The TETRA_VOLUME function computes properties of a tetrahedral mesh array. The basic property is the volume. An auxiliary data array may be supplied which specifies weights at each vertex which are interpolated through the volume during integration. Higher order moments (with respect to the X, Y, and Z axis) may be computed as well (with or without weights).
Returns the cumulative (weighted) volume of the tetrahedrons in the mesh.
Array of vertices [3, n].
Tetrahedral connectivity array.
Array of input auxiliary data (one value per vertex). If present, these values are used to weight a vertex. The volume area integral will linearly interpolate these values. The volume integral will linearly interpolate these values within each tetrahedra. The default weight is 1.0 which results in a basic volume.
Set this keyword to a named variable that will contain a three-element float vector which corresponds to the first order moments computed with respect to the X, Y and Z axis. The computation is:
where v is the (weighted) volume of the tetrahedron and c is the centroid of the tetrahedron, thus
yields the (weighted) centroid of the tetrahedral mesh.