Triangular Surface Patch Model

Some nonaxisymmetric particle shapes such as ellipsoids, quadratic prisms and regular polyhedral prisms are directly included in the Fortran program 

The particle shape data is based on a surface description using a triangular surface patch model. There are various 3D object file formats suitable for a meshed particle shape. We decided for the Wavefront. obj file format but the 

To compute the T-matrix elements by surface integrals we employ a modified midpoint or centroid quadrature. The integral over each surface patch is approximated by multiplying the value of the integrand at the centroid by the patch area [79] 

For a sufficiently large number of surface patches, the use of this centroid integration is satisfactorily accurate. In convergence checks versus the number of triangular faces, we found that this centroid quadrature is quite stable and the computational results are not much influenced by the number of integration elements. 

As an example, we consider a sphere which has been cut at a quarter of its diameter on the z-axis as shown in Fig. 3.28. The cut sphere has been meshed 

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