Predicates

Страница в процессе перевода.

This section lists predicates that can be used to check properties of geometric objects, both of themselves and relative to other geometric objects.

One important note to make is that these predicates are not necessarily exact. For example, rather than checking if a point p is exactly in a sphere of radius r centered at c, we check if norm(p-c) ≈ r with an absolute tolerance depending on the point type, so p might be slightly outside the sphere but still be considered as being inside. This absolute tolerance can be adjusted in specific scopes as discussed in the Tolerances section.

Robust predicates are often expensive to apply and approximations typically suffice. If needed, consider ExactPredicates.jl or AdaptivePredicates.jl.

isparametrized

# Meshes.isparametrized — Function

isparametrized(object)

Tells whether or not the geometric object is parametrized, i.e. can be called as object(u₁, u₂, ..., uₙ) with local coordinates (u₁, u₂, ..., uₙ) ∈ [0,1]ⁿ where n is the parametric dimension.

isperiodic

# Meshes.isperiodic — Function

isperiodic(topology)

Tells whether or not the topology is periodic along each parametric dimension.

isperiodic(geometry)

Tells whether or not the geometry is periodic along each parametric dimension.

isperiodic(grid)

Tells whether or not the grid is periodic along each parametric dimension.

issimplex

# Meshes.issimplex — Function

issimplex(geometry)

Tells whether or not the geometry is a simplex.

issimplex(connectivity)

Tells whether or not the connectivity is a simplex.

isclosed

# Meshes.isclosed — Function

isclosed(chain)

Tells whether or not the chain is closed.

A closed chain is also known as a ring.

isconvex

# Meshes.isconvex — Function

isconvex(geometry)

Tells whether or not the geometry is convex.

issimple

# Meshes.issimple — Function

issimple(polygon)

Tells whether or not the polygon is simple. See https://en.wikipedia.org/wiki/Simple_polygon.

issimple(chain)

Tells whether or not the chain is simple.

A chain is simple when all its segments only intersect at end points.

hasholes

# Meshes.hasholes — Function

hasholes(geometry)

Tells whether or not the geometry contains holes.

point₁ ≤ point₂

# Base.:< — Method

<(A::Point, B::Point)

The lexicographical order of points A and B (<).

A < B if the tuples of coordinates satisfy (a₁, a₂, ...) < (b₁, b₂, ...).

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

# Base.:> — Method

>(A::Point, B::Point)

The lexicographical order of points A and B (>).

A > B if the tuples of coordinates satisfy (a₁, a₂, ...) > (b₁, b₂, ...).

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

# Base.:≤ — Method

≤(A::Point, B::Point)

The lexicographical order of points A and B (\le).

A ≤ B if the tuples of coordinates satisfy (a₁, a₂, ...) ≤ (b₁, b₂, ...).

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

# Base.:≥ — Method

≥(A::Point, B::Point)

The lexicographical order of points A and B (\ge).

A ≥ B if the tuples of coordinates satisfy (a₁, a₂, ...) ≥ (b₁, b₂, ...).

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

point₁ ⪯ point₂

# Meshes.:≺ — Method

≺(A::Point, B::Point)

The product order of points A and B (\prec).

A ≺ B if aᵢ < bᵢ for all coordinates aᵢ and bᵢ.

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

# Meshes.:≻ — Method

≻(A::Point, B::Point)

The product order of points A and B (\succ).

A ≻ B if aᵢ > bᵢ for all coordinates aᵢ and bᵢ.

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

# Meshes.:⪯ — Method

⪯(A::Point, B::Point)

The product order of points A and B (\preceq).

A ⪯ B if aᵢ ≤ bᵢ for all coordinates aᵢ and bᵢ.

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

# Meshes.:⪰ — Method

⪰(A::Point, B::Point)

The product order of points A and B (\succeq).

A ⪰ B if aᵢ ≥ bᵢ for all coordinates aᵢ and bᵢ.

See https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets

point ∈ geometry

# Base.in — Method

point ∈ geometry

Tells whether or not the point is in the geometry.

geometry₁ ⊆ geometry₂

# Base.issubset — Method

geometry₁ ⊆ geometry₂

Tells whether or not geometry₁ is contained in geometry₂.

intersects

# Meshes.intersects — Function

intersects(geometry₁, geometry₂)

Tells whether or not geometry₁ and geometry₂ intersect.

References

Gilbert, E., Johnson, D., Keerthi, S. 1988. A fast Procedure for Computing the Distance Between Complex Objects in Three-Dimensional Space

Notes

The fallback algorithm works with any geometry that has a well-defined supportfun.

# Meshes.supportfun — Function

supportfun(geometry, direction)

Support function of geometry for given direction.

References

Gilbert, E., Johnson, D., Keerthi, S. 1988. A fast Procedure for Computing the Distance Between Complex Objects in Three-Dimensional Space

outer = [(0,0),(1,0),(1,1),(0,1)]
hole1 = [(0.2,0.2),(0.4,0.2),(0.4,0.4),(0.2,0.4)]
hole2 = [(0.6,0.2),(0.8,0.2),(0.8,0.4),(0.6,0.4)]
poly  = PolyArea([outer, hole1, hole2])
ball1 = Ball((0.5,0.5), 0.05)
ball2 = Ball((0.3,0.3), 0.05)
ball3 = Ball((0.7,0.3), 0.05)
ball4 = Ball((0.3,0.3), 0.15)

intersects(poly, ball1)

true

intersects(poly, ball2)

true

intersects(poly, ball3)

true

intersects(poly, ball4)

true

iscollinear

# Meshes.iscollinear — Function

iscollinear(A, B, C)

Tells whether or not the points A, B and C are collinear.

iscoplanar

# Meshes.iscoplanar — Function

iscoplanar(A, B, C, D)

Tells whether or not the points A, B, C and D are coplanar.