1. An Approach to Automated Decomposition of Volumetric Mesh Chuhua Xian, Shuming Gao and Tianming Zhang Zhejiang University

3. Volumetric Mesh Decomposition

4. Overview Decompose the splitter groups based on min-flux rule Input Surface Mesh Segmentation and Feature Recognition Output Find the OBLFs of the adjacent features and construct the splitter groups

5. Decompose the splitter groups based on min-flux rule Input Surface Mesh Segmentation and Feature Recognition Output Find the OBLFs of the adjacent features and construct the splitter groups Overview

6. Decompose the splitter groups based on min-flux rule Input Surface Mesh Segmentation and Feature Recognition Output Find the OBLFs of the adjacent features and construct the splitter groups

7. Some Concepts the element is called surface element if one of its faces has no adjacent element. Otherwise, it is called inner element; Feature: we define a form feature as a semantic partial shape that has an engineering meaning, such as a protrusion. Outer boundary lines of two adjacent features (abbr. OBLF) is the set of the common edges of F0 and F1.

8. Surface Mesh Segmentation and Feature Recognition We use method of the following paper to segment the surface mesh and recognize the surface features: Gao, S., Zhao, W., Lin, H., Yang, F., Chen, X.. Feature suppression based CAD mesh model simplification. Computer- Aided Design 2010. We also allow users to select form features manually.

9. Find OBLFs of adjacent Features Inner elements Surface elements OBLFs

10. Construct the Splitter Group Elements of Splitter Group

11. Since the elements of the splitter group are obtained by BFS algorithm, it is single- connected.

12. After the splitter groups are constructed, the inner elements are partitioned. But the elements in the splitter groups are not. s

13. Decomposition of splitter group In our paper, we use the flux-based to decompose the splitter groups.

14. Flux Model Suppose is an electrified curve in, then the electric field of a point can be expressed as The flux of the surface S is

15. In the discrete form, these equation is rewritten as and

16. For l, there are may be many surface containing it. We choose the one with minimal flux, such as We regard it as the minimal flux rule.

17. Decomposition of splitter groups We formulate the cutting problem as a graph partition problem.

18. In the dual graph, each elements is a node, and there is an edge between two nodes if and only if their corresponding elements are face-adjacent. The source node and the target node should be added into the graph.

19. Weight Computation In this step, we compute the weight of the edge in the graph by this equation here, is computed by

20. Graph Cut Using the max-flow-min-cut algorithm, we will partition the elements of the splitter group into two subgroups. By assign them into corresponding adjacent groups, we obtain the final results.

21. Results

23. An example with different sizes of elements

24. Decompose a model into different ways

25. An example with overlap splitter group

26. Compared with the minimal area rule Minimal are ruleMinimal flux rule

27. Minimal are ruleMinimal flux rule weight Area

28. More examples…in our paper

29. Applications Form feature of volumetric mesh reuse

30. Applications Local re-mesh for volumetric mesh editing

31. Conclusions In this paper, we have presented an effective approach for the automated decomposition of a volumetric mesh. The quality of the decomposed semantic features, consisting of volumetric elements, is guaranteed by using our graph cut algorithm. The decomposed semantic features can be complex predefined features with complicated boundary surfaces and curves. The method is quite efficient and can handle both tetrahedral and hexahedral meshes.

32. Limitations Our resultAnother possible result

33. Thank you