change affects the resulting solid
Table 3: Quantitative results of deformation robust- ness under sketch modifications
Method
Med. CDJ
IoUt IR| ECD]
CAD-SIGNet 17
2.89
57.4
3.5
20.43
Ours
0.38
81.1
4.3
1.29

---

Sortch Trandfrmationn
Shetch Trensformation
Shetch Teeaformation
Ground Truth
Iniiial Model
Transformed Modill
Intial Model
Transformed Model
Inibia Modal
Traraformed Modhl
Figure 5: Qualitative comparison of the impact of the constraints by transformations applied on sketch points.
Table 4: Effect contextual embeddings on plane detection performance.
Contextual Emb.
Precision
Recall
F1
Mediann ECD
Time (5)
0.317 0.894
0.292
0.296 0.870
20
0.864
1.5
2
1.0
16
Table 5: datascts.
Plane detection performance across
0.5
Datasct
Precision
Recall
0.0
10
DeepCAD
0.894
0.864
0.870
2.5
5.0
Mamber ofdears
7.5
10.0
12.5
15.0
Fusion360
0.860
0.812
0.820
Figure 6: CD and ECD performance and inference
CC3D
0.803
0.790
0.777
times as a function of the number of extrusion vectors.
geometry, comparing it to a constrained ground-truth model modified with the same displacement. Due to unavailability of CAD constraints in DeepCAD and Fusion360 datasets, we form data for this experiment by extruding 1/ sketches with closed loops from the SketchGraphs dataset [34]. The impact of the displacement on the solid geometry is computed by integration with the FreeCAD API
We compare our method to that of 17]. Note that the output representation of generates closed sketch loops by construction, which implicitly enforces coincident constraints between sketch vertices. Results are reported in Table 3 Mi MiCADnngelo reverse-engineered models closely match the ground truth, application of CAD sketch constraints. edits in our method propagate correctly through sketch primitives, resulting in modified CAD models that retain structural consistency w.z. the ground-truth. In contrast, coincident constraints alone are insufficient to preserve overall geometry for [17] with displacements leading to geometric distortions. Note that learning sketch constraints might also impact sketch parameterization and the overall CAD reconstruction (e.g., inferring orthogonality constraint can help in enforcing the parameters of the predicted lines be orthogonal). While constraints are not strictly necessary for sketch primitive parameterization, prior work [35] has shown that jointly learning primitives and constraints benefits both tasks through shared structural information. We leave further exploration of improved geometry with constraints to future work.
after random sketch modifications. As illustrated in Figure [ due effective
5.3 Additional Experiments
We include additional experiments conducted to further evaluate MiCADangelo.
Plane Detection. Table/Taalltes the effect contextual embeddings slice encoding. Incorporating positional information to the geometric features of the cross-section leads to improved performance. Table shows robust plane detection performance with minimal drop in Fusion360 and CC3D datasets.

---

Input Scan
Cura
Ground Iruth
Scan
CAD-SKGNET
Ground Iruds
Figure 7: Qualitative comparison the performance on the real-world scans from CC3D.
Constrained Sketch Parameterization We eval- uate our constrained sketch parameterization net- work against the recent proposed [37]. To en- sure that ground-truth sketches correspond to valid cross-sections, this experiment is conducted on single-extrusion models from the DeepCAD test set. Due to fine-tuning synthetically gener- ated noisy closed loops, MiCADangelo outper- forms [37]
Table 6: Evaluation of sketch parameterization
on single-extrusion CAD models.
Method
Avg. SCD
Davinci 37
0.827
Ours
0.283
Extrusion Optimization. Tigure&report differentiable extrusion performance for a varying number of vectors. Performance improves steadily up to 8 vectors, with minimal impact inference time.
Robustness Real-world Scans. To evaluate performance on real imperfect scans, we include quantitative comparison on the challenging CC3D 41 42) dataset. This cross-dataset evaluation compares our method that of [77, both trained on DeepCAD and evaluated on CC3D scans that include realistic scanning artifacts, such as holes and misoriented normals. Results are shown in the Table 7 The proposed MiCADangelo outperforms [17 in this in-the-wild setting, demonstrating greater robustness to real-world noise. Figure 7 presents qualitative evaluation real-world 3D scans from the CC3D 42 dataset. The results demonstrate robustness our approach in handling real-world artifacts and producing cleaner, more accurate CAD models compared to 17
Table 7: Comparison between CADSIG-Net and our method on CC3D dataset.
Method
Med. CDJ
loUt
IR4
ECDJ
CADSIG-Net 17
2.90
42.6
4.4
8.68
Ours
1.69
50.8
2.2
5.93
Conclusion
In this work we proposed MiCADAngelo, novel CAD reverse engineering approach that transforms 3D scans into fully parametric CAD models. Our method is inspired by real-world CAD practices and uniquely incorporates cross-scctions and sketch primitives with constraints, enabling the preservation of both high-level parametric structure and fine-gra -nniineieed geometric detail. Evaluation is performed on standard benchmarks were our approach outperforms existing methods establishing new state-of- the-art in CAD model reconstruction from 3D scans.
Limitations. A detailed discussion on failure cases and limitations is provided in supplementary. Among CAD operations, the proposed method only supports extrusion as in previous works [77 20 8]. Extrusions are currently defined based on sketch plane normals, which can suboptimal for models with aon-axis-aligned extrusions. Note that such complex models are also challenging for 6 9 17
The current method does not yet support complex sketch primitives such as B-splines. Future works will address these limitations.
10

