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The dragon, a symbol of Chinese culture. The source data (reconstructed surface mesh ) can be found in The Stanford 3D Scanning Repository, also at Georgia Institute of Technology's Large Geometric Models Archive. The data size is huge (566,098 vertices, 1,132,830 triangles). Luckily, the one shown below can be downloaded from Inria's Free 3D Meshes Download page. The size is much smaller.

The input surface mesh, 21104 nodes, 41964 triangles.

The constrained Delaunay tetrahedralization, 22847 nodes, 74922 tetrahedra, and 44964 boundary faces.

The quality Delaunay tetrahedralization (Statistics).

[si@a302n3]# ~/tetgen-dbg/tetgen -pqV dragon-50,010.smesh Opening dragon-50,010.smesh. Constructing Delaunay tetrahedrization. Total flips: 898786, where T23 543115, T32 355671, T22 0, T44 0 Delaunay seconds: 10.08 Creating surface mesh. Constructing mapping from indices to points. Unifying segments. Constructing mapping from points to subfaces. Merging coplanar facets. Perturbing vertices. Constructing mapping from points to tetrahedra. 0 break points are inserted. Delaunizing segments. Marking segments have acute corners. Constructing mapping from points to segments. Constructing mapping from points to tetrahedra. 25952 protect points are inserted. Constraining facets. Constructing mapping from points to tetrahedra. The biggest cavity: 22 faces, 13 vertices Enlarged 0 times Segment and facet seconds: 13.37 Removing unwanted tetrahedra. Marking concavities for elimination. Marking neighbors of marked tetrahedra. Deleting marked tetrahedra. Hole seconds: 0.57 Removing degenerate tets. 0 degeneracies are removed. Repair seconds: 0.18 Adding Steiner points to enforce quality. Marking sharp subfaces. 806 subfaces have been marked. Marking skinny subfaces. 41395 subfaces have been marked. Initializing protecting spheres. Constructing mapping from points to tetrahedra. Splitting encroached subsegments. 327012 points are inserted. Splitting encroached subfaces. 87125 points are inserted. Splitting bad tetrahedra. 451977 points are inserted. Removing slivers. 19044 slivers are removed. 67 sliver(s) survived. 146 points are inserted. Total 866260 points are inserted. Quality seconds: 2124.14 Writing dragon-50,010.1.node. Writing dragon-50,010.1.ele. Writing dragon-50,010.1.face. Output seconds: 12.84 Total running seconds: -2133.79 Statistics: Input points: 50010 Input facets: 100040 Input holes: 0 Input regions: 0 Mesh points: 942222 Mesh tetrahedra: 3843078 Mesh faces: 8308678 Mesh subfaces: 1245336 Mesh subsegments: 663264 Mesh quality statistics: Smallest volume: 9.7226e-09 | Largest volume: 11697 Shortest edge: 0.001022 | Longest edge: 61.517 Smallest dihedral: 0.078977 | Largest dihedral: 179.8633 Radius-edge ratio histogram: < 0.707 : 33962 | 1.6 - 1.8 : 293726 0.707 - 1 : 982103 | 1.8 - 2 : 142219 1 - 1.1 : 487318 | 2 - 2.5 : 35400 1.1 - 1.2 : 474786 | 2.5 - 3 : 15942 1.2 - 1.4 : 814193 | 3 - 10 : 27362 1.4 - 1.6 : 534521 | 10 - : 1546 (A tetrahedron's radius-edge ratio is its radius of circumsphere divided by its shortest edge length) Aspect ratio histogram: 1.1547 - 1.5 : 0 | 15 - 25 : 46837 1.5 - 2 : 0 | 25 - 50 : 7966 2 - 2.5 : 39 | 50 - 100 : 563 2.5 - 3 : 74598 | 100 - 300 : 168 3 - 4 : 867452 | 300 - 1000 : 15 4 - 6 : 2121883 | 1000 - 10000 : 4 6 - 10 : 622929 | 10000 - 100000 : 0 10 - 15 : 100624 | 100000 - : 0 (A tetrahedron's aspect ratio is its longest edge length divided by the diameter of its inscribed sphere) Dihedral Angle histogram: 0 - 10 degrees: 68166 | 90 - 100 degrees: 695614 10 - 20 degrees: 334808 | 100 - 110 degrees: 884078 20 - 30 degrees: 983070 | 110 - 120 degrees: 752756 30 - 40 degrees: 1160238 | 120 - 130 degrees: 481053 40 - 50 degrees: 837180 | 130 - 140 degrees: 279815 50 - 60 degrees: 409134 | 140 - 150 degrees: 163749 60 - 70 degrees: 50479 | 150 - 160 degrees: 99296 70 - 80 degrees: 21980 | 160 - 170 degrees: 53642 80 - 90 degrees: 410609 | 170 - 180 degrees: 489

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Hang Si