Implementing isconvex(Hexahedron) (#1259)

* first commit for isconvex(Hexahedron).

* simplify isconvex using all()

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

* added condition 2 for hexahedron convexity check

* cleanup and optimization

* simplifying for our hexahedron implementation

* Refactor tests

---------

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

Author: souma4

src/predicates/isconvex.jl

@@ -64,6 +64,8 @@ _isconvex(p::Polygon, ::Val{2}) = Set(eachvertex(convexhull(p))) == Set(eachvert
 
 _isconvex(p::Polygon, ::Val{3}) = isconvex(proj2D(p))
 
+isconvex(h::Hexahedron) = all(isconvex, boundary(h))
+
 isconvex(m::Multi) = isapproxequal(measure(convexhull(m)), measure(m))
 
 # --------------

test/predicates.jl

@@ -247,6 +247,87 @@ end
   @test !isconvex(poly2)
   poly = PolyArea(cart.([(0, 0), (1, 0), (1, 1), (0.5, 0.5), (0, 1)]))
   @test !isconvex(poly)
+  h = Hexahedron(
+    cart(0, 0, 0),
+    cart(1, 0, 0),
+    cart(1, 1, 0),
+    cart(0, 1, 0),
+    cart(0, 0, 1),
+    cart(1, 0, 1),
+    cart(1, 1, 1),
+    cart(0, 1, 1)
+  )
+  @test isconvex(h)
+  h = Hexahedron(
+    cart(0, 0, 0),
+    cart(1, 0, 0),
+    cart(0.9, 0.9, 0),
+    cart(0, 1, 0),
+    cart(0, 0, 1),
+    cart(1, 0, 1),
+    cart(1, 1, 1),
+    cart(0, 1, 1)
+  )
+  @test !isconvex(h)
+  h = Hexahedron(
+    cart(0, 0, 0),
+    cart(1, 0, 0),
+    cart(1, 1, 0),
+    cart(0, 1, 0),
+    cart(0.25, 0.25, 0.2),
+    cart(0.75, 0.25, 0.2),
+    cart(0.75, 0.26, 0.2),
+    cart(0.25, 0.26, 0.2)
+  )
+  @test isconvex(h)
+  h = Hexahedron(
+    cart(0, 0, 0),
+    cart(1, 0, 0),
+    cart(1, 1, 0),
+    cart(0, 1, 0),
+    cart(0.25, 0.25, 0.2),
+    cart(0.75, 0.25, 0.2),
+    cart(0.75, 0.25, 0.21),
+    cart(0.25, 0.25, 0.21)
+  )
+  @test !isconvex(h)
+  h = Hexahedron(
+    cart(0, 0, 0.1),
+    cart(1, 0, 0.1),
+    cart(1, 1, 0.1),
+    cart(0, 1, 0.1),
+    cart(0, 0, 0.3),
+    cart(1, 0, 0.2),
+    cart(1, 1, 0.3),
+    cart(0, 1, 0.2)
+  )
+  @test !isconvex(h)
+  h = Hexahedron(
+    cart(0, 0, 0),
+    cart(1, 0, 0),
+    cart(1, 1, 0),
+    cart(0, 1, 0),
+    cart(0, 0, 1),
+    cart(1, 0, 1),
+    cart(1, 1, -1),
+    cart(0, 1, -1)
+  )
+  @test !isconvex(h)
+  h0 = Hexahedron(
+    cart(0, 0, 0),
+    cart(1, 0, 0),
+    cart(1, 1, 0),
+    cart(0, 1, 0),
+    cart(0.25, 0.25, 0.2),
+    cart(0.75, 0.25, 0.2),
+    cart(0.75, 0.26, 0.2),
+    cart(0.25, 0.26, 0.2)
+  )
+  h1 = h0 |> Affine(AngleAxis(T(0.75), T(1.0), T(0.5), T(0.25)), T[-5, 2, 2])
+  h2 = h0 |> Stretch(T(1.0), T(2.0), T(5.0))
+  @test isconvex(h0)
+  @test isconvex(h1)
+  @test isconvex(h2)
 end
 
 @testitem "issubset" setup = [Setup] begin