implement isconvex for Pyramid (#1266)

* implement specialized isconvex for Pyramid

* use internal field access instead of accessor in Pyramid

* Export base in Polytope section for consistency

* document pyramid base order and convexity requirement

* add test for pyramid base

* Incorporate Joshua's suggestions

* fix typo and use base function for pyramid

* Apply suggestion from @juliohm

* Add apex for Pyramid

* Update src/geometries/polytopes/pyramid.jl

Co-authored-by: Joshua Lampert <[email protected]>

* Apply suggestion from @juliohm

* Apply suggestion from @juliohm

* format test/predicates.jl

---------

Co-authored-by: Júlio Hoffimann <[email protected]>
Co-authored-by: Joshua Lampert <[email protected]>

Author: 3 people

src/Meshes.jl

@@ -226,6 +226,8 @@ export
   angles,
   innerangles,
   normal,
+  base,
+  apex,
   ≗,
 
   # multi-geometries

src/geometries/polytopes/pyramid.jl

@@ -6,22 +6,31 @@
     Pyramid(p1, p2, p3, p4, p5)
 
 A pyramid with points `p1`, `p2`, `p3`, `p4`, `p5`.
+
+The first four points form the base and the last is the apex.
 """
 @polytope Pyramid 3 5
 
 nvertices(::Type{<:Pyramid}) = 5
 
+function base(p::Pyramid)
+  a, b, c, d, o = p.vertices
+  Quadrangle(a, b, c, d)
+end
+
+apex(p::Pyramid) = last(p.vertices)
+
 ==(p₁::Pyramid, p₂::Pyramid) = p₁.vertices == p₂.vertices
 
 Base.isapprox(p₁::Pyramid, p₂::Pyramid; atol=atol(lentype(p₁)), kwargs...) =
   all(isapprox(v₁, v₂; atol, kwargs...) for (v₁, v₂) in zip(p₁.vertices, p₂.vertices))
 
-function (pyramid::Pyramid)(u, v, w)
+function (p::Pyramid)(u, v, w)
   if (u < 0 || u > 1) || (v < 0 || v > 1) || (w < 0 || w > 1)
-    throw(DomainError((u, v, w), "pyramid(u, v, w) is not defined for u, v, w outside [0, 1]³."))
+    throw(DomainError((u, v, w), "p(u, v, w) is not defined for u, v, w outside [0, 1]³."))
   end
-  a, b, c, d, o = vertices(pyramid)
-  q = Quadrangle(a, b, c, d)
+  q = base(p)
+  o = apex(p)
   s = Segment(q(u, v), o)
   s(w)
 end

src/predicates/isconvex.jl

@@ -66,6 +66,8 @@ _isconvex(p::Polygon, ::Val{3}) = isconvex(proj2D(p))
 
 isconvex(h::Hexahedron) = all(isconvex, boundary(h))
 
+isconvex(p::Pyramid) = isconvex(base(p))
+
 isconvex(m::Multi) = isapproxequal(measure(convexhull(m)), measure(m))
 
 # --------------

test/polytopes.jl

@@ -954,6 +954,8 @@ end
   equaltest(p)
   isapproxtest(p)
   vertextest(p)
+  @test base(p) == Quadrangle(cart(0, 0, 0), cart(1, 0, 0), cart(1, 1, 0), cart(0, 1, 0))
+  @test apex(p) == cart(0, 0, 1)
 
   p = Pyramid(cart(0, 0, 0), cart(1, 0, 0), cart(1, 1, 0), cart(0, 1, 0), cart(0, 0, 1))
   @test sprint(show, p) == "Pyramid((x: 0.0 m, y: 0.0 m, z: 0.0 m), ..., (x: 0.0 m, y: 0.0 m, z: 1.0 m))"

test/predicates.jl

@@ -328,6 +328,10 @@ end
   @test isconvex(h0)
   @test isconvex(h1)
   @test isconvex(h2)
+  p = Pyramid(cart(0, 0, 0), cart(1, 0, 0), cart(1, 1, 0), cart(0, 1, 0), cart(0, 0, 1))
+  @test isconvex(p)
+  p = Pyramid(cart(0, 0, 0), cart(1, 0, 0), cart(0.25, 0.25, 0), cart(0, 1, 0), cart(0, 0, 1))
+  @test !isconvex(p)
 end
 
 @testitem "issubset" setup = [Setup] begin