From 5e3feeeabada66a104261a4388d95851d93c08ef Mon Sep 17 00:00:00 2001
From: "Luiz M. Faria" <maltezfaria@gmail.com>
Date: Fri, 29 Sep 2023 21:24:51 +0200
Subject: [PATCH 1/6] first implementation of reference shapes + tests

---
 Project.toml                          |  5 +-
 src/Geometry/Geometry.jl              | 26 ++++++++++
 src/Geometry/referenceshapes.jl       | 72 +++++++++++++++++++++++++++
 src/Inti.jl                           |  8 ++-
 src/utils.jl                          | 13 +++++
 test/Geometry/referenceshapes_test.jl | 37 ++++++++++++++
 test/Project.toml                     |  2 +
 test/aqua_test.jl                     |  7 +++
 test/runtests.jl                      | 13 ++---
 9 files changed, 175 insertions(+), 8 deletions(-)
 create mode 100644 src/Geometry/Geometry.jl
 create mode 100644 src/Geometry/referenceshapes.jl
 create mode 100644 src/utils.jl
 create mode 100644 test/Geometry/referenceshapes_test.jl
 create mode 100644 test/aqua_test.jl

diff --git a/Project.toml b/Project.toml
index 973459ca..13d0de5a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,10 @@
 name = "Inti"
 uuid = "fb74042b-437e-4c5b-88cf-d4e2beb394d5"
-authors = ["Luiz M. Faria"]
 version = "0.1.0"
 
+[deps]
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
 [compat]
+StaticArrays = "1"
 julia = "1.6"
diff --git a/src/Geometry/Geometry.jl b/src/Geometry/Geometry.jl
new file mode 100644
index 00000000..580e2bbd
--- /dev/null
+++ b/src/Geometry/Geometry.jl
@@ -0,0 +1,26 @@
+#=
+
+Definition of basic geometrical concepts.
+
+=#
+
+
+"""
+    ambient_dimension(x)
+
+Dimension of the ambient space where `x` lives. For geometrical objects this can
+differ from its [`geometric_dimension`](@ref); for example a triangle in `ℝ³`
+has ambient dimension `3` but geometric dimension `2`, while a curve in `ℝ³` has
+ambient dimension 3 but geometric dimension 1.
+"""
+function ambient_dimension end
+
+"""
+    geometric_dimension(x)
+
+Number of independent coordinates needed to describe `x`. Lines have geometric
+dimension 1, triangles have geometric dimension 2, etc.
+"""
+function geometric_dimension end
+
+include("referenceshapes.jl")
diff --git a/src/Geometry/referenceshapes.jl b/src/Geometry/referenceshapes.jl
new file mode 100644
index 00000000..58fbb4b1
--- /dev/null
+++ b/src/Geometry/referenceshapes.jl
@@ -0,0 +1,72 @@
+"""
+    abstract type AbstractReferenceShape
+
+A fixed reference domain/shape. Used mostly for defining more complex shapes as
+transformations mapping an `AbstractReferenceShape` to some region of `ℜᴹ`.
+
+See e.g. [`ReferenceLine`](@ref) or [`ReferenceTriangle`](@ref) for some
+examples of concrete subtypes.
+"""
+abstract type AbstractReferenceShape end
+
+"""
+    struct ReferenceTriangle
+
+Singleton type representing the triangle with vertices `(0,0),(1,0),(0,1)`
+"""
+struct ReferenceTriangle <: AbstractReferenceShape end
+geometric_dimension(::ReferenceTriangle) = 2
+ambient_dimension(::ReferenceTriangle) = 2
+vertices(::ReferenceTriangle) = SVector(0, 0), SVector(1, 0), SVector(0, 1)
+Base.in(x, ::ReferenceTriangle) = 0 ≤ x[1] ≤ 1 && 0 ≤ x[2] ≤ 1 - x[1]
+center(::ReferenceTriangle) = svector(i -> 1 / 3, 3)
+
+"""
+    struct ReferenceTetrahedron
+
+Singleton type representing the tetrahedron with vertices
+`(0,0,0),(0,0,1),(0,1,0),(1,0,0)`
+"""
+struct ReferenceTetrahedron <: AbstractReferenceShape end
+geometric_dimension(::ReferenceTetrahedron) = 3
+ambient_dimension(::ReferenceTetrahedron) = 3
+vertices(::ReferenceTetrahedron) = SVector(0, 0, 0), SVector(1, 0, 0), SVector(0, 1, 0), SVector(0, 0, 1)
+Base.in(x,::ReferenceTetrahedron) = 0 ≤ x[1] ≤ 1 && 0 ≤ x[2] ≤ 1 - x[1] && 0 ≤ x[3] ≤ 1 - x[1] - x[2]
+center(::ReferenceTetrahedron) = svector(i -> 1 / 4, 4)
+
+
+# TODO: generalize structs above to `ReferenceSimplex{N}` and
+
+"""
+    struct ReferenceHyperCube{N} <: AbstractReferenceShape{N}
+
+Singleton type representing the axis-aligned hypercube in `N` dimensions with
+the lower corner at the origin and the upper corner at `(1,1,…,1)`.
+"""
+struct ReferenceHyperCube{N} <: AbstractReferenceShape end
+geometric_dimension(::ReferenceHyperCube{N}) where {N} = N
+ambient_dimension(::ReferenceHyperCube{N}) where {N} = N
+vertices(::ReferenceHyperCube{N}) where {N} = ntuple(i -> SVector(ntuple(j -> (i >> j) & 1, N)), 2^N)
+Base.in(x, ::ReferenceHyperCube{N}) where {N} = all(0 .≤ x .≤ 1)
+center(::ReferenceHyperCube{N}) where {N} = svector(i -> 0.5, N)
+
+"""
+    const ReferenceLine = ReferenceHyperCube{1}
+
+Singleton type representing the `[0,1]` segment.
+"""
+const ReferenceLine = ReferenceHyperCube{1}
+
+"""
+    const ReferenceSquare = ReferenceHyperCube{2}
+
+Singleton type representing the unit square `[0,1]²`.
+"""
+const ReferenceSquare = ReferenceHyperCube{2}
+
+"""
+    const ReferenceCube = ReferenceHyperCube{3}
+
+Singleton type representing the unit cube `[0,1]³`.
+"""
+const ReferenceCube = ReferenceHyperCube{3}
diff --git a/src/Inti.jl b/src/Inti.jl
index c23e615d..2e10a22a 100644
--- a/src/Inti.jl
+++ b/src/Inti.jl
@@ -1,5 +1,11 @@
 module Inti
 
