Mesh Database Library



Classical Papers in Software Design:

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

MeshEntity:


Entity Name
Figure
Simplices
Triangle
                       Triangle                                
Edge = {2,3}, {3,1}, {1,2}
Quad
          Quad
Edge = {1,2},{2,4}, {4,3}, {3,1}
Poly
Poly

Tet
            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
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.

tet0546
tet0576
tet0276
tet0715
tet0712
tet3712

Calculating Volume of tetrahedra :


                                                          tetvol

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