def getQuadratures(self, tag, squarequad, trianglequad):
""" For a boundary identified by tag, return a list of quadrature points, weights and normals for each element """
from mappings import buildaffine
from elements import refpyramid
bdy = set(self.boundaries[tag].__iter__())
sx,sw = squarequad
sx = np.hstack((sx, np.zeros((len(sx),1))))
tx,tw = trianglequad
tx = np.hstack((np.zeros((len(tx),1))))
for ppoints in self.pyramidpoints:
x = []
w = []
normals = []
pyramidcentre = np.sum(self.getPoints(ppoints), axis=0) / 5.0
for tripoints in [[0,1,4],[1,2,4],[2,3,4],[3,0,4]]:
if bdy.issuperset(ppoints[tripoints]):
m = buildaffine(refpyramid[[0,1,4]], self.getPoints(ppoints[tripoints]))
x.append(m.apply(tx))
w.append(numpy.abs(m.dets(tx))*tw)
x0 = m.apply(refpyramid[0])[0]
n = m.apply(refpyramid[3])[0] - x0
normals.append(np.tile(-n * np.sign(np.dot(pyramidcentre - x0, n)), (len(tx),1) ))
if bdy.issuperset(ppoints[0:4]):
m = buildaffine(refpyramid[[0,1,3]], self.getPoints(ppoints[[0,1,3]]))
x.append(m.apply(sx))
w.append(numpy.abs(m.dets(sx)) * sw)
x0 = m.apply(refpyramid[0])[0]
n = m.apply(refpyramid[4])[0] - x0
# print pyramidcentre, x0, n, -n * np.sign(np.dot(pyramidcentre - x0, n))
normals.append(np.tile(-n * np.sign(np.dot(pyramidcentre - x0, n)), (len(sx),1) ))
if x: yield numpy.vstack(x), numpy.concatenate(w), numpy.vstack(normals)
else: yield numpy.zeros((0,3)), numpy.zeros((0,0)), numpy.zeros((0,3))
def addPyramid(self, pointids):
from elements import refpyramid
from mappings import buildaffine
points = self.getPoints(pointids)
self.maps.append(buildaffine(refpyramid[[0,1,3,4]], points[[0,1,3,4]]))