Fix area for higher dimensions

src/polygons.jl

@@ -13,17 +13,27 @@ The above copyright notice and this permission notice shall be included in all c
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 =#
 
-function area(contour::AbstractVector{Point{N, T}}) where {N, T}
+function area(contour::AbstractVector{Point{2, T}}) where {T}
     n = length(contour)
     A = zero(T)
-    p=n; q=1
+    p=lastindex(contour)
+    q=firstindex(contour)
     while q <= n
         A += cross(contour[p], contour[q])
         p = q; q +=1
     end
     return A*T(0.5)
 end
 
+function area(contour::AbstractVector{Point{3, T}}) where {T}
+    A = zero(eltype(contour))
+    o = contour[1]
+    for i in (firstindex(contour)+1):(lastindex(contour)-1)
+        A += cross(contour[i] - o, contour[i+1] - o)
+    end
+    return norm(A)*T(0.5)
+end
+
 """
  InsideTriangle decides if a point P is Inside of the triangle
  defined by A, B, C.

test/polygons.jl

@@ -24,4 +24,53 @@
     @test facetype(mesh) == GLTriangle
 
 end
+
+@testset "area-2d" begin
+    points = Point2f0[
+        (0,0),
+        (1,0),
+        (1,1),
+        (0,1)
+    ]
+    @test area(points) ≈ 1f0
+    @test area(reverse(points)) ≈ -1f0
+end
+
+@testset "area-2d-nonconvex" begin
+    points = Point2f0[
+        (0,0),
+        (1,0),
+        (0.5,0.5),
+        (1,1),
+        (0,1),
+        (0.5,0.5)
+    ]
+    @test area(points) ≈ 0.5f0
+    @test area(reverse(points)) ≈ -0.5f0
+end
+
+@testset "area-3d" begin
+    points = Point3f0[
+        (0,0,0),
+        (1,0,0),
+        (1,1,0),
+        (0,1,0)
+    ]
+    @test area(points) ≈ 1f0
+    @test area(reverse(points)) ≈ 1f0
+end
+
+@testset "area-3d-nonconvex" begin
+    points = Point3f0[
+        (0,0,0),
+        (1,0,0),
+        (0.5,0.5,0),
+        (1,1,0),
+        (0,1,0),
+        (0.5,0.5,0)
+    ]
+    @test area(points) ≈ 0.5f0
+    @test area(reverse(points)) ≈ 0.5f0
+end
+
 end