-# Write your package code here.
+const PROJECT_ROOT = pkgdir(Inti)
+
+using StaticArrays
+
+include("utils.jl")
+include("Geometry/Geometry.jl")
+
 
 end
diff --git a/src/utils.jl b/src/utils.jl
new file mode 100644
index 00000000..1a19fe39
--- /dev/null
+++ b/src/utils.jl
@@ -0,0 +1,13 @@
+#=
+
+Utility functions that have nowhere obvious to go.
+
+=#
+
+"""
+    svector(f,n)
+
+Create an `SVector` of length n, computing each element as f(i), where i is the
+index of the element.
+"""
+svector(f,n)=  ntuple(f,n) |> SVector
diff --git a/test/Geometry/referenceshapes_test.jl b/test/Geometry/referenceshapes_test.jl
new file mode 100644
index 00000000..882355f4
--- /dev/null
+++ b/test/Geometry/referenceshapes_test.jl
@@ -0,0 +1,37 @@
+using Test
+import Inti
+using StaticArrays
+
+@testset "Line" begin
+    l = Inti.ReferenceLine()
+    @test Inti.ambient_dimension(l) == 1
+    @test Inti.geometric_dimension(l) == 1
+    x = SVector(0.5)
+    @test x ∈ l
+    x = SVector(1.0)
+    @test x ∈ l
+    x = SVector(1.1)
+    @test !in(x, l)
+end
+@testset "Triangle" begin
+    t = Inti.ReferenceTriangle()
+    @test Inti.ambient_dimension(t) == 2
+    @test Inti.geometric_dimension(t) == 2
+    x = SVector(0.5, 0.5)
+    @test x ∈ t
+    x = SVector(1.0, 0.0)
+    @test x ∈ t
+    x = SVector(1.1, 0.0)
+    @test !in(x, t)
+end
+@testset "Tetrahedron" begin
+    t = Inti.ReferenceTetrahedron()
+    @test Inti.ambient_dimension(t) == 3
+    @test Inti.geometric_dimension(t) == 3
+    x = SVector(0.5, 0.5, 0.0)
+    @test x ∈ t
+    x = SVector(1.0, 0.0, 0.0) # point on edge
+    @test x ∈ t
+    x = SVector(1.1, 0.0, 0.0)
+    @test !in(x, t)
+end
diff --git a/test/Project.toml b/test/Project.toml
index b35b5edd..5e3af3c7 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,3 +1,5 @@
 [deps]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/aqua_test.jl b/test/aqua_test.jl
new file mode 100644
index 00000000..19bfbfeb
--- /dev/null
+++ b/test/aqua_test.jl
@@ -0,0 +1,7 @@
+using Inti
+using Test
+using Aqua
+
+@testset "Aqua" begin
+    Aqua.test_all(Inti)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 7fc3bc2b..9b203116 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,10 +1,11 @@
 using Inti
-using Test
+using SafeTestsets
 using Aqua
 
