implements a region in orientation space The region is bounded by planes normal to quaternions N i.e., all quaternions q inside a region satisfy the condition dot(q, N) <= 0 or dot(-q, N) <= 0 for all N
The most common one is the fundamental region of a pair of symmetries, which is what fundamentalRegion returns and what project2FundamentalRegion projects into. Setting antipodal identifies q and inv(q), i.e. adds grain exchange symmetry.
Syntax
oR = fundamentalRegion(cs1,cs2)
oR = orientationRegion(N)
oR = orientationRegion(N,'antipodal')Input
| N | quaternion, the normals of the bounding faces |
| cs1, cs2 | crystalSymmetry |
Output
| oR | orientationRegion |
Options
| antipodal | identify q and inv(q) |
Class Properties
| N | quaternion, the normals of the bounding faces |
| V | orientation, the vertices |
| F | the faces as indices into V |
| E | the edges |
| faceCenter | orientation, center of each face |
| CS1, CS2 | the two symmetry |
| antipodal | identify q and inv(q) |
Example
oR = fundamentalRegion(crystalSymmetry('432'))oR = orientationRegion
crystal symmetry: 432
max angle: 62.7994°
face normales: 14
vertices: 24