--- a/src/Grids/Grids.jl	Mon Feb 03 15:39:26 2025 +0100
+++ b/src/Grids/Grids.jl	Mon Feb 03 15:43:00 2025 +0100
@@ -79,5 +79,6 @@
 include("equidistant_grid.jl")
 include("zero_dim_grid.jl")
 include("mapped_grid.jl")
+include("geometry.jl")
 
 end # module

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Grids/geometry.jl	Mon Feb 03 15:43:00 2025 +0100
@@ -0,0 +1,67 @@
+###
+# Geometry
+###
+
+abstract type Curve end
+abstract type Surface end
+
+
+struct Line{PT} <: Curve
+    p::PT
+    tangent::PT
+end
+
+(c::Line)(s) = c.p + s*c.tangent
+
+
+struct LineSegment{PT} <: Curve
+    a::PT
+    b::PT
+end
+
+(c::LineSegment)(s) = (1-s)*c.a + s*c.b
+
+
+function linesegments(ps...)
+    return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
+end
+
+
+function polygon_edges(ps...)
+    n = length(ps)
+    return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
+end
+
+struct Circle{T,PT} <: Curve
+    c::PT
+    r::T
+end
+
+function (C::Circle)(θ)
+    (;c, r) = C
+    c + r*@SVector[cos(θ), sin(θ)]
+end
+
+struct TransfiniteInterpolationSurface{T1,T2,T3,T4} <: Surface
+    c₁::T1
+    c₂::T2
+    c₃::T3
+    c₄::T4
+end
+
+function (s::TransfiniteInterpolationSurface)(u,v)
+    c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
+    P₀₀ = c₁(0)
+    P₁₀ = c₂(0)
+    P₁₁ = c₃(0)
+    P₀₁ = c₄(0)
+    return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
+        (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
+    )
+end
+
+function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
+    s(ξ̄...)
+end
+
+# TODO: Implement jacobian() for the different mapping helpers

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/Grids/geometry_test.jl	Mon Feb 03 15:43:00 2025 +0100
@@ -0,0 +1,23 @@
+@testset "Line" begin
+    @test_broken false
+end
+
+@testset "LineSegment" begin
+    @test_broken false
+end
+
+@testset "linesegments" begin
+    @test_broken false
+end
+
+@testset "polygon_edges" begin
+    @test_broken false
+end
+
+@testset "Circle" begin
+    @test_broken false
+end
+
+@testset "TransfiniteInterpolationSurface" begin
+    @test_broken false
+end