---

7 Acknowledgements
This work is supported by the National Research Fund (FNR), Luxembourg, under the BRIDGESSDD11///14459999RREE project and by Artec3D.
References
[1] Dassault Systèmes, Solidworks, 2025,
[2] PTC Inc. Onshape, 2025, URL
[3] FreeCAD Community. Freecad, 2025, URL
freecad org
[4] Ari Seff, Wenda Zhou, Nick Richardson, and Ryan Adams. Vitruvion: A generative model parametric cad sketches. In ICLR, 2022.
[5] Polyga Inc. Reverse engineering 101: Scan to cad, 2025. URL httpe://wwwt www.w/pwpppp......//.//mm....... polyga.com/ com/ eovarae-engineering--100
Accessed: 2025-05-13.
[6] Rundi Wu, Chang Xiao, and Changxi Zheng. Deepcad: deep generative network computer-aides design models. In ICCV, 2021.
[7] Daxuan Ren, Jianmin Zheng, Jianfei Cai, Jiatong Li, Junzhe Zhang. Extrudenet: Unsupervised inverse sketch-and-extrude for shape parsing. In ECCV, 2022.
[8] Mikaela Angelina Uy, Yen-Yu Chang, Minhyuk Sung, Purvi Goel, Joseph Lambourne, Tolga Birdal, and Leonidas Guibas. Point2cyl: Reverse engineering 3d objects from point clouds to extrusion cylinders. In CVPR, 2022.
[9] Weijian Ma, Shuaiqi Chen, Yunzhong Lou, Xueyang Li, and Xiangdong Zhou. Draw step by step: Reconstructing cad construction sequences from point clouds via multimodal diffusion. In CVPR, 2024.
[10] Joseph George Lambourne, Karl Willis, Pradeep Kumar Jayaraman, Longfei Zhang, Aditya Sanghi, and Kamal Rahimi Malekshan. Reconstructing editable prismatic cad from rounded voxel models. In SIGGRAPH Asia, 2022.
[11] Danila Rukhovich, Elona Dupont, Dimitrios Maliis, Kseniya Cherenkova, Anis Kacem, and Djamila Aouada. Cad-recode: Reverse engineering cad code from point clouds. In ICCV, 2025.
[12] Dimitrios Mallis, Ahmet Serdar Karadeniz, Sebastian Cavada, Danila Rukhovich, Niki Foteinopoulou, Kseniya Cherenkova, Anis Kacem, and Djamila Aouada. Cad-assistant: tool-augmented vllms as generic cad task solvers. In ICCV, 2025.
[13] Lingxiao Li, Minhyuk Sung, Anastasia Dubrovina, Li Yi, and Leonidas J Guibas. Supervised fitting of geometric primitives to 3d point clouds. CVPR, 2019.
[14] Gopal Sharma, Difan Liu, Subhransu Maji, Evangelos Kalogerakis, Siddhartha Chaudhuri, and Radomír Mëch. Parsenet: A parametric surface fitting network for 3d point clouds. ECCV, 2020.
[15] Xiaogang Wang, Yuelang Kai Xu, Andrea Tagliasacchi,
Zhou, Ali Mahdavi-Amin and Hao Zhang. Pic-net: Parametric inference of point cloud edges. In NeurlPS, 2020.
[16] Kseniya Cherenkova, Elona Dupont, Anis Kacem, Ilya Arzhannikov, Gleb Gusev, and Djamila Aouada. Sepienet: Sharp edges recovery by parametric inference of curves in 3d shapes. In CVPRW, 2023.
[17] Mohammad Sadil Khan, Elona Dupont, Sk Aziz Ali, Kseniya Cherenkova, Anis Kacem, and Djamila Aouada. Cad-signet: Cad language inference from point clouds using layer-wise sketch instance guided attention, In CVPR, 2024.
[18] Karl D. D. Willis, Yewen Pu, Jicliang Luo, Hang Chu, Tao Du, Joseph G. Lambourne, Armando Solar- Lezama, and Wojciech Matusik. Fusion 360 gallery: A dataset and environment for programmatic cad construction from human design sequences. ACM Transactions Graphics (TOG), 40(4), 2021.
[19] Xiang Xu, Pradeep Kumar Jayaraman, Joseph George Lambourne, Karl D. D. Willis, and Yasutaka Furukawa. Hierarchical neural coding for controllable CAD model generation. In ICML, 2023.
[20] Pu Li. Jianwei Guo, Xiaopeng Zhang, and Dong-Ming Yan. Secad-net: Self supervised cad reconstruction by learning sketch-extrude operations. In CVPR, 2023.

---

[21] Yaroslav Ganin, Sergey Bartunov. Yujia Li, Ethan Keller. and Stefano Saliceti. Computer-aided design as language. In NeurlPS, 2021.
[22] Tao Du, Jeevana Priya Inala, Yewen Pu, Andrew Spielherg, Adriana Schulz, Daniela Rus, Armando Solar-Lezamaa, and Wojeiech Matusik. Inverseesg; Automatic conversion of 3d models to esg trees. ACM Transactions on Graphics (TOG), 37(6). 2018.
[23] Markus Friedrich, Pierre-Alain Fayolle, Thomas Gabor, and Claudia Linnhoff Popieen. Optimizing evolutionary esg tree extraction. In Proceedings of the Genetic and Evolutionary Computation Conference, 2019.
[24] Kacper Kania, Maciej Zieba, and Tomasz Kajdanowicz. Uesg- net-unsupervised discovering of constructive solid geometry tree. In NeurlPS, 2020.
[25] Constructive Solid Geometry. Neural shape parsers for constructive solid geometry. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(5), 2022.
[26] Fenggen Yu, Zhiqin Chen, Manyi Li, Aditya Sanghi, Hooman Shayani, Mahdavi-Ami Amiri, and Hao Zhang. Capri-net: Learning compact cad shapes with adaptive primitive assembly. CVPR, 2022.
[27] Fenggen Yu, Qimin Chen, Maham Tanveer, Ali Mahdavi Amiri, and Hao Zhang. D2 esg: Unsupervised learning of compact esg trees with dual complements and dropouts. In NewrIPS, 2023.
[28] Daxuan Ren, Jianmin Zheng, Jianfci Cai, Jiatong Li, Haiyong Jiang, Zhongang Cai, Junzhe Zhang, Liang Pan, Mingyuan Zhang, Haiyu Zhao, et al. Csg-stump: A learning friendly csg-like representation for interpretable shape parsing. In ICCV, 2021.
[29] Joseph G Lambourne, Karl DD Willis, Pradeep Kumar Jayaraman, Aditya Sanghi, Peter Meltzer, and Hooman Shayani. Brepnet: A topological message passing system for solid models. In CVPR, 2021.
[30] Xianghao Xu, Wenzhe Peng. Chin-Ye Yin-Yiiee Cheng, Karl DD Willis, and Daniel Ritchie. Inferring cad modeling sequences using zone graphs. In CVPR, 2021.
[31] Pradeep Kumar Jayaraman, Aditya Sanghi, Joseph G Lambourne, Karl DD Willis, Thomas Davies, Hooman Shayani, and Nigel Morris. Uv-net: Learning from boundary representations. In CVPR, 2021.
[32] Yingzhong Zhang and Xiaofang Luo. Design intent information exchange of -base cad models. WRI CSIE, 2009.
[33] Jeffrey M. Otey, Manuel Contero, and Jorge D. Camba. Revisiting the design intent concept in the context of mechanical cad education. Computer-aided Design and Applications, 15(1), 2018.
[34] Ari Seff, Yaniv Ovadia, Wenda Zhou, and Ryan P. Adams. SketchGraphs: A large-scale dataset for modeling relational geometry in computer-aided design. In JCMLW, 2020.
[35] Wamiq Para, Shariq Bhat, Paul Guerrero, Tom Kelly, Niloy Mitra, Lconidas J Guibas, and Peter Wonka. Sketchgen: Generating constrained cad sketches. In NewrIPS, 2021.
[36] Ahmet Serdar Karadeniz, Dimitrios Mallis, Nesryne Mejri, Kseniya Cherenkova, Anis Kacem, and Djamila Aouada. Picasso: A feed-forward framework for parametric inference of cad sketches via rendering self- supervision. In WACV, 2025.
[37] Ahmet Serdar Karadeniz, Dimitrios Mallis, Nesryne Mcjri, Kseniya Cherenkova, Anis Kacem, and Djamila Aouada. Davinei: single-stage architecture for constrained cad sketch inference. In BMVC, 2024.
[38] Sifan Wu, Amir Hosein Khasahmadi, Mor Katz, Pradeep Kumar Jayaraman, Yewen Pu, Karl Willis, and Bang Liu. Cadvim: Bridging language and vision in the generation of parametric cad sketches. In ECCV, 2024.
[39] Yuezhi Yang and Hao Pan. Discovering design concepts for cad sketches. In NeurlPS, 2022.
[40] Evan Casey, Tianyu Zhang, Shu Ishida, John Roger Thompson, Amir Khasahmadi, Joseph George Lambourne, Pradeep Kumar Jayaraman, and Karl DD Willis. Aligning constraint generation with design intent in parametric cad, arXiv preprint arXiv:2504. 13178, 2025.
[41] Kseniya Cherenkova. Djamila Aouada, and Gleb Gusev. autoencoding cad construction in 3d. In ICIP, 2020.
Pydeconv: Point-voxel deconvolution for
[42] Dimitrios Mallis, Ali Sk Aziz, Elona Dupont, Kseniya Cherenkova, Ahmet Serdar Karadeniz, Moham- mad Sadil Khan, Anis Kacem, Gleb Gusev, and Djamila Aouada. Sharp challenge 2023: Solving cad history and parameters recovery from point clouds and 3d scans. overview, datasets, metrics, and baselines. In CVPRW. 2023.
12