-@testset "Inti.jl" begin
-    @testset "Code quality (Aqua.jl)" begin
-        Aqua.test_all(Inti)
-    end
-    # Write your tests here.
+@safetestset "Code quality" begin
+    include("aqua_test.jl")
+end
+
+@safetestset "Geometry" begin
+    @safetestset "Reference shapes" include("Geometry/referenceshapes_test.jl")
 end

From 24ae4d35702101f8a7770359c20a4f00fa6c18ae Mon Sep 17 00:00:00 2001
From: "Thomas G. Anderson" <tanderson@alumni.caltech.edu>
Date: Sat, 30 Sep 2023 20:24:14 -0500
Subject: [PATCH 2/6] Add reference n-simplex

---
 src/Geometry/referenceshapes.jl       | 23 ++++++++++++++++++++++-
 test/Geometry/referenceshapes_test.jl | 13 ++++++++++++-
 2 files changed, 34 insertions(+), 2 deletions(-)

diff --git a/src/Geometry/referenceshapes.jl b/src/Geometry/referenceshapes.jl
index 58fbb4b1..17d9ef2a 100644
--- a/src/Geometry/referenceshapes.jl
+++ b/src/Geometry/referenceshapes.jl
@@ -34,8 +34,29 @@ vertices(::ReferenceTetrahedron) = SVector(0, 0, 0), SVector(1, 0, 0), SVector(0
 Base.in(x,::ReferenceTetrahedron) = 0 ≤ x[1] ≤ 1 && 0 ≤ x[2] ≤ 1 - x[1] && 0 ≤ x[3] ≤ 1 - x[1] - x[2]
 center(::ReferenceTetrahedron) = svector(i -> 1 / 4, 4)
 
+"""
+    struct ReferenceSimplex{N}
 
-# TODO: generalize structs above to `ReferenceSimplex{N}` and
+Singleton type representing the N-simplex with N+1 vertices
+`(0,...,0),(0,...,0,1),(0,...,0,1,0),(1,0,...,0)`
+"""
+struct ReferenceSimplex{N} <: AbstractReferenceShape end
+geometric_dimension(::ReferenceSimplex{N}) where {N} = N
+ambient_dimension(::ReferenceSimplex{N}) where {N} = N
+function Base.in(x, ::ReferenceSimplex{N}) where {N}
+    for i in range(1, N)
+        0 ≤ x[i] ≤ 1 - sum(x[1:i-1]) || return false
+    end
+    return true
+end
+
+function standard_basis_vector(T, ::Val{I}, ::Val{N}) where {I,N}
+    v = zero(MVector{N,T})
+    v[I] = one(T)
+    SVector(v)
+end
+
+vertices(::ReferenceSimplex{N}) where {N} = ntuple(i -> standard_basis_vector(Int64, Val{i}, Val{N}), N) |> SVector
 
 """
     struct ReferenceHyperCube{N} <: AbstractReferenceShape{N}
diff --git a/test/Geometry/referenceshapes_test.jl b/test/Geometry/referenceshapes_test.jl
index 882355f4..1b7e33dd 100644
--- a/test/Geometry/referenceshapes_test.jl
+++ b/test/Geometry/referenceshapes_test.jl
@@ -1,5 +1,5 @@
 using Test
-import Inti
+using Inti
 using StaticArrays
 
