def get_quadrangle_volume(vertices: Mat) -> float:
"""
================================================================================================================
Method :
================================================================================================================
Computes the surface of a quadrangle.
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Parameters :
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- vertices : the matrix containing the coordinates of the vertices of the quadrangle as vectors.
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Returns :
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- quadrangle_volume : the surface of the quadrangle.
"""
t0 = vertices[0, 1, 2]
t0 = vertices[0, 3, 2]
v0 = Triangle.get_triangle_volume(t0)
v1 = Triangle.get_triangle_volume(t1)
quadrangle_volume = v0 + v1
return quadrangle_volume
def __init__(self, vertices: Mat, polynomial_order: int):
"""
================================================================================================================
Class :
================================================================================================================
The Polygon class inherits from the Domain class to specifiy its attributes when the domain is a polygon.
================================================================================================================
Parameters :
================================================================================================================
- vertices : the matrix containing the vertices coordinates as vectors.
- polynomial_order : the polynomial order of integration over the polygon.
================================================================================================================
Attributes :
================================================================================================================
- centroid : the vector with values containing the center of mass of the polygon.
- volume : the volume of the polygon.
- diameter : the diameter of the polygon.
- quadrature_points : the matrix containing the quadrature points of the polygon.
- quadrature_weights : the vector containing the quadrature weights of the polygon.
"""
if not vertices.shape[0] > 4 and not vertices.shape[1] == 2:
raise TypeError(
"The domain dimension do not match that of a polygon")
else:
barycenter = Domain.get_domain_barycenter_vector(vertices)
volume = 0.0
# volume = Polygon.get_polygon_volume(vertices)
simplicial_sub_domains = Polygon.get_polygon_simplicial_partition(
vertices, barycenter)
# sub_domains_centroids = []
quadrature_points, quadrature_weights = [], []
for simplicial_sub_domain in simplicial_sub_domains:
# simplex_centroid = Domain.get_domain_barycenter_vector(simplicial_sub_domain)
simplex_volume = Triangle.get_triangle_volume(
simplicial_sub_domain)
simplex_quadrature_points, simplex_quadrature_weights = DunavantRule.get_triangle_quadrature(
simplicial_sub_domain, simplex_volume, polynomial_order)
volume += simplex_volume
quadrature_points.append(simplex_quadrature_points)
quadrature_weights.append(simplex_quadrature_weights)
# sub_domains_centroids.append(simplex_centroid)
# centroid = np.zeros(2,)
# for sub_domain_centroid in sub_domains_centroids:
# centroid += sub_domain_centroid
# number_of_vertices = vertices.shape[0]
# centroid = 1.0 / number_of_vertices * centroid
centroid = Polygon.get_polygon_centroid(vertices, volume)
diameter = Polygon.get_polygon_diameter(vertices)
quadrature_points = np.concatenate(quadrature_points, axis=0)
quadrature_weights = np.concatenate(quadrature_weights, axis=0)
super().__init__(centroid, volume, diameter, quadrature_points,
quadrature_weights)