def __init__(self, datamodel, points):
"""precomputations which are identical for all mappings"""
self.datamodel = datamodel
self.hierarchy = self.datamodel.hierarchy
self.complex = self.hierarchy[-1]
self.group = self.complex.group
#cache the index a point is in. if it remains unchanged, no need to update
count = len(points)
self.index = np.zeros((3, count), np.int8)
#precompute subtriangles
primal = self.complex.geometry.primal[ self.complex.topology.FV]
mid = util.normalize(np.roll(primal, +1, 1) + np.roll(primal, -1, 1))
dual = self.complex.geometry.dual
basis = np.empty((self.complex.topology.D0, 3, 2, 3, 3))
for i in range(3):
basis[:,i,0,0,:] = primal[:,i ,:]
basis[:,i,1,0,:] = primal[:,i ,:]
basis[:,i,0,1,:] = mid [:,i-2,:]
basis[:,i,1,1,:] = mid [:,i-1,:]
basis[:,:,:,2,:] = dual [:,None, None,:] #each subtri shares the dual vert
self.subdomain = util.adjoint(basis) #precompute all we can for subdomain compu
self.subdomain[:,:,1,:,:] *= -1 #flip sign
self.subdomain = self.subdomain.reshape(-1,6,3,3) #fold sign axis
self.update(points)
def triangle_invert(self):
"""
pre-invert triangle support.
this is useful for computing projections on triangles
adjoint is fine; we normalize coords anyway
"""
tri_coords = util.gather(self.topology.FV, self.primal)
self.inverted_triangle = util.adjoint(tri_coords)
def subdivide_position(self, position):
"""calc primal coords from parent"""
#one child for each parent
vertex_vertex = position
#each new vert lies at midpoint
edge_vertex = util.normalize(self.edge_mid*vertex_vertex)
#ordering convention is vertex-vertex + edge-vertex
position = np.vstack((vertex_vertex, edge_vertex))
#calc subdivision planes
central = util.gather(self.FEi, edge_vertex)
planes = util.adjoint(central)
return position, planes