Mesh Database Library

Classical Papers in Software Design:

On the Criteria To Be Used in Decomposing Systems into Modules

D.L. Parnas

End-to-End Arguments in System Design

J.H. Saltzer, D.P. Reed and D.D. Clark

MeshEntity:

Entity Name	Figure	Simplices
Triangle		Edge = {2,3}, {3,1}, {1,2}
Quad		Edge = {1,2},{2,4}, {4,3}, {3,1}
Poly
Tet		Edge = {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {4,1} Face = {2,3,4}, {1,4,3}, {1,2,4}, {1,3, 2} Note: All face normals are outside the cell.
Penta5
Penta6
Hex		Edge = {1,2}, {1,5}, {2,4}, {3,1}, {3,7}, {4,3}, {5,7}, {6,2}, {6,5}, {7,8}, {8,4}, {8,6} Face = {1,5,3,7}, {2,4,6,8}, // x-Planes {1,2,5,6}, {3,7,4,8}, // y-Planes {1,3,2,4}, {5,6,7,8}, // z-Planes Note: All face normals are outside the cell.

Hexahedral to Tetrahedra Conversion:

{0,1,2,3,4,5,6,7,8}

{0,5,4,6}

{0,7,5,6}

{0,2,7,6}

{0,7,1,5}

{0,1,7,2}

{3,7,1,2}

Note: All the tetrahedra have
+ve Volume.

Calculating Volume of tetrahedra :

Given four points (pa,pb,pc,pd) of the tetrahedron, the determinant is +ve, of the point "pd" lies
below the plane passing through (pa,pb,pc); "Below" is defined so that (pa,pb,pc) appear in
counterclockwise order when viewed from above the plane. Returns a negative value if "pd"
lies above the plane.

Ref:   Arbitrary Precision Floating-Point Arithmatic and Fast Robust Geometric Predicates.
         Jonathan R. Shewchuck

Relations:

Relation{I1i2i3} : Start from MeshEntity I1, Go througth I2, and stop at I3.

Mesh Entity

Relations

Vertex

Relation00
Relation01
Relation02
Relation03

Edge

Relation10
Relation101
Relation102
Relation112

Face

Cell

References :

1. Miscalculating Area and Angles of a Needle-like Triangle
Prof. W. Kahan. http.cs.berkeley.edu/~wkahan/Triangle.pdf