def _triangle_area_centroid_normal(nodes):
"""
Returns area,centroid,unitNormal
@param nodes:
list of three triangle vertices
@code
n = Normal = a x b
Area = 1/2 * |a x b|
V = <v1,v2,v3>
|V| = sqrt(v1^0.5+v2^0.5+v3^0.5) = norm(V)
Area = 0.5 * |n|
unitNormal = n/|n|
@endcode
"""
(n0, n1, n2) = nodes
vector = cross(n0 - n1, n0 - n2)
length = norm(vector)
normal = vector / length
if allclose(norm(normal), 1.) == False:
raise RuntimeError('function _triangle_area_centroid_normal, check...'
'\na = {0}\nb = {1}\nnormal = {2}\nlength = {3}\n'.format(
n0 - n1, n0 - n2, normal, length))
return (0.5 * length, (n0 + n1 + n2) /3, normal)
def _triangle_area_centroid_normal(nodes):
"""
Returns area,centroid,unitNormal
@param nodes:
list of three triangle vertices
@code
n = Normal = a x b
Area = 1/2 * |a x b|
V = <v1,v2,v3>
|V| = sqrt(v1^0.5+v2^0.5+v3^0.5) = norm(V)
Area = 0.5 * |n|
unitNormal = n/|n|
@endcode
"""
(n0, n1, n2) = nodes
vector = cross(n0 - n1, n0 - n2)
length = norm(vector)
normal = vector / length
if allclose(norm(normal), 1.) == False:
raise RuntimeError(
'function _triangle_area_centroid_normal, check...'
'\na = {0}\nb = {1}\nnormal = {2}\nlength = {3}\n'.format(
n0 - n1, n0 - n2, normal, length))
return (0.5 * length, (n0 + n1 + n2) / 3, normal)
def _normal(a, b):
"""Finds the unit normal vector of 2 vectors"""
vector = cross(a, b)
normal = vector / norm(vector)
assert allclose(norm(normal), 1.)
return normal
def _normal(a, b):
"""Finds the unit normal vector of 2 vectors"""
vector = cross(a, b)
normal = vector / norm(vector)
assert allclose(norm(normal), 1.)
return normal