Produces mapping between panels, segment and vertices of a surface. Grid elements are identified through the indices (m,n), where:
m: chordwise index
n: spanwise index
The same indexing is applied to panel, vertices and segments.
Elements: - panels=(M,N) - vertices=(M+1,N+1) - segments: these are divided in segments developing along the chordwise and spanwise directions.
Mapping structures: - Mpv: for each panel (mp,np) returns the chord/span-wise indices of its vertices, (mv,nv). This has size (M,N,4,2) - Mps: maps each panel (mp,np) to the ii-th segment. This has size (M,N,4,2)
# - Mps_extr: for each panel (m,n) returns the indices of the extrema of each side # of the panel.
Note: - mapping matrices are stored as np.int16 or np.int32 arrays
For each panel (m,n) it provides the ms,ns indices of each segment.
From panel of indices (m,n) to indices of vertices
Returns the panel for which the vertex is locally numbered as 0,1,2,3. Returns a (4,2) array such that its elements are:
[vv_local,(m,n) of panel]
where vv_local is the local verteix number.
Important: indices -1 are possible is the vertex does not have local index 0,1,2 or 3 with respect to any panel.
Mapping from panel of segments. self.Mpv is a (M,N,4,2) array such that:
- [m, n, local_segment_number,
chordwise/spanwise index of segment,]
Mapping from panel of vertices. self.Mpv is a (M,N,4,2) array such that its element are:
[m, n, local_vertex_number, spanwise/chordwise indices of vertex]
Mapping: - FROM: the index of a scalar quantity defined at panel collocation point and stored in 1D array. - TO: index of a scalar quantity defined at vertices and stored in 1D
- The Mpv1d_scalar has size (K,4) where:
[1d index of panel, index of vertex 0,1,2 or 3]
Maps from vertices to panels. Produces a (M+1,N+1,4,2) array, associating vertices to panels. Its elements are:
- [m vertex,
- n vertex,
- vertex local index,
chordwise/spanwise panel indices]
Mapping: - FROM: the index of a scalar quantity defined at vertices and stored in 1D array. - TO: index of a scalar quantity defined at panels and stored in 1D
- The Mpv1d_scalar has size (Kzeta,4) where:
[1d index of vertex, index of vertex 0,1,2 or 3 w.r.t. panel]