High-precision reconstruction of swept surfaces with a planar path

doi:10.11996/JG.j.2095-302X.2025020425

Abstract

Abstract:

The reconstruction of CAD modeling process from triangular mesh is a key focus in reverse engineering, and efficient, high-precision swept surface reconstruction is of great engineering value. Targeting the mesh representation surface generated by planar path sweeping composed of line and arc segments, sweeping reconstruction based on profile and path automatic extraction was proposed to achieve high-precision reconstruction of swept surfaces. Firstly, the initial path was automatically obtained based on the unified curvature vector field of the triangular mesh, and the profile was generated using Gaussian mapping iteration, registration, and fitting. Then, the scattered point set of the path was computed inversely. The straight line and arc segments in the path were identified using a tangent space representation, and the fitting optimization model was established based on the tangent geometric constraints to optimize the initial path. Finally, the swept surface was reconstructed by performing a sweeping operation with the calculated profile and path. Experimental results demonstrated that the proposed method achieved automatic extraction of profile and path curves, thereby reconstructing the modeling process of the sweeping model. This approach reduced tedious manual interactions, and the extracted profiles and paths effectively avoided the accumulation of discrete errors, resulting in a higher precision in the final reconstructed sweeping surface. The method was also applicable to models with noisy data and those with missing data.

Key words: reverse engineering, surface reconstruction, swept surface, Gaussian mapping, geometric constraint

CLC Number:

TP391

LIU Shengjun, TAO Shanshan, WANG Haibo, LI Qinsong, LIU Xinru. High-precision reconstruction of swept surfaces with a planar path[J]. Journal of Graphics, 2025, 46(2): 425-436.

Figures/Tables 22

Fig. 1 Algorithm pipeline

Fig. 2 Unify curvature field ((a) Original minimum curvature field; (b) Distinguish different types of curvature points; (c) Align strong curvature points; (d) Smooth the area with weak curvature points; (e) Initial tracking path result)

Fig. 3 Rules for initial path tracking ((a) pi+1 falls at the apex or edge; (b) pi+1 falls inside the triangle)

Fig. 4 Gaussian mapping iterative process

Fig. 5 A set of cross-sectional profile examples

Fig. 6 Accumulation of discrete error in path tracking

Fig. 7 Quasi uniform non rational cubic B-spline approximation results ((a)~(c) Quasi uniform non rational cubic B-Spline approximation results with 6, 16, and 64 control points, respectively; (d) Curvature comb for quasi uniform non rational cubic B-Spline approximation (64 control points); (e) Curvature comb for line-arc fitting)

Fig. 8 Tangent space representation of ordered point sets

Fig. 9 Detection of line arc segments using tangent space representation method ((a) The midpoint line segment in the tangent space representation; (b) Path segmentation results)

Fig. 10 Comparison chart of profile ((a) Global view; (b) Side view))

Table 1 Comparison of profile curve errors

方法	最大误差	中间误差	平均误差
文献[10]	0.054 5	0.009 4	0.013 2
本文方法	0.014 7	0.004 0	0.006 9

Fig. 11 Comparison of paths generated by different methods with the real path and corresponding sweeping results ((a)~(c) The results of fitting paths using different methods; (d)~(f) The swept surfaces of the true contour along different fitting path)

Table 2 Comparison of path curve errors

方法	最大误差	中间误差	平均误差
文献[10]	0.099 9	0.038 6	0.041 6
B样条拟合	0.035 0	0.017 7	0.015 7
直线-圆弧段拟合	0.031 0	0.006 8	0.009 0

Table 3 Comparison of surface reconstruction errors

模型	方法	误差
模型	方法	MAE	RMSE
①	文献[10]	0.001 84	0.002 99
①	本文方法	0.000 70	0.000 88
②	文献[10]	0.000 37	0.000 60
②	本文方法	0.000 11	0.000 15
③	文献[10]	0.000 20	0.0002 96
③	本文方法	0.000 16	0.000 18
④	文献[10]	0.000 88	0.001 19
④	本文方法	0.000 32	0.000 39

Fig. 12 Profile, path extraction results, and surface reconstruction errors of model ① ((a) Original triangular mesh; (b) Side view of the profile; (c) Top view of the path; (d) Reference[10]; (e) Ours)

Fig. 13 Profile, path extraction results, and surface reconstruction errors of model ② ((a) Original triangular mesh; (b) Side view of the profile; (c) Top view of the path; (d) Reference [10]; (e) Ours)

Fig. 14 Profile, path extraction results, and surface reconstruction errors of model ③ ((a) Original triangular mesh; (b) Side view of the profile; (c) Top view of the path; (d) Reference [10]; (e) Ours)

Fig. 15 Profile, path extraction results, and surface reconstruction errors of model ④ ((a) Reference [10]; (b) Ours)

Fig. 16 Reconstruction results of noisy models with Gaussian noise ((a) Std=1.00; (b) Std=0.10; (c) Std=0.01)

Table 4 Reconstruction error of noisy models

噪声标准差	误差
噪声标准差	MAE	RMSE
Std=1.00	-	-
Std=0.10	0.000 523	0.000 62
Std=0.01	0.000 356	0.000 43

Fig. 17 Reconstruction results of data missing models ((a) Partial missing corners; (b) Missing along the path)

Table 5 Reconstruction error of data missing models

模型	对比	误差
模型	对比	MAE	RMSE
部分缺角	缺失数据	0.000 335	0.000 414
部分缺角	模型④	0.000 344	0.000 420
沿路径缺失	缺失数据	0.000 403	0.000 490
沿路径缺失	模型④	0.000 402	0.000 489

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