High-quality mesh generation for human hip based on ideal element size: methods and evaluation

Figures & data

Figure 1. Simplified results of femur model. (a) Original model, (b) 40% simplification, (c) 80% simplification, (d) 97.5% simplification and (e) Local amplification.

Figure 2. Mean and Hausdorff measurements of simplified model. (a) Mean distance of simplified model and (b) Hausdorffdistance of simplified model.

Figure 3. Mesh generation for femur. (a) Simplified model, (b) Partial model, (c) Surface mesh model, (d) Mesh refinement and (e) Body mesh model.

Figure 4. Mesh generation for vastus lateralis muscle. (a) Surface mesh model of vastus lateralis muscle and (b) Cutaway view of volume mesh of vastus lateralis.

Figure 5. Assembled model of hip.

Figure 6. Partial graphs of femur mesh. (A1) Mesh generation result of proposed method, (A2) Mesh generation result of proposed method, (B1) Mesh generation result of hypermesh software and (B2) Mesh generation result of hypermesh software.

Table 1. Quality of surface triangular element.

					Angular distribution of the minimum angle (%)
Algorithm example	Global size (mm)	Number of triangles	Maximum angle (°)	Minimum angle (°)	0°–15°	15°–30°	30°–45°	45°–60°
Wang’s algorithm	5	8306	167.36	3.31	0.36	0.79	0.79	90.85
	6	6672	167.36	3.31	0.45	1.09	9.71	88.74
Existing software	5	6706	172.85	3.52	1.92	7.81	12.36	77.75
	4.5	8434	163.94	3.50	1.06	3.78	13.79	81.37
Simplified model	—	25000	169.92	3.31	32.55	30.51	24.75	12.18

Table 2. Mean and Haurdorff distances of surface mesh.

Algorithm	Global dimension (mm)	Number of nodes	Number of triangles	Mean	Hausdorff	Local refinement
Wang’s algorithm	5	4157	8306	0.098799	1.100910	Yes
	6	3390	6672	0.183113	1.545679	Yes
Exiting software	5	3357	6706	0.188196	6.445955	No
	4.5	4221	8434	0.144433	2.258001	No

Figure 7. Quality analysis results for volume-mesh generation. (a) Quality analysis of volume-mesh generation for femur and (b) Quality analysis of volume-mesh generation for vastus lateralis muscle.

Figure 8. Tet collapse value distribution. (a) Tet collapse distribution of femur and (b) Tet collapse distribution of vastus lateralis muscle.

Table 3. Meshing efficiency analysis (unit: s).

Model	Ne	T	Tf	Tl	Ts	Tt
Femur	32392	207.61	18.16	18.86	84.12	86.47
Vastuslateralis	40424	214.29	16.39	17.12	83.94	96.84