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The main claims presented in the abstract and introduction accurately represent the paper's 's contributions and scope.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: Gincluuess discussion of the limitations, with more detailed analysis provided the supplementary material.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (c.g.. independence assumptions, noiseless settings, model sellsspeciiiationn asymptotic approximations only holding locally). ). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-tex, system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
13

---

Answer:
[NA]
Justification:
The paper does not include any theoretical proof.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proof's can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided not)?
Question:
Answer: [Yes]
Justification: The detailed setting of the experiments provided in Section and the supplementary material.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, descríbing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is new model (e-g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should possible for other researchers to have some path to reproducing verifying the results.
5. Open access to data and code
14

---

Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: [No]
Justification: The data used in this study is publicly available. Scripts for preprocessing the data and extracting additional information used in our work will also be made publicly accessible. However, the code for the method and training cannot currently be released under an open-source license that permits use, modification, and distribution, due to constraints related to the industrial collaboration under which this work was conducted, Nonetheless, all necessary details for reproducing the results are thoroughly provided in the paper and the accompanying supplementary materials.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips.. cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
/ ctipss.cc/pbllc///ue wwtpc///wiiiseeeee Swtp///oooeSSsssiieeieeeea wwnniisssinioccyoy.o for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: The paper provides sufficient details on the training and testing procedures, evaluation metrics, hyperparameters, and optimizer choice, enabling other researchers to potentially reproduce the results.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [No]
Justification: The experiments presented in the paper are computationally intensive. Further- more, repeated training runs using the same hyperparameters showed no significant variation in validation metrics.
15

---

Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by enror bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
should be clear whether the error bar is the standard deviation the standard error of the mean.
is OK to report I-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information the puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: The paper clearly states the compute resources used for the experiments and the compute time of the method in Section 5) and the supplementary material.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (c.g., preliminary or failed experiments that didn't make it into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive socictal impacts and negative socictal impacts of the work performed?
Answer: [Yes]
16

---

The paper aims to appropriately highlight the potential positive societal impact in the problem introduction and its motivation. The authors do not anticipate any negative consequences resulting from their work.
Justification:
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation. generating fake profiles, surveillance), faimess considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The authors do not anticipate any potential risks associated with the release of their method, data, or model.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards challenging, and many papers do not require this, but encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: All assets used in this work, including data and code, are properly cited within the paper.
Guidelines:
The answer NA means that the paper does not existing assets.
17

---

The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset. For scraped data from a particular source (c.g.. website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re- re-packaged, both the original license and the license of the derived asset (if has changed) should provided.
If this information is not available online, the authors are encouraged to reach out to the asset's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: The extended versions of the public datasets are clearly described in the paper and the supplementary.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification: This work did not involve human subjects or the use of crowdsourcing.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: This work did not involve human subjects the of crowdsourcing.
18

---

Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with
human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Question:
Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification:
The development of the method does not include any LLMs component.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our L.LM policy for what should or should not be described.
19


