Cylinder meshing

In this example we will see how to define generalized cylindric shapes, how we to generate their meshes and compute their intersection mesh. The Cylinder objects are distinct from their mesh and CloudMesher objects will allow to compute their meshes. Then knowing their meshes are convex by definition we can use the IntersectionMesher to compute the intersection.

import openturns as ot
import openturns.viewer as otv
import otmeshing as otm

Define a 3D cylinder with a disc-shaped base

N = 10
M = 2
dim = 3
print("Build cylinder 1")
xc1 = 0.0
yc1 = 0.0
R1 = 1.0
H1 = 4.0
f1 = ot.SymbolicFunction(
    ["x", "y"], [f"(x-({xc1}))^2+(y-({yc1}))^2"]
)
levelSet1 = ot.LevelSet(f1, ot.LessOrEqual(), R1**2)
base1 = ot.LevelSetMesher([N] * 2).build(
    levelSet1, ot.Interval([xc1 - R1, yc1 - R1], [xc1 + R1, yc1 + R1])
)
extension1 = ot.Interval([-H1 / 2] * (dim - 2), [H1 / 2] * (dim - 2))
injection1 = list(range(2, dim))
cyl1 = otm.Cylinder(base1, extension1, injection1, M)

Build cylinder 1

Define an other cylinder in another direction

yc2 = 0.8
zc2 = 0.0
R2 = 0.5
H2 = 4.0
f2 = ot.SymbolicFunction(
    ["y", "z"], [f"(y-({yc2}))^2+(z-({zc2}))^2"]
)
levelSet2 = ot.LevelSet(f2, ot.LessOrEqual(), R2**2)
base2 = ot.LevelSetMesher([N] * 2).build(
    levelSet2, ot.Interval([yc2 - R2, zc2 - R2], [yc2 + R2, zc2 + R2])
)
extension2 = ot.Interval([-H2 / 2] * (dim - 2), [H2 / 2] * (dim - 2))
injection2 = [0] + list(range(3, dim))
cyl2 = otm.Cylinder(base2, extension2, injection2, M)

Compute the mesh of both cylinders

method = otm.CloudMesher.BASIC
mesh1 = otm.CloudMesher(method).build(cyl1.getVertices())
mesh2 = otm.CloudMesher(method).build(cyl2.getVertices())

Plot cylinder1

shading = False
thetaX, thetaY, thetaZ = 6.1, 2.7, 3.3
drawEdge = True
graph1 = mesh1.draw3D(drawEdge, thetaX, thetaY, thetaZ, shading)
graph1.setLegendPosition("upper left")
graph1.setTitle("Cylinder1 mesh")
view = otv.View(graph1)

Plot cylinder2

graph2 = mesh2.draw3D(drawEdge, thetaX, thetaY, thetaZ, shading)
graph2.setLegendPosition("upper left")
graph2.setTitle("Cylinder1 mesh")
view = otv.View(graph2)

Compute the intersection, we know both meshes are convex by definition

inter12 = otm.IntersectionMesher().buildConvex([mesh1, mesh2])

Plot intersection

graph = inter12.draw3D(drawEdge, thetaX, thetaY, thetaZ, shading)
graph.setLegendPosition("upper left")
graph.setTitle("Cylinder intersection")
view = otv.View(graph)

otv.View.ShowAll()