MiCADangelo: Neural CAD Reverse Engineering

• MiCADangelo is a neural reverse engineering approach that reconstructs editable, parametric CAD models from 3D scans using multi-plane cross-section analysis.
• It recovers fine geometric details and sketch-level constraints, ensuring interoperability with commercial CAD systems.
• The pipeline integrates ResNet34-based sketch detection and differentiable extrusion optimization to achieve superior fidelity and editability.

MiCADangelo is a neural reverse engineering approach designed for the fine-grained reconstruction of editable, constraint-aware parametric Computer-Aided Design (CAD) models directly from 3D scans. By mimicking the manual workflows of human designers and leveraging multi-plane cross-section analysis, MiCADangelo is the first method to recover both fine geometric details and sketch-level design constraints, yielding outputs that are directly interoperable with commercial CAD systems and robust to future modifications (Karadeniz et al., 27 Oct 2025).

1. Problem Formulation and Key Challenges

MiCADangelo addresses the task of CAD reverse engineering, specifically converting unstructured triangle meshes derived from 3D scans into fully parametric and editable CAD models. Conventional approaches are divided into bottom-up (geometry-first) methods that fit geometric primitives and top-down (sequence-driven) strategies that predict CAD operations, both exhibiting critical deficits:

• Bottom-up techniques fail to produce structured, parametric outputs compatible with CAD tools.
• Top-down methods lose spatial and topological detail, particularly in small or non-global features.

A major limitation in prior art is the absence of sketch-level constraints—relational operators such as parallelism, orthogonality, and coincidence—that define the logic and editability of true CAD models. These constraints are essential for the practical usability of CAD outputs, as they preserve design intent and allow robust downstream editing.

2. MiCADangelo Pipeline and Methodological Contributions

The pipeline of MiCADangelo is designed to mirror human CAD modeling strategies and is structured as follows:

1. Multi-Plane Cross-Section Sampling: The input mesh is sliced along $N$ planes per axis ($N=40$; total 120), producing 2D raster images of cross sections that highlight underlying geometric features.
2. Sketch Plane Detection: A ResNet34-based encoder, combined with contextual positional embeddings and a transformer, classifies slices as "key sketch planes" likely to contain critical CAD sketch information. Contextual embeddings encode axis, position, and normalization, enhancing selective accuracy.
3. 2D Loop Extraction and Rasterization: Key planes are analyzed for closed, non-self-intersecting loops. Each loop is rasterized into $128 \times 128$ binary images that serve as input to subsequent neural modules.
4. Sketch Parameterization and Constraint Prediction: A transformer encoder-decoder architecture processes rasterized loops to predict both primitive geometry (lines, circles, arcs; via quantized parameter bins) and constraints between primitives (parallel, tangent, perpendicular, coincident, vertical, horizontal). This module is pretrained/fine-tuned on SketchGraphs, with synthetic noise augmentation to ensure robustness.
5. Differentiable Extrusion Optimization: For each predicted sketch, extrusion parameters (direction, length, add/remove flag) are optimized via gradient descent to fit the extruded solid to the input mesh:
   • Sample anchor points on the 2D sketch boundary.
   • Extrude along plane normal vector $\mathbf{v}_j$ for length $h_j$.
   • Minimize mean squared distance between mesh points and extruded volumes (plus regularization on extrusion lengths):

   $$\mathcal{L}_{\text{extr}} = \frac{1}{n_M} \sum_{l=1}^{n_M} d(\mathbf{q}_l, \rho_{\text{min}})^2 + \lambda \sum_{i,j} h_j^2$$

6. Assembly: The model outputs a CAD sequence: a set of constraint-rich 2D sketches and their corresponding extrusions, directly compatible with CAD workflows.

3. Algorithms and Formulations

Key Mathematical Elements

• Chamfer Distance (CD):

$$\operatorname{CD} = \frac{1}{2N} \sum_{i=1}^N \min_{\hat{\mathbf{p}}_j} \left\| \mathbf{p}_i - \hat{\mathbf{p}}_j \right\|_2^2 + \frac{1}{2N} \sum_{j=1}^N \min_{\mathbf{p}_i} \left\| \hat{\mathbf{p}}_j - \mathbf{p}_i \right\|_2^2$$

• Constraint Representation:

$\mathbf{c} = (\mathbf{p}_i, \mathbf{p}_j, c_t)$

with $c_t$ denoting constraint types (coincident, parallel, etc.).

Technical Advancements

MiCADangelo's contextual transformer architecture for sketch plane selection, explicit constraint recovery in the parameterization network, and differentiable extrusion optimization collectively distinguish it from previous approaches that lack either parametric detail, editability, or constraint-awareness.

4. Experimental Evaluation and Benchmarks

MiCADangelo was evaluated against state-of-the-art models (DeepCAD, Point2Cyl, CAD-Diffuser, CAD-SIGNet) on DeepCAD, Fusion360 Gallery, and CC3D datasets. Metrics include Chamfer Distance (CD), Intersection-over-Union (IoU), Edge Chamfer Distance (ECD), invalid CAD ratio (IR), and sketch-specific Chamfer Distance (SCD).

Method	Med. CD ↓	IoU ↑	IR ↓	ECD ↓
DeepCAD	9.64	46.7	7.1	–
Point2Cyl	4.27	73.8	3.9	–
CAD-Diffuser	3.02	74.3	1.5	–
CAD-SIGNet	0.28	77.6	0.9	0.74
MiCADangelo	0.20	80.6	2.6	0.46

MiCADangelo achieves superior geometric and edge-level fidelity, with pronounced gains in preserving fine and complex features. On models with multiple loops or extrusions, it outperforms CAD-SIGNet by factors of 2–5 in CD/ECD, demonstrating greater robustness to complexity and noise. Ablation studies confirm that contextual embedding, increased cross-section sampling, and data augmentation are all necessary for optimal performance.

5. CAD Constraint Recovery and Editability

MiCADangelo is the first framework to explicitly recover sketch-level constraints during CAD model reconstruction. Controlled experiments show that when model outputs are modified (e.g., via point displacement), those incorporating constraints preserve structural relationships (e.g., rectangular orthogonality) whereas unconstrained models degrade. This supports true editability—modified models remain physically plausible and consistent with design intent, akin to native CAD authoring.

6. Limitations and Prospective Extensions

MiCADangelo currently supports extrusion-based modeling. Revolved features, lofts, and complex spline-based surfaces are not handled and remain challenging for all competitors. Advanced non-axis-aligned features and compositions present persistent difficulties. Extensions to broader CAD operations are suggested as future research directions.

7. Significance and Impact

MiCADangelo establishes a new standard for reverse engineering from 3D scans, enabling the creation of constraint-rich, parametric CAD models with fine geometric detail. Outputs are directly usable in commercial CAD environments, enhancing practical workflows in manufacturing, design reuse, automated model authoring, and digital reconstruction. The method's robustness to scanning artifacts and its preservation of design constraints significantly advance the state-of-the-art in CAD model recovery from real-world objects.