Add method for integrating Tetrahedron (#41)

* Add tetrahedron to tests * Add QuadGK method for integrating Tetrahedron * Fix copy/paste error * Bugfix - domain correction * Bugfix - domain correction * Bump package version * Update support matrix
JuliaGeometry · Apr 14, 2024 · 77a2b06 · 77a2b06 · mikeingold · Apr 14, 2024
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diff --git a/Project.toml b/Project.toml
@@ -1,7 +1,7 @@
 name = "MeshIntegrals"
 uuid = "dadec2fd-bbe0-4da4-9dbe-476c782c8e47"
 authors = ["Mike Ingold <[email protected]>"]
-version = "0.11.6"
+version = "0.11.7"
 
 [deps]
 FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"

diff --git a/README.md b/README.md
@@ -54,7 +54,7 @@ integral(f, unit_circle_bz, GaussKronrod())
 |--------|---------|
 | :white_check_mark: | Implemented, passes tests |
 | :x: | Planned but not yet implemented |
-| :warning: | Unable to implement until parameterization not available (see [Issue #28](https://github.com/mikeingold/MeshIntegrals.jl/issues/28)) |
+| :warning: | Unable to implement: parameterization not available (see [Issue #28](https://github.com/mikeingold/MeshIntegrals.jl/issues/28)) |
 
 ### Integral
 | Geometry | Gauss-Legendre | Gauss-Kronrod | H-Adaptive Cubature |
@@ -85,5 +85,6 @@ integral(f, unit_circle_bz, GaussKronrod())
 | `SimpleMesh{Dim,T,V}` | :x: | :x: | :x: |
 | `Sphere{2,T}` | :white_check_mark: | :white_check_mark: | :white_check_mark: |
 | `Sphere{3,T}` | :white_check_mark: | :white_check_mark: | :white_check_mark: |
+| `Tetrahedron{3,T}` | :x: | :white_check_mark: | :x: |
 | `Triangle{T}` | :white_check_mark: | :white_check_mark: | :white_check_mark: |
 | `Torus{T}` | :white_check_mark: | :white_check_mark: | :white_check_mark: |
diff --git a/src/integral_volume.jl b/src/integral_volume.jl
@@ -33,6 +33,43 @@ function _integral_3d(
 end
 
 
+################################################################################
+#                  Specialized Methods for Tetrahedron
+################################################################################
+
+function integral(
+    f::F,
+    tetrahedron::Meshes.Tetrahedron{3,T},
+    settings::GaussLegendre
+) where {F<:Function, T}
+    error("Integrating a Tetrahedron{3,T} with GaussLegendre not supported.")
+end
+
+function integral(
+    f::F,
+    tetrahedron::Meshes.Tetrahedron{3,T},
+    settings::GaussKronrod
+) where {F<:Function, T}
+    # Validate the provided integrand function
+    _validate_integrand(f,3,T)
+
+    inner∫₂(v,w) = QuadGK.quadgk(u -> f(tetrahedron(u,v,w)), T(0), T(1-v-w); settings.kwargs...)[1]
+    inner∫₁(w) = QuadGK.quadgk(v -> inner∫₂(v,w), T(0), T(1-w); settings.kwargs...)[1]
+    outer∫ = QuadGK.quadgk(w -> inner∫₁(w), T(0), T(1); settings.kwargs...)[1]
+
+    # Apply barycentric domain correction (volume: 1/6 → actual)
+    return 6 * volume(tetrahedron) * outer∫
+end
+
+function integral(
+    f::F,
+    tetrahedron::Meshes.Tetrahedron{3,T},
+    settings::HAdaptiveCubature
+) where {F<:Function, T}
+    error("Integrating a Tetrahedron{3,T} with HAdaptiveCubature not supported.")
+end
+
+
 ################################################################################
 #                         Unsupported Placeholders
 ################################################################################

diff --git a/test/runtests.jl b/test/runtests.jl
@@ -102,18 +102,19 @@ end
     segment(T)  = Segment(pt_e(T), pt_n(T))
     sphere2d(T) = Sphere(origin2d(T), T(2.5))
     sphere3d(T) = Sphere(origin3d(T), T(2.5))
+    tetra(T)    = Tetrahedron(pt_n(T), pt_w(T), pt_e(T), pt_n(T)+ẑ(T))
     triangle(T) = Ngon(pt_e(T), pt_n(T), pt_w(T))
     torus(T)    = Torus(origin3d(T), ẑ(T), T(3.5), T(1.25))
 
     SUPPORT_MATRIX(T) = [
     # Name, T type, example,    integral,line,surface,volume,    GaussLegendre,GaussKronrod,HAdaptiveCubature
-        SupportItem("Ball{2,$T}", T, ball2d(T),          1, 0, 1, 0,   1, 1, 1),
-        SupportItem("Ball{3,$T}", T, ball3d(T),          1, 0, 0, 1,   1, 0, 1),
+        SupportItem("Ball{2,$T}", T, ball2d(T),             1, 0, 1, 0,   1, 1, 1),
+        SupportItem("Ball{3,$T}", T, ball3d(T),             1, 0, 0, 1,   1, 0, 1),
         # Ball{Dim,T}
         SupportItem("BezierCurve{$T}", T, bezier(T),        1, 1, 0, 0,   1, 1, 1),
-        SupportItem("Box{1,$T}", T, box1d(T),            1, 1, 0, 0,   1, 1, 1),
-        SupportItem("Box{2,$T}", T, box2d(T),            1, 0, 1, 0,   1, 1, 1),
-        SupportItem("Box{3,$T}", T, box3d(T),            1, 0, 0, 1,   1, 0, 1),
+        SupportItem("Box{1,$T}", T, box1d(T),               1, 1, 0, 0,   1, 1, 1),
+        SupportItem("Box{2,$T}", T, box2d(T),               1, 0, 1, 0,   1, 1, 1),
+        SupportItem("Box{3,$T}", T, box3d(T),               1, 0, 0, 1,   1, 0, 1),
         # Box{Dim,T}
         SupportItem("Circle{$T}", T, circle(T),             1, 1, 0, 0,   1, 1, 1),
         # Cone
@@ -133,6 +134,7 @@ end
         # SimpleMesh
         SupportItem("Sphere{2,$T}", T, sphere2d(T),         1, 1, 0, 0,   1, 1, 1),
         SupportItem("Sphere{3,$T}", T, sphere3d(T),         1, 0, 1, 0,   1, 1, 1),
+        SupportItem("Tetrahedron", T, tetra(T),             1, 0, 0, 1,   0, 1, 0),
         SupportItem("Triangle{$T}", T, triangle(T),         1, 0, 1, 0,   1, 1, 1),
         SupportItem("Torus{$T}", T, torus(T),               1, 0, 1, 0,   1, 1, 1),
     ]