Reviews:
[{"review_id": "212Dz6heVh", "reviewer": "Reviewer_wdwr", "summary": "This work addresses the task of CAD reconstruction from 3D scans or meshes and proposes a novel approach that incorporates sketch constraints into the reconstruction process. Extensive experiments are conducted to demonstrate the effectiveness of the proposed method.", "questions": "1. How does the choice of N (as mentioned in Line 146) affect the model's performance?\n\n2. Were all models (e.g., DeepCAD, CAD-Diffuser) retrained on the same training data for fair comparison?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "*Strengths*:\n\n1. The paper is clearly structured and well-written. Furthermore, the notation and symbols are clearly defined and explained, making the methodology easy to follow.\n\n2. To my knowledge, the proposed method is novel. The pipeline emulates the workflow of human designers, which is both intuitive and reasonable.\n\n3. The model demonstrates impressive performance. As shown in Figures 3, 4, and 7, the proposed method significantly outperforms baseline methods, particularly on complex models with fine-grained geometric details.\n\n*Weaknesses*:\n\n1. **Effect of Sketch Constraints**: While the authors state that incorporating sketch constraints benefits CAD reconstruction, the mechanism by which this improvement occurs is not sufficiently clear. Although quantitative results are presented in Table 3, additional visualizations or analysis of intermediate steps would help to better demonstrate the practical impact of sketch constraints on the CAD construction process.\n\n2. **Pipeline Complexity and Error Accumulation**: The proposed method comprises four distinct steps, making it notably more complex than end-to-end baselines such as [15]. Since these steps are performed sequentially, there is a risk of error accumulation throughout the pipeline, which is not thoroughly analyzed or discussed.\n\n3. **Role and Impact of Contextual Embeddings**: As indicated in Table 4, contextual embeddings are important for model performance. However, the authors only report the quantitative results of this step. It would be helpful to provide qualitative examples or further analysis of how contextual embeddings affect the quality of reconstructed CAD models. Additionally, the reported precision and recall are below 90%, which is relatively low. Does this limitation explain the model's weaker performance on the IR metric?", "was_revised": true, "final_justification": "The authors' response has addressed my concerns well. I have also read the other reviewers' comments and discussions, and it seems that our opinions have converged.", "rebuttal": "## Effect of Sketch Constraints\n\nSketch constraints are a core component of CAD modeling, as they govern how a design adapts when modified. When designers apply constraints (e.g., orthogonality) to sketch primitives (e.g., two lines), any changes made to one primitive are automatically adjusted to preserve these relationships. For example, if the parameters of one line are modified, the other will update accordingly to maintain orthogonality. In a reverse engineering context, it is highly desirable not only to infer accurate CAD geometry from input scans but also to recover the underlying *design intent*, ensuring that the reconstructed model responds to modifications in a manner consistent with how a designer would have originally constrained it. This is exactly what the experiment conducted in Section 5.2 (results in Table 3 and Figure 5) is intended to show. Specifically, we applied identical random perturbations to the sketch primitives of both the ground-truth and the predicted CAD models—using our method and that of [15]—and evaluated the similarity of the resulting geometries with respect to the modified ground-truth. In the presence of constraints (e.g., orthogonality), perturbing one primitive (e.g., the endpoint of a line) can influence others (e.g., the parameters of the other line). If the constraints are correctly inferred, such modifications should propagate consistently across the geometry, resulting in similar outcomes. As shown in Table 3 and Figure 5, our method produces CAD geometries that closely match the perturbed ground-truth, demonstrating its ability to capture constraint-aware editability.\n\nTaking another perspective, one can think that the learning of sketch constraints might have an effect on improving the sketch parameterization, hence the overall CAD reconstruction (e.g., inferring orthogonality constraint can help in enforcing the parameters of the predicted lines to be orthogonal). Prior work [35] has shown that at the sketch-level, jointly learning sketch parameterization and a constraint prediction similar to the one performed in MiCADangelo, can improve performance in both tasks due to shared information between them. We leave further exploration of improved sketch parameterization with constraints to future work.\n\nWe thank the reviewer for this question and we will clarify this and add intermediate visualizations in the updated version of the paper. \n\n## Error Accumulation\n\nError accumulation is an inherent challenge in all recent CAD reverse engineering approaches including MiCADangelo. This is due to the fact that a CAD model is typically represented as a sequence that is generated over a number of steps. Recent top-down approaches [15, 9] generate a CAD sequence autoregressively, meaning that inaccurately predicted sequence tokens are fed back into the model, potentially compounding errors and degrading the accuracy of subsequent token predictions. Similarly, bottom-up approaches [8, 18, 7] involve multiple sequential stages, such as per-point segmentation, base or barrel label prediction, and extrusion parameter estimation, with error propagating at each stage. Nevertheless, to assess the robustness of the different steps of MiCADangelo, we evaluate its core stages independently (plane detection, sketch parameterization, and extrusion parameter optimization) in the following tables. In each case, we observe improved performance compared to the corresponding stages in related methods, which explains the superior overall performance achieved by our approach. \n\n- Plane Detection: We compare MiCADangelo’s plane detection performance against CAD-SIGNet [15], using standard precision, recall, and F1-score. Note that CADSIG-Net is designed to align plane detection with design history, hence its predicted and ground-truth planes are anchored in the original DeepCAD design planes. In contrast, MiCADangelo targets reverse engineering and thus operates on cross-sectional planes obtained by pre-processing DeepCAD (detailed in Appendix A.1). The Table below shows that MiCADangelo achieves strong performance in cross-sectional plane detection, with notably higher metrics than CAD-SIGNet’s performance in the design-plane detection setting.\n\n\n| **Method** | **Precision** | **Recall** | **F1** |\n| --- | --- | --- | --- |\n| CADSIG-Net [15] | 0.701 | 0.696 | 0.686 |\n| Ours | 0.894 | 0.864 | 0.870 |\n\n\n- Sketch Parameterization: We extend our evaluation on Table 5 of the main paper with the addition of an autoregressive baseline, Vitruvion [4]. We show in the Table below that MiCADangelo outperforms both Vitruvion [4] and Davinci [35] in cross-section parameterization in terms of Sketch Chamfer Distance (SCD).\n\n| **Method** | **SCD** |\n| --- | --- |\n| Vitruvion [4] | 1.236 |\n| Davinci [35] | 0.827 |\n| Ours | 0.283 |\n\n- Extrusion Performance: To evaluate extrusion performance, we compare MiCADangelo with Point2Cyl [8], a bottom-up method that estimates extrusion cylinders from 3D point clouds. We use 100 CAD models from the dataset provided in [8] and, for each model, match each ground-truth extrusion cylinder to its closest predicted counterpart from both methods using Chamfer Distance (CD). We then report the average CD across all matched pairs. As shown in the table below, MiCADangelo achieves a lower average CD, indicating more accurate extrusion recovery.\nIt is worth noting that, due to the high computational cost of Point2Cyl (over 4 hours for 100 samples), this evaluation was limited to 100 models.