## 3 Overview  
Our proposed computational paradigm unfolds in two primary phases, as illustrated in Figure 1.  
Extracting feature paths. The principal curvatures of each vertex in the triangular meshes are calculated, and every segmented patch is considered a distinct solid feature for reconstruction. To acquire feature sections, initial sampling points are determined based on the vertex principal curvature values, and the initial feature section (\(S^{\prime}\)) is defined by the vertex principal directions. Utilizing Gaussian mapping of (\(S^{\prime}\)) and iterative optimization of its direction, the feature section (\(S\)) is obtained. The acquisition of feature paths involves obtaining all vertices of the triangular mesh model intersected by each feature section, calculating the centroids of these vertices, sequentially connecting the centroids to form a polyline \(\Lambda\), identifying various line patterns (line, arc, B-spline) within the polyline (\(\Lambda\)), and ultimately deriving the characteristic path \(\Gamma\).  
Extracting cross-sectional sketches. Based on the intersection points of the characteristic section and the triangular surface fragment, the initial section sketch is generated. The types of lines (line, arc, B-spline) are selected based on the curvatures and normal vectors of the individual points within the sketch. Segment fitting and application of geometric constraints are then carried out for each line type. Furthermore, global geometric constraint optimization equations are developed and resolved to obtain the optimal cross-sectional sketch (\(C\)) globally, thus avoiding concerns arising from excessive constraint definition. Ultimately, guided by the feature path \(\Gamma\) and the set of cross-sectional sketch curves \(C(t)\), the segmented feature patch is reconstructed to incorporate the designated basic features, such as stretching, rotating, sweeping, and releasing, utilizing the feature modeling capabilities of Open CASCADE [30].  
In the CAD software for solid modeling, solid features are defined as a geometric entity that embodies the design intent, influenced by cross-sectional sketch curves and feature paths, while also facilitating parametric editing [31]. Hence, to reconstruct solid features from manifold meshes, it is essential to extract two fundamental components from the segmented triangular mesh patches: the cross-section sketch curves and the feature paths. Four typical entity features--extrusion, rotation, sweep, and loft--are classified into a generalized sweep volume (GSV), thereby establishing a unified mathematical representation for various basic features. GSV is formulated as  
\[\text{GSV}=\int_{\Gamma}C(t)ds=\int_{0}^{L}C(t)ds \tag{1}\]  
where \(C(t)\) represents the cross-sectional sketch curves that evolve over the parameter \(t\), where \(t\) ranges from 0 to 1. \(\Gamma\) denotes the feature path, and \(ds\) represents the differential of the arc length along the feature path \(\Gamma\), where s ranges from 0 to the full length of the arc \(L\). Essentially, GSV involves the spatial curve integral of the cross-sectional sketch curve along the feature path. Figure 2 illustrates the GSV representations of the four typical solid features.  
Figure 1: The computational paradigm used to reconstruct solid CAD features consists of two primary phases: the extraction of feature paths and cross-sectional sketches, separately.