Predicates
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.
Exact arithmetic is expensive to apply and approximations are typically sufficient; exact predicates are available in ExactPredicates.jl if you need them.
isparametrized
Meshes.isparametrized — Functionisparametrized(geometry)Tells whether or not the geometry is parametrized, i.e. can be called as geometry(u₁, u₂, ..., uₙ) with local coordinates (u₁, u₂, ..., uₙ) ∈ [0,1]ⁿ where n is the parametric dimension.
See also paramdim.
Meshes.paramdim — Functionparamdim(geometry)Return the number of parametric dimensions of the geometry. For example, a sphere embedded in 3D has 2 parametric dimensions (polar and azimuthal angles).
See also isparametrized.
paramdim(polytope)Return the parametric dimension or rank of the polytope.
paramdim(connectivity)Return the parametric dimension of the connectivity.
paramdim(domain)Return the number of parametric dimensions of the domain as the number of parametric dimensions of its elements.
isperiodic
Meshes.isperiodic — Functionisperiodic(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 — Functionissimplex(geometry)Tells whether or not the geometry is a simplex.
issimplex(connectivity)Tells whether or not the connectivity is a simplex.
isclosed
Meshes.isclosed — Functionisclosed(chain)Tells whether or not the chain is closed.
A closed chain is also known as a ring.
isconvex
Meshes.isconvex — Functionisconvex(geometry)Tells whether or not the geometry is convex.
issimple
Meshes.issimple — Functionissimple(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 — Functionhasholes(geometry)Tells whether or not the geometry contains holes.
point ∈ geometry
Base.in — Methodpoint ∈ geometryTells whether or not the point is in the geometry.
geometry₁ ⊆ geometry₂
Base.issubset — Methodgeometry₁ ⊆ geometry₂Tells whether or not geometry₁ is contained in geometry₂.
intersects
Meshes.intersects — Functionintersects(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 — Functionsupportfun(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 = Point2[(0,0),(1,0),(1,1),(0,1)]
hole1 = Point2[(0.2,0.2),(0.4,0.2),(0.4,0.4),(0.2,0.4)]
hole2 = Point2[(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)trueintersects(poly, ball2)falseintersects(poly, ball3)falseintersects(poly, ball4)trueiscollinear
Meshes.iscollinear — Functioniscollinear(A, B, C)Tells whether or not the points A, B and C are collinear.
iscoplanar
Meshes.iscoplanar — Functioniscoplanar(A, B, C, D)Tells whether or not the points A, B, C and D are coplanar.