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#! /usr/bin/env python
import openturns as ot
import math as m
ot.PlatformInfo.SetNumericalPrecision(6)
# 1D example
mesh1D = ot.Mesh()
print("Default 1D mesh=", mesh1D)
vertices = ot.Sample(0, 1)
vertices.add([0.5])
vertices.add([1.5])
vertices.add([2.1])
vertices.add([2.7])
simplicies = [[]] * 3
simplicies[0] = [0, 1]
simplicies[1] = [1, 2]
simplicies[2] = [2, 3]
mesh1D = ot.Mesh(vertices, simplicies)
mesh1Ddomain = ot.MeshDomain(mesh1D)
tree = ot.KDTree(vertices)
enclosingSimplex = ot.EnclosingSimplexAlgorithm(vertices, simplicies)
print("1D mesh=", mesh1D)
print("Is empty? ", mesh1D.isEmpty())
print("vertices=", mesh1D.getVertices())
print("simplices=", mesh1D.getSimplices())
print("volume=", "%.3f" % mesh1D.getVolume())
print("simplices volume=", mesh1D.computeSimplicesVolume())
p = [1.3]
print("is p=", p, " in mesh? ", p in mesh1Ddomain)
point = [1.8]
print("Nearest index(", point, ")=", tree.query(point))
simplex = enclosingSimplex.query(point)
found, coordinates = mesh1D.checkPointInSimplexWithCoordinates(point, simplex)
print(
"Nearest index(",
point,
"), found=",
found,
"simplex=",
int(simplex),
"coordinates=",
coordinates,
)
point = [-1.8]
simplex = enclosingSimplex.query(point)
found, coordinates = mesh1D.checkPointInSimplexWithCoordinates(point, simplex)
print(
"Nearest index(",
point,
"), found=",
found,
"simplex=",
int(simplex),
"coordinates=",
coordinates,
)
points = [[-0.25], [2.25]]
print("Nearest index(", points, ")=", tree.query(points))
print("P1 gram=\n", mesh1D.computeP1Gram())
# 2D case
vertices = [[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [1.5, 1.0], [2.0, 1.5], [0.5, 1.5]]
simplicies = [[0, 1, 2], [1, 2, 3], [2, 3, 4], [2, 4, 5], [0, 2, 5]]
mesh2D = ot.Mesh(vertices, simplicies)
tree = ot.KDTree(vertices)
print("2D mesh=", mesh2D)
print("volume=", "%.3f" % mesh2D.getVolume())
print("simplices volume=", mesh2D.computeSimplicesVolume())
point = [1.8] * 2
print("Nearest index(", point, ")=", tree.query(point))
points = [[-0.25] * 2, [2.25] * 2]
print("Nearest index(", points, ")=", tree.query(points))
print("P1 gram=\n", mesh2D.computeP1Gram())
# 3D case
vertices = ot.Sample(0, 3)
vertices.add([0.0, 0.0, 0.0])
vertices.add([0.0, 0.0, 1.0])
vertices.add([0.0, 1.0, 0.0])
vertices.add([0.0, 1.0, 1.0])
vertices.add([1.0, 0.0, 0.0])
vertices.add([1.0, 0.0, 1.0])
vertices.add([1.0, 1.0, 0.0])
vertices.add([1.0, 1.0, 1.0])
simplicies = [[]] * 6
simplicies[0] = [0, 1, 2, 4]
simplicies[1] = [3, 5, 6, 7]
simplicies[2] = [1, 2, 3, 6]
simplicies[3] = [1, 2, 4, 6]
simplicies[4] = [1, 3, 5, 6]
simplicies[5] = [1, 4, 5, 6]
mesh3D = ot.Mesh(vertices, simplicies)
tree = ot.KDTree(vertices)
print("3D mesh=", mesh3D)
print("volume=", "%.3f" % mesh3D.getVolume())
print("simplices volume=", mesh3D.computeSimplicesVolume())
point = [1.8] * 3
print("Nearest index(", point, ")=", tree.query(point))
points = [[-0.25] * 3, [2.25] * 3]
print("Nearest index(", points, ")=", tree.query(points))
print("P1 gram=\n", mesh3D.computeP1Gram())
rotation = ot.SquareMatrix(3)
rotation[0, 0] = m.cos(m.pi / 3.0)
rotation[0, 1] = m.sin(m.pi / 3.0)
rotation[1, 0] = -m.sin(m.pi / 3.0)
rotation[1, 1] = m.cos(m.pi / 3.0)
rotation[2, 2] = 1.0
# isregular bug
time_grid = ot.RegularGrid(0.0, 0.2, 40963)
mesh = ot.Mesh(time_grid)
print(mesh.isRegular())
# numerical limit testcase
m1 = ot.IntervalMesher([1] * 2).build(ot.Interval([0.0] * 2, [1.0] * 2))
simplex = 0
point = [0.8, 0.2]
found, coordinates = m1.checkPointInSimplexWithCoordinates(point, simplex)
assert found, "not inside"
# Fix https://github.com/openturns/openturns/issues/1547
# We force the checking
try:
vertices = [[2.1], [2.8], [3.5], [4.2], [4.9], [5.6], [6.3], [7.0]]
simplices = [[3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]
mesh = ot.Mesh(vertices, simplices, True)
weights = mesh.computeWeights()
except Exception:
print("ok")
# sub-mesh
n = 4
m2 = ot.IntervalMesher([n] * 2).build(ot.Interval([0.0] * 2, [1.0] * 2))
submesh = m2.getSubMesh([0, 2])
print(f"submesh={submesh}")
assert len(submesh.getSimplices()) == 2
assert sum(submesh.computeSimplicesVolume()) == 1 / 16, "wrong submesh"
if ot.PlatformInfo.HasFeature("boost"):
vertices1 = [[0.0, 0.0], [2.0, 0.0], [0.0, 1.0]]
simplices1 = [[0, 1, 2]]
mesh1 = ot.Mesh(vertices1, simplices1)
mesh2 = ot.IntervalMesher([2] * 2).build(ot.Interval([-1.0] * 2, [1.0] * 2))
intersection = mesh1.intersect(mesh2)
vertices3 = [[0, 1], [0, 0], [1, 0], [0, 1], [1, 0], [1, 0.5]]
simplices3 = [[0, 1, 2], [3, 4, 5]]
mesh3 = ot.Mesh(vertices3, simplices3)
assert intersection == mesh3, "wrong intersection"
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