\n\n| **Method** | **Extrusion CD** |\n| --- | --- |\n| Point2Cyl [8] | 27.9 |\n| Ours | 10.1 |\n\n\n\n## Contextual Embeddings \n\n\nIn Table 4 of the main submission, we ablate the impact of contextual embeddings on plane detection performance. Following the reviewer’s suggestion, we have extended this analysis to evaluate their effect on the full CAD reconstruction pipeline. The results are presented in the Table below. We observe that contextual embeddings have an effect on the overall CAD reconstruction performance on all reported metrics. \n\n| **Method** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| w/o contextual embeddings | 8.80 | 0.39 | 3.5 | 69.4 | 2.25 |\n| w/ contextual embeddings | 2.27 | 0.20 | 2.6 | 80.6 | 0.46 |\n\nNonetheless, it is interesting to observe that, despite significantly underperforming in cross-section plane detection, our method without contextual embeddings still achieves reasonable overall CAD reconstruction performance. This can be attributed to the robustness of the subsequent stages—sketch parameterization and extrusion optimization—which are capable of recovering plausible reverse engineering design paths, even when the detected cross-section planes deviate from the ground truth. \n\nAs for Invalidity Ratio (IR), we did not observe a drastic drop in performance when omitting the contextual embeddings. This means that a low cross-section plane detection performance does not necessarily imply a high IR. It is important to note that our method achieves an invalidity ratio comparable to CAD‑SIGNet [15] (2.6 for MiCADangelo compared to 0.9 for CAD‑SIGNet on DeepCAD dataset). Invalid outputs are common in recent CAD reconstruction approaches and may arise from various issues (e.g., prediction of self-intersecting sketches). CAD‑SIGNet reduces its invalidity ratio through test‑time sampling (dropping it from 4.4 to 0.9). Our framework could benefit from similar techniques, for example by evaluating intermediate design sequences for validity, which we leave for future work.\n\nWe thank the reviewer for the suggestion and we will provide this experiment and discussion along with additional qualitative results as the reviewer suggested in the revised version.\n\n\n## Choice of N\n\nThe value of  $N$ controls the density of cross-section slice sampling, determining the granularity of the input to the reconstruction pipeline. We conduct an ablation on DeepCAD dataset with different $N$ values in the following Table.\n\n\n| **N** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| 10 | 3.20 | 0.26 | 4.5 | 78.2 | 0.54 |\n| 20 | 3.17 | 0.25 | 4.3 | 78.4 | 0.53 |\n| 40 | 2.27 | 0.20 | 2.6 | 80.6 | 0.46 |\n\nWe observe that larger $N$ values provide the input model with a more dense input representation and slightly increase CAD reconstruction performance across metrics. In this work, we set $N$ to 40, which offers a good balance between accuracy and computational cost. A similar compromise arises in point‑cloud pipelines (as in all competitors [15, 9, 8, 6]), where the input cloud is routinely down‑sampled to a fixed number of points.\n\n## Training Data\n\nAll comparison methods are trained on the DeepCAD dataset. The plane detection module of MiCADangelo is likewise trained on DeepCAD. Since the DeepCAD dataset does not include parameterized cross-sections or constraint labels, the sketch parameterization module of MiCADangelo is trained on the SketchGraph dataset of constrained CAD sketches, along with synthetically generated closed loops. Notably, although our sketch parameterization module has not seen DeepCAD cross-sections during training, it generalizes well as demonstrated by the strong CAD reconstruction performance."}, {"review_id": "7rpEkPZdyq", "reviewer": "Reviewer_ZeA5", "summary": "This paper proposes MiCADangelo, a novel framework for CAD reverse engineering that mimics human design workflows. Given a 3D mesh from a scan, the method selects key cross-sections, infers constrained 2D sketches, and optimizes extrusion parameters to construct a fully parametric and editable CAD model. The method also incorporates CAD sketch constraints into 3D CAD reconstruction. Experiments on DeepCAD and Fusion360 demonstrate significant improvements over prior work in both reconstruction quality and downstream editability.", "questions": "- How does the method handle imperfect scans (with holes and mis-oriented normals), or scans with noise? It seems that the proposed stages are mostly sensitive to noise and it would be nice to show how robust the method is towards these issues.\n- How does the method perform on more complex geometries with multiple parts and intricate details? It would be interesting to apply the method to a larger mechanics and test the reconstruction quality and editability.", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n- The framework effectively bridges the gap between 3D scanning and CAD modeling, making it easier for designers to work with scanned data.\n- The incorporation of CAD sketch constraints allows for more intuitive and flexible design workflows.\n- Experimental results show significant improvements in reconstruction quality and editability compared to prior methods.\n\nWeaknesses:\n- The reliance on key cross-sections may limit the framework's ability to capture complex geometries. The performance of the framework on highly detailed or intricate models is not fully explored. For example, the method only handles extrusion-based models, which may not be suitable for all types of CAD designs (such as lofts or sweeps).\n- Most parts of the method are rule-based, and the entire pipeline consists of multiple steps that might introduce cumulative errors. It would be interesting to have some high-level schematic comparisons w.r.t. other rule-based methods in terms of pipeline design choices.", "was_revised": true, "final_justification": "As claimed in the discussion phase, I'm happy to remain unchanged about my previous positive review of the paper.", "rebuttal": "## Complex Geometries\n\nWe conduct an experiment on complex models from DeepCAD dataset in Table 3 of the main submission. Complex models are defined as models having more than four loops (1391 models). MiCADangelo is shown to outperform the method of [15] by a large margin on this partition. We further extend this analysis by evaluating a subset of highly complex models containing more than eight loops (271 models). These models represent parts with multiple intricate geometric details. A quantitative comparison for this partition is presented in the Table below. \n\n| **Method** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CADSIG-Net | 6.48 | 1.64 | 5.1 | 41.07 | 4.84 |\n| Ours | 5.47 | 0.45 | 5.5 | 64.30 | 2.12 |\n\n\nAdditionally, we report results on models from DeepCAD containing more than two extrusions (132 models), which pose further challenges for accurate reconstruction.\n\n| **Method** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CADSIG-Net | 17.7 | 3.95 | 5.4 | 40.6 | 9.81 |\n| Ours | 4.42 | 0.46 | 3.0 | 64.8 | 2.27 |\n\nIn the revised version, we will include visual examples of CAD reconstructions of these complex models.\n\nIt is worth noting that all recent methods, including both top-down and bottom-up approaches, focus exclusively on sketch-extrude CAD models. These models represent the entire set of samples in the DeepCAD and Fusion 360 datasets. Handling more complex CAD operations such as lofts and sweeps remains an open challenge. However, the proposed method can, in principle, be extended to support these operations by generalizing the differentiable extrusion optimization framework. This could involve defining parameterized curves that guide operations like sweeps and lofts, instead of relying on the extrusion vectors used in this work, and optimizing the parameters of these curves. We consider this a promising direction for future research.\n\n\n\n## Error Accumulation\n\nAs we noted to a related question from *Reviewer wdwr*, error accumulation is an inherent challenge in all recent CAD reverse engineering approaches. Top-down methods [15, 9] generate a CAD sequence autoregressively, meaning that inaccurately predicted sequence tokens condition future generation, leading to compounding errors. Bottom-up approaches [8, 18, 7] involve multiple sequential stages, such as per-point segmentation, base or barrel label prediction, and extrusion parameter estimation, with error accumulating at each stage. Following the reviewer’s suggestion, we provide a quantitative comparison of MiCADangelo’s performance against alternative design choices on the primary pipeline stages (plane detection, sketch parameterization, and extrusion parameter optimization). The results are presented in the Tables below. We observe that MiCADangelo consistently outperforms other methods, resulting in reduced error accumulation and better overall performance.\n\n- Plane Detection: We compare MiCADangelo’s plane detection performance against CAD-SIGNet [15], using standard precision, recall, and F1-score. Note that CADSIG-Net is designed to align plane detection with design history, hence its predicted and ground-truth planes are anchored in the original DeepCAD design planes. In contrast, MiCADangelo targets reverse engineering and thus operates on cross-sectional planes obtained by pre-processing DeepCAD (detailed in Appendix A.1). The Table below shows that MiCADangelo achieves strong performance in cross-sectional plane detection, with notably higher metrics than CAD-SIGNet’s performance in the design-plane detection setting.