 @testset "Line" begin
@@ -35,3 +35,14 @@ end
     x = SVector(1.1, 0.0, 0.0)
     @test !in(x, t)
 end
+@testset "NSimplex" begin
+    t = Inti.ReferenceSimplex{4}()
+    @test Inti.ambient_dimension(t) == 4
+    @test Inti.geometric_dimension(t) == 4
+    x = SVector(0.5, 0.4, 0.0, 0.05)
+    @test x ∈ t
+    x = SVector(1.0, 0.0, 0.0, 0.0)
+    @test x ∈ t
+    x = SVector(1.1, 0.0, 0.0, 0.0)
+    @test !in(x, t)
+end
\ No newline at end of file

From 78752f0d6b39fd196091e4d5ac3bbb5b6845246e Mon Sep 17 00:00:00 2001
From: "Thomas G. Anderson" <tanderson@alumni.caltech.edu>
Date: Sat, 30 Sep 2023 20:34:41 -0500
Subject: [PATCH 3/6] Fix ranges for v1.6

---
 src/Geometry/referenceshapes.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/Geometry/referenceshapes.jl b/src/Geometry/referenceshapes.jl
index 17d9ef2a..2b9cd387 100644
--- a/src/Geometry/referenceshapes.jl
+++ b/src/Geometry/referenceshapes.jl
@@ -44,7 +44,7 @@ struct ReferenceSimplex{N} <: AbstractReferenceShape end
 geometric_dimension(::ReferenceSimplex{N}) where {N} = N
 ambient_dimension(::ReferenceSimplex{N}) where {N} = N
 function Base.in(x, ::ReferenceSimplex{N}) where {N}
-    for i in range(1, N)
+    for i in 1:N
         0 ≤ x[i] ≤ 1 - sum(x[1:i-1]) || return false
     end
     return true

From 49fac720de4ebd64c86fc9d7c278165990e2026c Mon Sep 17 00:00:00 2001
From: "Thomas G. Anderson" <tanderson@alumni.caltech.edu>
Date: Sat, 30 Sep 2023 20:57:06 -0500
Subject: [PATCH 4/6] Make ReferenceTriangle and ReferenceTetrahedron instances
 of ReferenceSimplex

This also fixes errors in the center function for those shapes.
---
 src/Geometry/referenceshapes.jl | 43 ++++++++++++---------------------
 1 file changed, 16 insertions(+), 27 deletions(-)

diff --git a/src/Geometry/referenceshapes.jl b/src/Geometry/referenceshapes.jl
index 2b9cd387..e512fb7a 100644
--- a/src/Geometry/referenceshapes.jl
+++ b/src/Geometry/referenceshapes.jl
@@ -9,31 +9,6 @@ examples of concrete subtypes.
 """
 abstract type AbstractReferenceShape end
 
-"""
-    struct ReferenceTriangle
-
-Singleton type representing the triangle with vertices `(0,0),(1,0),(0,1)`
-"""
-struct ReferenceTriangle <: AbstractReferenceShape end
-geometric_dimension(::ReferenceTriangle) = 2
-ambient_dimension(::ReferenceTriangle) = 2
-vertices(::ReferenceTriangle) = SVector(0, 0), SVector(1, 0), SVector(0, 1)
-Base.in(x, ::ReferenceTriangle) = 0 ≤ x[1] ≤ 1 && 0 ≤ x[2] ≤ 1 - x[1]
-center(::ReferenceTriangle) = svector(i -> 1 / 3, 3)
-
-"""
-    struct ReferenceTetrahedron
-
-Singleton type representing the tetrahedron with vertices
-`(0,0,0),(0,0,1),(0,1,0),(1,0,0)`
-"""
-struct ReferenceTetrahedron <: AbstractReferenceShape end
-geometric_dimension(::ReferenceTetrahedron) = 3
-ambient_dimension(::ReferenceTetrahedron) = 3
-vertices(::ReferenceTetrahedron) = SVector(0, 0, 0), SVector(1, 0, 0), SVector(0, 1, 0), SVector(0, 0, 1)
-Base.in(x,::ReferenceTetrahedron) = 0 ≤ x[1] ≤ 1 && 0 ≤ x[2] ≤ 1 - x[1] && 0 ≤ x[3] ≤ 1 - x[1] - x[2]
-center(::ReferenceTetrahedron) = svector(i -> 1 / 4, 4)
-
 """
     struct ReferenceSimplex{N}
 
