# Boolean Operations
# ==================

# Perform boolean operations with closed (manifold) surfaces.
# Boolean/topological operations (intersect, union, difference) methods
# are implemented for `pyvista.PolyData` mesh types only and are
# accessible directly from any `pyvista.PolyData` mesh. Check out
# `pyvista.PolyDataFilters` and take a look at the following
# filters:
# `pyvista.PolyDataFilters.boolean_difference()`
# `pyvista.PolyDataFilters.boolean_union()`
# `pyvista.PolyDataFilters.boolean_intersection()`
# Essentially, boolean union, difference, and intersection are all the
# same operation. Just different parts of the objects are kept at the
# end.
# The `-` operator can be used between any two `pyvista.PolyData`
# meshes in PyVista to cut the first mesh by the second.  These meshes
# must be all triangle meshes, which you can check with
# `pyvista.PolyData.is_all_triangles`.

# NOTE:
#     For merging, the `+` operator can be used between any two meshes
#     in PyVista which simply calls the `.merge()` filter to combine
#     any two meshes.  This is different from the operator `|` in PyVista
#     which simply calls the `boolean_union` filter as it simply superimposes
#     the two meshes without performing additional calculations on the result.
#     The `&` operator in PyVista simply calls the `boolean_intersection`.

# WARNING:
#     If your boolean operations don't react the way you think they
#     should (i.e. the wrong parts disappear), one of your meshes
#     probably has its normals pointing inward. Use
#     `pyvista.PolyDataFilters.plot_normals()` to visualize the normals.

import pyvista as pv

sphere_a = pv.Sphere()
sphere_b = pv.Sphere(center=(0.5, 0, 0))

# Boolean Union
# -------------

# Perform a boolean union of `A` and `B` using the
# `pyvista.PolyDataFilters.boolean_union()` filter.
# The union of two manifold meshes `A` and `B` is the mesh
# which is in `A`, in `B`, or in both `A` and `B`.
# Order of operands does not matter for boolean union (the operation is
# commutative).
result = sphere_a | sphere_b
pl = pv.Plotter()
_ = pl.add_mesh(sphere_a, color='r', style='wireframe', line_width=3)
_ = pl.add_mesh(sphere_b, color='b', style='wireframe', line_width=3)
_ = pl.add_mesh(result, color='lightblue')
pl.camera_position = 'xz'
pl.show()

# Boolean Difference
# ------------------

# Perform a boolean difference of `A` and `B` using the
# `pyvista.PolyDataFilters.boolean_difference()` filter or the
# `-` operator since both meshes are `pyvista.PolyData`.
# The difference of two manifold meshes `A` and `B` is the volume
# of the mesh in `A` not belonging to `B`.
# Order of operands matters for boolean difference.
result = sphere_a - sphere_b
pl = pv.Plotter()
_ = pl.add_mesh(sphere_a, color='r', style='wireframe', line_width=3)
_ = pl.add_mesh(sphere_b, color='b', style='wireframe', line_width=3)
_ = pl.add_mesh(result, color='lightblue')
pl.camera_position = 'xz'
pl.show()

# Boolean Intersection
# --------------------

# Perform a boolean intersection of `A` and `B` using the
# `pyvista.PolyDataFilters.boolean_intersection()` filter.
# The intersection of two manifold meshes `A` and `B` is the mesh
# which is the volume of `A` that is also in `B`.
# Order of operands does not matter for boolean intersection (the
# operation is commutative).
result = sphere_a & sphere_b
pl = pv.Plotter()
_ = pl.add_mesh(sphere_a, color='r', style='wireframe', line_width=3)
_ = pl.add_mesh(sphere_b, color='b', style='wireframe', line_width=3)
_ = pl.add_mesh(result, color='lightblue')
pl.camera_position = 'xz'
pl.show()

# Behavior due to flipped faces
# =============================

# Note that these boolean filters behave differently depending on the
# orientation of the faces. This is because the orientation determines
# which parts are considered to be the "outside" or the "inside" portion
# of the mesh. This example uses `flip_faces()`
# to flip the faces.
# Boolean difference with both cube and sphere faces oriented
# outward.  This is the "normal" behavior.
cube = pv.Cube().triangulate().subdivide(3)
sphere = pv.Sphere(radius=0.6)
result = cube.boolean_difference(sphere)
result.plot(color='lightblue')

# Boolean difference with cube faces outward, sphere faces inward.
cube = pv.Cube().triangulate().subdivide(3)
sphere = pv.Sphere(radius=0.6).flip_faces()
result = cube.boolean_difference(sphere)
result.plot(color='lightblue')

# Boolean difference with cube faces inward, sphere faces outward.
cube = pv.Cube().triangulate().subdivide(3).flip_faces()
sphere = pv.Sphere(radius=0.6)
result = cube.boolean_difference(sphere)
result.plot(color='lightblue')

# Both cube and sphere faces inward.
cube = pv.Cube().triangulate().subdivide(3).flip_faces()
sphere = pv.Sphere(radius=0.6).flip_faces()
result = cube.boolean_difference(sphere)
result.plot(color='lightblue')

# ----------------------------------------------------------------------
# Generated by sphinx-examples-as-code https://github.com/pyvista/sphinx-examples-as-code