\n\n\n| **Method** | **Precision** | **Recall** | **F1** |\n| --- | --- | --- | --- |\n| CADSIG-Net [15] | 0.701 | 0.696 | 0.686 |\n| Ours | 0.894 | 0.864 | 0.870 |\n\n\n- Sketch Parameterization: We extend our evaluation on Table 5 of the main paper with the addition of an autoregressive baseline, Vitruvion [4]. We show in the Table below that MiCADangelo outperforms both Vitruvion [4] and Davinci [35] in cross-section parameterization in terms of Sketch Chamfer Distance (SCD).\n\n| **Method** | **SCD** |\n| --- | --- |\n| Vitruvion [4] | 1.236 |\n| Davinci [35] | 0.827 |\n| Ours | 0.283 |\n\n- Extrusion Performance: To evaluate extrusion performance, we compare MiCADangelo with Point2Cyl [8], a bottom-up method that estimates extrusion cylinders from 3D point clouds. We use 100 CAD models from the dataset provided in [8] and, for each model, match each ground-truth extrusion cylinder to its closest predicted counterpart from both methods using Chamfer Distance (CD). We then report the average CD across all matched pairs. As shown in the table below, MiCADangelo achieves a lower average CD, indicating more accurate extrusion recovery.\nIt is worth noting that, due to the high computational cost of Point2Cyl (over 4 hours for 100 samples), this evaluation was limited to 100 models.\n\n| **Method** | **Extrusion CD** |\n| --- | --- |\n| Point2Cyl [8] | 27.9 |\n| Ours | 10.1 |\n\n\n\n## Imperfect Scans \n\nTo evaluate performance on real imperfect scans, we include a quantitative comparison on the challenging CC3D dataset. This cross-dataset evaluation compares our method to that of [15], both trained on DeepCAD and evaluated on CC3D scans that include realistic scanning artifacts, such as holes and misoriented normals, as noted by the reviewer. Results are shown in the Table below. The proposed MiCADangelo outperforms [15] in this in-the-wild setting, demonstrating greater robustness to real-world noise.\n\n\n**CC3D Results**\n\n| **Method** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CADSIG-Net [15] | 14.80 | 2.90 | 4.4 | 42.6 | 8.68 |\n| Ours | 9.55 | 1.69 | 2.20 | 50.8 | 5.93 |\n\nNote that in all experiments, including those conducted on the DeepCAD and Fusion 360 datasets, we introduce noise during the training of the sketch parameterization module through data augmentations. Specifically, we apply small perturbations to the coordinates of sketch primitives, resulting in deformations of the input sketch images. These augmentations can lead to primitive disconnections, mimicking artifacts commonly introduced by scanning technologies in real-world cross-sections. This strategy enhances the robustness of the sketch parameterization module when processing noisy scan data. Nevertheless, we believe that further training our pipeline on the CC3D scans, for which the sketch-extrude sequences have unfortunately not yet been released, could significantly enhance its robustness to imperfections and artifacts commonly found in real-world scan data."}, {"review_id": "88AZ71mvc2", "reviewer": "Reviewer_2uf7", "summary": "This paper proposes a new CAD reverse engineering method, MiCADangelo, that reconstructs fully parametric CAD models from 3D scans. This method addresses the limitations of existing techniques by preserving fine geometric details and incorporating sketch constraints. Specifically, it analyzes 3D scans via 2D cross-sections to identify sketch planes, extracts closed loops into parametric curves, and optimizes extrusions based on local mesh geometry. Both quantitative and qualitative experiments demonstrate that the proposed method outperforms existing methods in CAD reverse modeling.", "questions": "As listed in the weaknesses section, I would like to know the answers to the first 4 points, i.e.,\n1. While the method is generally well-explained, some details of the constrained sketch parameterization network and the loss functions are not clear to me. For example, in the second term of the loss function, why do we need to minimize the square of Hi, and what does the subscript i refer to?\n2. For the quantitative evaluation, I think the mean Chamfer distance results should be provided, but I only found the median Chamfer distance results.\n3. For the evaluation of \"Robustness to Real-world Scans\", are there any testing results for inputs with noisy or incomplete 3D scans? I think it is common in real scenarios.\n4. Since the sketch planes are detected from a set of 2D cross-section slices that are equally sampled along three axes, I wonder how to ensure the desired sketch planes fall in these?", "limitations": "Yes.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. This paper introduces a new and effective method that incorporates sketch-level constraints for CAD reverse engineering to improve the performance.\n2. Overall, this paper is well organized, and the proposed method is easy to understand.\n\nWeaknesses:\n1. While the method is generally well-explained, some details of the constrained sketch parameterization network and the loss functions are not clear to me. For example, in the second term of the loss function, why do we need to minimize the square of Hi, and what does the subscript i refer to?\n2. For the quantitative evaluation, I think the mean Chamfer distance results should be provided, but I only found the median Chamfer distance results.\n3. For the evaluation of \"Robustness to Real-world Scans\", are there any testing results for inputs with noisy or incomplete 3D scans? I think it is common in real scenarios.\n4. Since the sketch planes are detected from a set of 2D cross-section slices that are equally sampled along three axes, I wonder how to ensure the desired sketch planes fall in these?\n5. As the limitation stated in this paper, this method only supports extrusion, and extrusions are defined based on sketch plane normals, which can be suboptimal for models with non-axis-aligned extrusions.", "was_revised": true, "final_justification": "After carefully reading the rebuttal and discussions, I care about the concerns of Reviewer WG8f.  On the other hand, considering the authors have almost answered my questions, I would like to raise my score to \"borderline accept\" but decrease my confidence score to 2.", "rebuttal": "## Loss function details\n\nThe second term in the loss function minimizes the square of $h_j$ to regularize extrusion height and prevent it from growing unnecessarily large. Without this term, the optimization may favor extrusions with excessive height. We note that the extrusion parameter optimization is performed jointly for all the sketch loops over the detected key slice planes. The subscript $i$ refers to the key slice planes, and $j$ refers to the individual sketch loops. We thank the reviewer for pointing out this and we will clarify in the revised version of the paper.\n\n\n## Mean Chamfer distance\n\nAs in [9], we initially omitted the mean Chamfer Distance metric due to its sensitivity to outliers, as a small number of poorly reconstructed CAD models can significantly distort the overall value. However, for completeness, the Table below reports the mean Chamfer Distance for both our method and CAD-SIGNet [15] on the DeepCAD and Fusion 360 datasets. Our method outperforms CAD-SIGNet in terms of mean CD as well.\n\n**DeepCAD Results**\n\n| **Method** | **Mean CD** | **Median CD** | **IoU** | **IR** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CADSIG-Net | 3.43 | 0.28 | 77.6 | 0.9 | 0.74 |\n| Ours | 2.27 | 0.2 | 80.6 | 2.6 | 0.46 |\n\n**Fusion 360 Results**\n\n| **Method** | **Mean CD** | **Median CD** | **IoU** | **IR** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CADSIG-Net | 7.37 | 0.56 | 65.6 | 1.6 | 4.14 |\n| Ours | 5.53 | 0.48 | 68.73 | 3.2 | 2.66 |\n\n\n## Robustness to real scans.\n\nWe extend our evaluation on real-word scans by reporting quantitative results on the challenging CC3D dataset. This cross-dataset evaluation compares our method to that of [15], both trained on DeepCAD and evaluated on CC3D scans that include realistic realistic scanning artifacts, such as holes and misoriented normals. Results are shown in the Table below. The proposed MiCADangelo outperforms [15] in this evaluation, demonstrating robustness to noisy input scans.