@@ -49,14 +24,28 @@ function Base.in(x, ::ReferenceSimplex{N}) where {N}
     end
     return true
 end
-
 function standard_basis_vector(T, ::Val{I}, ::Val{N}) where {I,N}
     v = zero(MVector{N,T})
     v[I] = one(T)
     SVector(v)
 end
-
 vertices(::ReferenceSimplex{N}) where {N} = ntuple(i -> standard_basis_vector(Int64, Val{i}, Val{N}), N) |> SVector
+center(::ReferenceSimplex{N}) where {N} = svector(i -> 1 / (N + 1), N )
+
+"""
+    struct ReferenceTriangle
+
+Singleton type representing the triangle with vertices `(0,0),(1,0),(0,1)`
+"""
+const ReferenceTriangle = ReferenceSimplex{2}
+
+"""
+    struct ReferenceTetrahedron
+
+Singleton type representing the tetrahedron with vertices
+`(0,0,0),(0,0,1),(0,1,0),(1,0,0)`
+"""
+const ReferenceTetrahedron = ReferenceSimplex{3}
 
 """
     struct ReferenceHyperCube{N} <: AbstractReferenceShape{N}

From 4d6b7e8a51ab79cb254cb09be12fb73080e7ed89 Mon Sep 17 00:00:00 2001
From: "Thomas G. Anderson" <tanderson@alumni.caltech.edu>
Date: Sun, 1 Oct 2023 11:00:49 -0500
Subject: [PATCH 5/6] Reference shapes: more tests; fix simplex vertices

---
 src/Geometry/referenceshapes.jl       | 2 +-
 test/Geometry/referenceshapes_test.jl | 8 ++++++++
 2 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/src/Geometry/referenceshapes.jl b/src/Geometry/referenceshapes.jl
index e512fb7a..77b158ba 100644
--- a/src/Geometry/referenceshapes.jl
+++ b/src/Geometry/referenceshapes.jl
@@ -29,7 +29,7 @@ function standard_basis_vector(T, ::Val{I}, ::Val{N}) where {I,N}
     v[I] = one(T)
     SVector(v)
 end
-vertices(::ReferenceSimplex{N}) where {N} = ntuple(i -> standard_basis_vector(Int64, Val{i}, Val{N}), N) |> SVector
+vertices(::ReferenceSimplex{N}) where {N} = ntuple(i -> i == 1 ? zero(SVector{N, Int64}) : standard_basis_vector(Int64, Val(i-1), Val(N)), N+1) |> SVector
 center(::ReferenceSimplex{N}) where {N} = svector(i -> 1 / (N + 1), N )
 
 """
diff --git a/test/Geometry/referenceshapes_test.jl b/test/Geometry/referenceshapes_test.jl
index 1b7e33dd..033a7ed5 100644
--- a/test/Geometry/referenceshapes_test.jl
+++ b/test/Geometry/referenceshapes_test.jl
@@ -12,6 +12,8 @@ using StaticArrays
     @test x ∈ l
     x = SVector(1.1)
     @test !in(x, l)
+    @test Inti.center(l) == SVector(1/2)
+    @test Inti.vertices(l) == (SVector(0), SVector(1))
 end
 @testset "Triangle" begin
     t = Inti.ReferenceTriangle()
@@ -23,6 +25,8 @@ end
     @test x ∈ t
     x = SVector(1.1, 0.0)
     @test !in(x, t)
+    @test Inti.center(t) == SVector(1/3, 1/3)
+    @test Inti.vertices(t) == SVector{3, SVector{2, Int64}}([0, 0], [1, 0], [0, 1])
 end
 @testset "Tetrahedron" begin
     t = Inti.ReferenceTetrahedron()
@@ -34,6 +38,8 @@ end
     @test x ∈ t
     x = SVector(1.1, 0.0, 0.0)
     @test !in(x, t)
+    @test Inti.center(t) == SVector(1/4, 1/4, 1/4)
+    @test Inti.vertices(t) == SVector{4, SVector{3, Int64}}([0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1])
 end
 @testset "NSimplex" begin
     t = Inti.ReferenceSimplex{4}()
@@ -45,4 +51,6 @@ end
     @test x ∈ t
     x = SVector(1.1, 0.0, 0.0, 0.0)
     @test !in(x, t)
+    @test Inti.center(t) == SVector(1/5, 1/5, 1/5, 1/5)
+    @test Inti.vertices(t) == SVector{5, SVector{4, Int64}}([0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1])
 end
\ No newline at end of file

