Research on unified representation technology for manifold/non-manifold shapes based on manifold assembly

doi:10.11996/JG.j.2095-302X.2026030629

Abstract

Abstract:

To address the limitations of current kernels in solid representation and the efficiency bottlenecks in complex solid modeling, a manifold/non-manifold unified solid representation method based on the manifold assembly concept was proposed. By interpreting non-manifold solids as a union of finite manifold subsets, this approach overcome the limitation of traditional approaches, which relied on non-manifold entities or non-manifold constraints to represent non-manifold solids. The construction logic of the solid representation data structure was simplified without compromising the range of solid representations. This laid the foundation for improving the efficiency and versatility of manifold/non-manifold modeling algorithms. Furthermore, a bidirectional and flexible topological linking mechanism, along with a hybrid topological-link maintenance strategy, was proposed. While ensuring topological consistency, the proposed method improved the topological retrieval efficiency of complex models (containing topological entities at the 10⁴ level) by nearly 90% compared with OCC, approaching the performance of leading international commercial kernels such as CGM. This provided technical support for further enhancing system modeling efficiency.

Key words: non-manifold, manifold assembly, shape representation, topological structure, topological link

CLC Number:

TP391.72

XU Baowen, CHEN Hui, LI Jixing, ZHANG Bowen, LAN Jianwen. Research on unified representation technology for manifold/non-manifold shapes based on manifold assembly[J]. Journal of Graphics, 2026, 47(3): 629-640.

Figures/Tables 19

Fig. 1 The developmental trajectory of data structures for shape representation ((a) Winged-edge structure; (b) Radial-edge structure; (c) Hybrid-edge structure; (d) S-set representation; (e) Selective geometric complex; (f) Simplicial complex)

Fig. 2 A comparative analysis of the representational domain scope of data structures for shape representation

Fig. 3 Non-manifold modeling topological structure based on complex theory [10]

Fig. 4 The relationship diagram of Edge, Vertex, CoEdge and CoVertex

Fig. 5 Schematic illustration of the decomposition process for bodies across different dimensions ((a) 0-dimension; (b) 1-dimension; (c) 2-dimension; (d) 3-dimension)

Fig. 6 Two Non-Manifold shape representation methods in existing approaches ((a) By introducing non-manifold relationships; (b) By Introducing non-manifold topological elements)

Fig. 7 Schematic illustration of a non-manifold shape represented by the proposed method

Fig. 8 The limitation relationships between topological objects

Fig. 9 Topological structure shape representation diagram based on manifold assembly

Fig. 10 Three types of non-manifold shapes ((a) Low- dimensional connectivity; (b) Boundary reuse; (c) Mixed dimensions)[25]

Fig. 11 Two representation methods for complex non- manifold shapes ((a) Existing method; (b) Ours)

Fig. 12 The direction of the Loop determines the storage order of CoEdges

Fig. 13 Relative direction of CoEdge and Loop

Fig. 14 Topological relationship storage schemes in various kernels diagram ((a) Topological relationship; (b) Topological relationship of this paper)

Fig. 15 Local and global update diagram ((a) Local update; (b) Global update)

Fig. 16 Diagram of the non-manifold body constructed by the method in this paper

Fig. 17 Summary of test models ((a) Guide tube mounting seat model; (b) Annular part model; (c) Beam structure model; (d) Cylinder head model; (e) Wall panel model; (f) Powerplant assembly model; (g) Housing/Casing model; (h) Helicopter assembly model)

Table 1 Test results of downward topological link efficiency/ms

测试模型/(拓扑对象数量级)	CGM	OCC	ACIS	本文方法
直升机组装模型/(3×10⁴)	7.84	72.74	27.32	16.77
导筒安装座模型/(7×10³)	1.85	18.13	5.91	2.35
某环形零件模型/(4×10³)	0.97	10.20	3.94	1.32
某汽缸盖零件模型/(2×10³)	0.42	8.67	2.40	0.63
某对称件零件模型/(2×10³)	0.39	8.62	1.93	0.57
某动力装置模型/(2×10³)	0.52	8.24	2.17	0.55
某梁体零件模型/(2×10³)	0.37	7.90	2.53	0.34
某机壳零件模型/(1×10³)	0.23	6.01	1.40	0.21

Table 2 Test results of upward topological link efficiency/ms

测试模型/(拓扑对象数量级)	CGM	OCC	ACIS	本文方法
直升机组装模型/(3×10⁴)	15.61	8.25×10⁶	98.68	56.23
导筒安装座模型/(7×10³)	4.23	4.80×10⁵	18.22	10.68
某环形零件模型/(4×10³)	2.47	1.57×10⁵	11.74	5.27
某汽缸盖零件模型/(2×10³)	1.74	6.07×10⁴	7.51	2.71
某对称件零件模型/(2×10³)	1.12	4.51×10⁴	6.64	2.87
某动力装置模型/(2×10³)	1.36	4.64×10⁴	5.26	2.44
某梁体零件模型/(2×10³)	0.76	2.82×10⁴	8.33	1.92
某机壳零件模型/(1×10³)	0.68	2.05×10⁴	5.34	1.66

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