diff -r 5d34b88e5733 -r 52e5ab4a96d5 src/Grids/parameter_space.jl
--- a/src/Grids/parameter_space.jl	Wed Feb 26 23:57:35 2025 +0100
+++ b/src/Grids/parameter_space.jl	Thu May 01 14:57:09 2025 +0200
@@ -18,6 +18,13 @@
 abstract type ParameterSpace{D} end
 Base.ndims(::ParameterSpace{D}) where D = D
 
+@doc """
+    in(x, S::ParameterSpace)
+    ∈(x, S::ParameterSpace)
+
+Test if the point `x` is in the parameter space `S`.
+""" Base.in(x,::ParameterSpace)
+
 """
     Interval{T} <: ParameterSpace{1}
 
@@ -47,6 +54,8 @@
 
 boundary_identifiers(::Interval) = (LowerBoundary(), UpperBoundary())
 
+Base.in(x, i::Interval) = i.a <= x <= i.b
+
 """
     unitinterval(T=Float64)
 
@@ -102,6 +111,11 @@
     end
 end
 
+function Base.in(x, box::HyperBox)
+    return all(eachindex(x)) do i
+        box.a[i] <= x[i] <= box.b[i]
+    end
+end
 
 """
     unitsquare(T=Float64)
@@ -150,6 +164,20 @@
     return Simplex(Tuple(convert(T,v) for v ∈ verticies))
 end
 
+function Base.in(x, s::Simplex)
+    v₁ = s.verticies[1]
+    V = map(s.verticies) do v
+        v - v₁
+    end
+
+    A = hcat(V[2:end]...) # Matrix with edge vectors as columns
+    λ = A \ (x - v₁)
+
+    λ_full = (1 - sum(λ), λ...) # Full barycentric coordinates
+
+    return all(λᵢ -> zero(λᵢ) ≤ λᵢ ≤ one(λᵢ), λ_full)
+end
+
 """
     verticies(s::Simplex)
 

diff -r 5d34b88e5733 -r 52e5ab4a96d5 test/Grids/parameter_space_test.jl
--- a/test/Grids/parameter_space_test.jl	Wed Feb 26 23:57:35 2025 +0100
+++ b/test/Grids/parameter_space_test.jl	Thu May 01 14:57:09 2025 +0200
@@ -1,6 +1,7 @@
 using Test
 
 using Diffinitive.Grids
+using StaticArrays
 
 @testset "ParameterSpace" begin
     @test ndims(HyperBox([1,1], [2,2])) == 2
@@ -22,6 +23,13 @@
     @test limits(unitinterval(Int)) == (0,1)
 
     @test boundary_identifiers(unitinterval()) == (LowerBoundary(), UpperBoundary())
+
+    @test 0 ∈ Interval(0,1)
+    @test 0. ∈ Interval(0,1)
+    @test 1. ∈ Interval(0,1)
+    @test 2 ∉ Interval(0,1)
+    @test -1 ∉ Interval(0,1)
+    @test -1. ∉ Interval(0,1)
 end
 
 @testset "HyperBox" begin
@@ -59,6 +67,13 @@
         CartesianBoundary{3,LowerBoundary}(),
         CartesianBoundary{3,UpperBoundary}(),
     ]
+
+    @test @SVector[1.5, 3.5] ∈ HyperBox([1,2], [3,4])
+    @test @SVector[1, 2] ∈ HyperBox([1,2], [3,4])
+    @test @SVector[3, 4] ∈ HyperBox([1,2], [3,4])
+
+    @test @SVector[0.5, 3.5] ∉ HyperBox([1,2], [3,4])
+    @test @SVector[1.5, 4.5] ∉ HyperBox([1,2], [3,4])
 end
 
 @testset "Simplex" begin
@@ -77,4 +92,32 @@
     @test verticies(unittetrahedron()) == ([0,0,0], [1,0,0], [0,1,0],[0,0,1])
 
     @test unitsimplex(4) isa Simplex{Float64,4}
+
+    @testset "Base.in" begin
+        @testset "2D" begin
+            T₂ = Simplex([0.0, 0.0], [1.0, 0.0], [0.0, 1.0])
+            @test [0.1, 0.1] ∈ T₂
+            @test [0.3, 0.3] ∈ T₂
+            @test [1.0, 0.0] ∈ T₂
+            @test [0.0, 0.0] ∈ T₂
+            @test [0.0, 1.0] ∈ T₂
+            @test [0.5, 0.5] ∈ T₂
+
+            @test [0.6, 0.6] ∉ T₂
+            @test [-0.1, 0.1] ∉ T₂
+        end
+
+        @testset "3D" begin
+            T₃ = Simplex([0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0])
+            @test [0.1, 0.1, 0.1] ∈ T₃
+            @test [0.0, 0.0, 0.0] ∈ T₃
+            @test [1.0, 0.0, 0.0] ∈ T₃
+            @test [0.25, 0.25, 0.25] ∈ T₃
+            @test [0.5, 0.5, 0.0] ∈ T₃
+            @test [0.3, 0.3, 0.3] ∈ T₃
+
+            @test [0.5, 0.5, 1.0] ∉ T₃
+            @test [0.3, 0.3, 0.5] ∉ T₃
+        end
+    end
 end