From 9e3e08ce7b2499de84afea6a2b875c98662cec27 Mon Sep 17 00:00:00 2001
From: "Luiz M. Faria" <maltezfaria@gmail.com>
Date: Mon, 2 Oct 2023 11:22:40 +0200
Subject: [PATCH 6/6] reduce verbosity, simplify `standard_basis_vector`

---
 src/Geometry/referenceshapes.jl |  7 +------
 src/utils.jl                    |  7 +++++++
 test/referenceshapes_test.jl    | 37 +++++++++++++++++++++++++++++++++
 3 files changed, 45 insertions(+), 6 deletions(-)
 create mode 100644 test/referenceshapes_test.jl

diff --git a/src/Geometry/referenceshapes.jl b/src/Geometry/referenceshapes.jl
index 77b158ba..46074341 100644
--- a/src/Geometry/referenceshapes.jl
+++ b/src/Geometry/referenceshapes.jl
@@ -24,12 +24,7 @@ function Base.in(x, ::ReferenceSimplex{N}) where {N}
     end
     return true
 end
-function standard_basis_vector(T, ::Val{I}, ::Val{N}) where {I,N}
-    v = zero(MVector{N,T})
-    v[I] = one(T)
-    SVector(v)
-end
-vertices(::ReferenceSimplex{N}) where {N} = ntuple(i -> i == 1 ? zero(SVector{N, Int64}) : standard_basis_vector(Int64, Val(i-1), Val(N)), N+1) |> SVector
+vertices(::ReferenceSimplex{N}) where {N} = svector(i -> i == 1 ? zero(SVector{N, Int64}) : standard_basis_vector(i-1, Val(N)), N+1)
 center(::ReferenceSimplex{N}) where {N} = svector(i -> 1 / (N + 1), N )
 
 """
diff --git a/src/utils.jl b/src/utils.jl
index 1a19fe39..2b5911a8 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -11,3 +11,10 @@ Create an `SVector` of length n, computing each element as f(i), where i is the
 index of the element.
 """
 svector(f,n)=  ntuple(f,n) |> SVector
+
+"""
+    standard_basis_vector(k, ::Val{N})
+
+Create an `SVector` of length N with a 1 in the kth position and zeros elsewhere.
+"""
+standard_basis_vector(k, n::Val{N}) where {N} = svector(i-> i == k ? 1 : 0, n)
diff --git a/test/referenceshapes_test.jl b/test/referenceshapes_test.jl
new file mode 100644
index 00000000..882355f4
--- /dev/null
+++ b/test/referenceshapes_test.jl
@@ -0,0 +1,37 @@
+using Test
+import Inti
+using StaticArrays
+
+@testset "Line" begin
+    l = Inti.ReferenceLine()
+    @test Inti.ambient_dimension(l) == 1
+    @test Inti.geometric_dimension(l) == 1
+    x = SVector(0.5)
+    @test x ∈ l
+    x = SVector(1.0)
+    @test x ∈ l
+    x = SVector(1.1)
+    @test !in(x, l)
+end
+@testset "Triangle" begin
+    t = Inti.ReferenceTriangle()
+    @test Inti.ambient_dimension(t) == 2
+    @test Inti.geometric_dimension(t) == 2
+    x = SVector(0.5, 0.5)
+    @test x ∈ t
+    x = SVector(1.0, 0.0)
+    @test x ∈ t
+    x = SVector(1.1, 0.0)
+    @test !in(x, t)
+end
+@testset "Tetrahedron" begin
+    t = Inti.ReferenceTetrahedron()
+    @test Inti.ambient_dimension(t) == 3
+    @test Inti.geometric_dimension(t) == 3
+    x = SVector(0.5, 0.5, 0.0)
+    @test x ∈ t
+    x = SVector(1.0, 0.0, 0.0) # point on edge
+    @test x ∈ t
+    x = SVector(1.1, 0.0, 0.0)
+    @test !in(x, t)
+end