\n\n**CC3D Results**\n\n| **Method** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CADSIG-Net | 14.80 | 2.90 | 4.4 | 42.6 | 8.68 |\n| Ours | 9.55 | 1.69 | 2.2 | 50.8 | 5.93 |\n\n\n## 2D cross-sectional slice selection\n\nOur slice plane detection network is provided with $N = 40$ slices along each axis, resulting in a dense input representation. We conduct an ablation on different $N$ values in the following Table.\n\n| **N** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| 10 | 3.20 | 0.26 | 4.5 | 78.2 | 0.54 |\n| 20 | 3.17 | 0.25 | 4.3 | 78.4 | 0.53 |\n| 40 | 2.27 | 0.20 | 2.6 | 80.6 | 0.46 |\n\nWe set $N = 40$ as it provides the best accuracy while maintaining computational efficiency. This trade-off is similar to point cloud-based pipelines (including all competitors [6, 8, 9, 15]), where the input cloud is typically down-sampled to a fixed size to balance fidelity and computational cost. Note that as correctly spotted by the reviewer there is no guarantee that the desired sketch planes fall perfectly with the $N$ equally spaced planes. Nevertheless, as shown in Table 4 of the main paper, our method achieves strong performance in cross-section plane detection with $N = 40$ on the DeepCAD dataset. Following a request from *Reviewer WG8f*, the Table below includes cross-section plane detection results on the Fusion 360 and CC3D datasets in addition to DeepCAD, showcasing consistent performance across different datasets. \n\n| **Dataset** | **Precision** | **Recall** | **F1** |\n| --- | --- | --- | --- |\n| Deepcad | 0.894 | 0.864 | 0.870 |\n| Fusion360 | 0.860 | 0.812 | 0.820 |\n| CC3D | 0.803 | 0.790 | 0.777 |\n\n\nWe thank the reviewer for this question and we will include a discussion on this in the revised version of the paper.\n\n## Non-axis-aligned extrusions\n\nIn this work, we focus on axis-aligned extrusions, as these are the types represented in the DeepCAD dataset. Our analysis shows that axis-aligned extrusions account for 99.6% of all extrusions in DeepCAD. To extend our method beyond axis-aligned extrusions, a representative training dataset is required, one that includes non-axis-aligned extrusions and allows for the generation of corresponding cross-section plane annotations (as described in Appendix A.1). With such a dataset, the same framework can be applied by training the sketch plane detection network on cross-section planes sampled along different orientations. As such setting was not investigated due to the lack of a representative dataset, we stated this aspect as a limitation of our work in the main paper. We will clarify this in the revised version."}, {"review_id": "RfQEeGeh0O", "reviewer": "Reviewer_WG8f", "summary": "This work approaches parametric CAD reverse engineering, with a particular focus on sketch-extrusion models. The paper introduces a cross-section-based approach for sketch prediction and constraints discovery. Quantitative evaluations demonstrate superior performance compared to prior works, while qualitative results indicate an enhanced capability in handling more complex CAD models than existing approaches.", "questions": "+ Since the plane detection network is trained on DeepCAD dataset, the reviewer is curious about its generality on Fusion360 and CC3D dataset, an evaluation is suggested. \n\n+ The paper would benefit from a visual result illustrating how a complete reconstruction is decomposed into a set of sketch-extrusions. Such a figure should clearly highlight the intermediate sketches and their corresponding extrusions, including at least one example of a cut extrusion.", "limitations": "The authors have discussed the limitations of orthogonal plane detections. It would be interesting to see discussions about the interference of different extrusions during the optimization process.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n+ This work incorporates sketch constraint modeling into 3D CAD reverse engineering, which looks interesting but lacks further constraint optimization.\n+ During extrusion optimization, the method jointly optimizes multiple extrusion heights to enhance stability and performance. Experiments (e.g., Fig. 6) demonstrate the effectiveness of this approach.\n\nWeakness\n+ The idea of using cross-section has been explored in several prior works, such as CAD-SIGNet[1], PS-CAD[2], and PlankAssembly[3]. This paper lacks a detailed discussion on how its approach differs from or improves upon these works, raising concerns about the contribution. \nFurthermore, due to the hierarchical and nested nature of CAD construction steps, cross sections cannot fully capture all sketch information. For instance, the sketch of a cut feature may not be visible in the CAD geometry or any extracted cross-section.\n+ The modeling of sketch constraints is incremental with a naive network. Similar constraint modeling techniques have been extensively explored in prior works [4, 5] on 2D sketches, and it is uncertain about its novelty. It would be interesting to incorporate sketch constraints for better sketch prediction, but I did not see explicit designs to explore this possiblity. \n+ The paper does not justify the advantages of its differentiable extrusion optimization over prior approaches. Prior works, e.g. Point2Cyl and SECAD-Net, employ an implicit function-based optimization strategy. From a practical standpoint, implicit methods are considered more robust since they can better handle noisy input. Why does this work adopt an explicit optimization formulation?\n\n[1] Khan, Mohammad Sadil, et al. \"Cad-signet: Cad language inference from point clouds using layer-wise sketch instance guided attention.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.\n\n[2] Yang, Bingchen, et al. \"PS-CAD: Local Geometry Guidance via Prompting and Selection for CAD Reconstruction.\" ACM Transactions on Graphics 44.3 (2025): 1-21.\n\n[3] Hu, Wentao, et al. \"Plankassembly: Robust 3d reconstruction from three orthographic views with learnt shape programs.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023.\n\n[4] Yang, Yuezhi, and Hao Pan. \"Discovering design concepts for cad sketches.\" Advances in Neural Information Processing Systems 35 (2022): 28803-28814.\n\n[5] Seff, Ari, et al. \"Vitruvion: A generative model of parametric cad sketches.\" arXiv preprint arXiv:2109.14124 (2021).", "was_revised": true, "final_justification": "I appreciate the idea of using constraints to improve the CAD modelling pipeline. However, I think the technical contribution, including introducing constraints as an additional prediction task without detailed analysis of the impact of different cases of predicted constraints, is incremental. However, the evaluation of technical contribution is usually subjective; therefore, I downgraded my voting confidence and raised my score.", "rebuttal": "## Contribution and cross-sections \n\n**Contribution:** The primary goal of MiCADangelo is to predict CAD sequences from 3D scans with *fine-grained details*. These sequences should be *seamlessly integrable* into CAD software, enabling *design-intent-aware editability through the inferred constraints*. To achieve this, MiCADangelo mimics the process typically followed by human designers when reconstructing CAD models from scans. These steps consist of: \n\n1- selecting a 2D cross-section from the 3D scan, which is handled by a dedicated cross-section plane detection model, described in Section 4.2. \n\n2- parameterizing and constraining the sketch within the extracted cross-section. This is accomplished using a specialized, constraint-aware sketch parameterization model that operates at the image level (see Section 4.3). \n\n3- applying a CAD operation, such as extrusion, to the parameterized sketch in order to generate a solid. This is modeled using our differentiable extrusion optimization, detailed in Section 4.4.\n\n\nWe believe that **explicitly** modeling the steps of the reverse engineering process, as performed by human designers, and making thoughtful technical design choices for each stage, constitutes a valuable contribution. This approach can also serve as a foundation for future research, encouraging exploration of alternative methods and extensions to the proposed design choices at each stage.