def test2to3(self):
""" build an affine map to map 3 points in 2-space to 3 points in 3-space """
for _ in range(self.N):
pf = numpy.random.random((3,2))
pt = numpy.random.random((3,3))
A = buildaffine(pf, pt)
numpy.testing.assert_array_almost_equal(A.apply(pf), pt)
def test3to3(self):
""" build an affine map to map 4 points in 3-space to 4 other points in 3-space """
for _ in range(self.N):
pf = numpy.random.random((4,3))
pt = numpy.random.random((4,3))
A = buildaffine(pf, pt)
numpy.testing.assert_array_almost_equal(A.apply(pf), pt)
numpy.testing.assert_array_almost_equal(A.applyinv(A.apply(pf)), pf)
def pyramid(self, points, degrees):
indices = sum([d.indices for d in degrees if d is not None], [])
ninternal = self.pyramidform.nfns - len(indices)
indices.extend(range(self.index, self.index + ninternal))
self.index += ninternal
map = buildaffine(points[[0,1,3,4]], refpyramid[[0,1,3,4]])
pullback = self.createpullback(map)
elt = Element(self.pyramidform, degrees, pullback, map.applyinv, indices)
return elt
def test3to3missing(self):
""" build an affine map to map 3 points in 3-space to 3 points in 3-space, preserving orthogonal vectors"""
for _ in range(self.N):
pf = numpy.random.random((3,3))
pt = numpy.random.random((3,3))
A = buildaffine(pf, pt)
numpy.testing.assert_array_almost_equal(A.apply(pf), pt)
# construct the orthogonal vector
fognal = numpy.cross(pf[1] - pf[0], pf[2] - pf[0]) + pf[0]
numpy.testing.assert_array_almost_equal(numpy.dot(A.apply(fognal) - pt[0], (pt[1:] - pt[0]).transpose()), [[0,0]])
numpy.testing.assert_array_almost_equal(A.applyinv(A.apply(pf)), pf)
def createExternalDegree(vertices):
if len(refvertices) == 0:
pullback = Pullback(lambda p: vertices[numpy.ix_([0])])
else:
map = buildaffine(refvertices, vertices[0:len(refvertices)])
pullback = self.createpullback(map)
# print "vertices", vertices
# print "affine", map.linear
indices = range(self.index, self.index + len(dofs))
self.index += len(dofs)
return ExternalDegree(pullback, refpoints, dofs, indices)