\n\n\n**Cross-section in prior works:** While CAD-SIGNet [a] and PS-CAD [b] mentioned by the reviewer attempt to use a slightly similar concept to the introduced cross-sections in our work, they *do not* employ *explicit* cross-sectional slicing. Instead, they incorporate *implicit* mechanisms to condition sketch inference on a relevant subset of the input cloud. CAD-SIGNet [a] introduces a Sketch Instance Guided Attention module that predicts attention scores for vertices relevant to sketch token predictions. PS-CAD [b] uses RANSAC to detect planes within the point cloud and embeds the points lying on these planes. These embedded points are then used as prompts to condition the sketch/extrude decoder. MiCADangelo’s key advantage w.r.t to these works is in its *explicit* modeling of cross-sections and the reformulation of sketch parameterization, shifting from conditioning on subsets of point cloud vertices to operating on rasterized cross-sectional images. This allows for the use of an image-based model dedicated to sketch parameterization and constraint inference. We believe that this explicit modeling enables more accurate handling of fine-grained details, which remains a significant challenge for both CAD-SIGNet [a] (as shown in Table 1 of our paper) and PS-CAD [b] (as noted in the conclusion of their paper). Finally, the PlankAssembly [c] work mentioned by the reviewer focuses on converting 2D line drawings from 3 orthographic views into 3D CAD models made of only cuboids. While this is a valuable contribution, its connection to our work and the broader topic of CAD reverse engineering is less clear.\n\nWe thank the reviewer for suggesting these works and we will highlight their differences w.r.t our work in the revised version. \n\n\n**Cross sections cannot fully capture sketch information:** Indeed, as the reviewer mentions, the sketch of a cut feature may not be visible in any extracted cross-section. However, this does not prevent MiCADangelo from effectively reconstructing the CAD model. The key distinction is that MiCADangelo does not need to replicate the original construction history followed by the CAD designer. When a cut removes material, the remaining shape taken after the cut already contains the modified profile, so the necessary shape information is still present. A human designer performing manual reverse engineering would operate in a similar way, that is, by slicing the mesh, tracing the visible profiles, and building an alternative sequence of sketches and features that yields the same solid. MiCADangelo automates this reverse-engineering paradigm. Even though the reconstruction may use a different series of operations, the resulting model reconstructs the target CAD geometry. \n\nTo further demonstrate MiCADangelo’s effectiveness on models including cuts, we report the performance of our method and that of CAD-SIGNet on a subset of models from DeepCAD that each contain at least one cut extrusion. The results are presented in the Table below. We observe that our method outperforms CAD-SIGNet on this partition.\n\n| **Method** | **Mean CD** | **Median CD** | **IR** | **IoU** | **ECD** |\n| --- | --- | --- | --- | --- | --- |\n| CAD-SIGNet [15] | 4.95 | 0.77 | 3.0 | 65.5 | 3.97 |\n| Ours | 4.26 | 0.64 | 3.5 | 71.8 | 3.13 |\n\n\n**Visual result illustrating how a complete reconstruction is decomposed into a set of sketch-extrusions:** We thank the reviewer for the suggestion and we will include a figure showcasing sequential sketch-extrusions (including cuts) in the revised version. As due to NeurIPS guidelines, we are unable to include additional figures in the rebuttal.\n\n\n[a] Cad-signet, CVPR 2024.\n[b] PS-CAD, ACM TOG 2025.\n[c] Plankassembly, ICCV 2023.\n\n\n## Sketch constraints \n\n**Modeling of sketch constraints is incremental:** We clarify that the novelty of this work is not in proposing a new constraint modeling approach. Instead, we are the first to integrate constraint prediction into 3D reverse engineering. By reformulating the problem as cross-section image parameterization, we operate in the image domain where sketch primitives and constraints can be inferred more easily and accurately, compared to the more challenging task of predicting them directly from point clouds. Notably, learning constrained sketch sequences directly from point clouds in a CAD-SIGNet-style framework would drastically expand the solution space, as the resulting sequences are significantly longer and more complex to model. This proposed formulation also enables us to leverage large-scale sketch datasets such as SketchGraphs as no suitable datasets exist for learning sketch constraints directly from point clouds. \n\nIt is important to note, however, that unlike [d, e], we adopt a dedicated model that jointly learns both sketch primitive parameters and their constraints in a single forward pass, directly from rasterized sketch images. This design choice, inspired by [35], enables the model to leverage shared information between primitives and constraints.\n\n\n**Sketch constraints for better sketch prediction:** We emphasize that CAD constraints in our framework are not introduced as a mechanism to boost sketch prediction. Existing methods in the CAD sketch literature do not use constraints to enhance parameterization performance [d,e]. Instead, CAD constraints are a fundamental aspect of CAD modeling as they dictate how an object responds to future CAD modifications. In the evaluation presented in section 5.2, we demonstrate the CAD models reconstructed with MiCADangelo closely follow the ground-truth under modification in contrast to the unconstrained sequences generated by CAD-SIGNet. Note that while constraints are not strictly necessary for sketch parameterization, it has been shown in [35] that jointly learning primitives and constraints can marginally improve prediction accuracy for both tasks by leveraging the shared information between them. Further investigation on improved sketch parameterization with constraints is left for future work. \n\n[d] SketchConcepts, Neurips 2022.\n[e] Vitruvion, ICLR 2022.\n\n## Differentiable extrusion\n\n**Advantages of differentiable extrusion optimization over prior approaches:** We thank the reviewer for raising this point. Implicit function-based methods such as Point2Cyl [8] and SECAD-Net [18] predict SDFs, which can be robust for surface reconstruction but do not produce native geometric primitives like lines and arcs. This limits their editability and compatibility with downstream CAD workflows, which require parametric representations. For extrusions, these methods depend on point cloud segmentation or bounding box detection to estimate extrusion length, introducing dependencies and potential error propagation. We also note that the differentiable extrusion in SECAD-Net enables end-to-end supervision but does not directly optimize extrusion parameters. In contrast, our method explicitly optimizes the extrusion length, guided by local geometry around each sketch loop. Rather than relying on segmentation or bounding box detection, our method infers extrusion length directly from local geometry, avoiding error-prone intermediate stages. As requested by *Reviewer wdwr* regarding multi-step error accumulation, including the extrusion optimization stage, we compared our extrusion optimization method to that of Point2Cyl [8]. The results show that our approach produces more accurate extrusions. We thank the reviewer and will clarify this in the paper.\n\n\n**Interference of different extrusions:** All extrusion parameters are optimized jointly across sketch loops and key cross-section planes. While joint optimization could introduce interactions between nearby or overlapping extrusions, in practice, we observe minimal interference due to the spatial separation of most sketch loops. We totally agree with the reviewer that this is one limitation of the proposed extrusion optimization. As future work, a penalty term can be incorporated into the loss function that discourages overlapping or conflicting extrusions. We thank the reviewer and we will add this in the limitations of the paper.\n\n\n## Plane detection generalization \n\nWe thank the reviewer for the suggestion. We evaluate the plane detection model on Fusion360 and CC3D datasets. The results show robust plane detection performance with minimal drop.\n\n| **Dataset** | **Precision** | **Recall** | **F1** |\n| --- | --- | --- | --- |\n| DeepCAD | 0.894 | 0.864 | 0.870 |\n| Fusion360 | 0.860 | 0.812 | 0.820 |\n| CC3D | 0.803 | 0.790 | 0.777 |"}]

Author rebuttal:

Meta-review: The submission received four positive recommendations. The reviewers liked the idea, the writing, and the performance improvement. At the same time, the reviewers were also concerned about the novelty over the previous methods, the justification, and the performance on real-world data. I believe the authors did a good job of addressing reviewers’ concerns in the rebuttal and author-reviewer discussion period. The reviewers reached a consensus without a brief discussion among reviewers afterwards. The AC also read through the manuscript, all reviews, the rebuttal, discussions, the confidential comments to AC, and the final justifications. The AC agreed with the reviewers and made a decision of acceptance. The decision was approved by the Senior AC.
Decision: Accept (poster)