diff --git a/docs/src/lib/representations.md b/docs/src/lib/representations.md
index b5d05ea555..dee2cd8da4 100644
--- a/docs/src/lib/representations.md
+++ b/docs/src/lib/representations.md
@@ -158,6 +158,7 @@ dim(::HalfSpace)
 σ(::AbstractVector{Real}, ::HalfSpace{Real})
 ∈(::AbstractVector{Real}, ::HalfSpace{Real})
 an_element(::HalfSpace{N}) where {N<:Real}
+rand(::Type{HalfSpace})
 isempty(::HalfSpace)
 constraints_list(::HalfSpace{N}) where {N<:Real}
 constrained_dimensions(::HalfSpace{N}) where {N<:Real}
@@ -177,6 +178,7 @@ dim(::Hyperplane)
 σ(::AbstractVector{Real}, ::Hyperplane{Real})
 ∈(::AbstractVector{Real}, ::Hyperplane{Real})
 an_element(::Hyperplane{N}) where {N<:Real}
+rand(::Type{Hyperplane})
 isempty(::Hyperplane)
 constrained_dimensions(::Hyperplane{N}) where {N<:Real}
 ```
@@ -255,6 +257,7 @@ dim(::Line)
 σ(::AbstractVector{Real}, ::Line{Real})
 ∈(::AbstractVector{Real}, ::Line{Real})
 an_element(::Line{N}) where {N<:Real}
+rand(::Type{Line})
 isempty(::Line)
 constrained_dimensions(::Line{N}) where {N<:Real}
 ```
diff --git a/src/HalfSpace.jl b/src/HalfSpace.jl
index acbf2bf7df..65bf5604ea 100644
--- a/src/HalfSpace.jl
+++ b/src/HalfSpace.jl
@@ -1,4 +1,6 @@
-import Base: ∈, isempty
+import Base: rand,
+             ∈,
+             isempty
 
 export HalfSpace, LinearConstraint,
        an_element,
@@ -119,6 +121,45 @@ function ∈(x::AbstractVector{N}, hs::HalfSpace{N})::Bool where {N<:Real}
     return dot(x, hs.a) <= hs.b
 end
 
+"""
+    rand(::Type{HalfSpace}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
+         [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing
+        )::HalfSpace{N}
+
+Create a random half-space.
+
+### Input
+
+- `HalfSpace` -- type for dispatch
+- `N`         -- (optional, default: `Float64`) numeric type
+- `dim`       -- (optional, default: 2) dimension
+- `rng`       -- (optional, default: `GLOBAL_RNG`) random number generator
+- `seed`      -- (optional, default: `nothing`) seed for reseeding
+
+### Output
+
+A random half-space.
+
+### Algorithm
+
+All numbers are normally distributed with mean 0 and standard deviation 1.
+Additionally, the constraint `a` is nonzero.
+"""
+function rand(::Type{HalfSpace};
+              N::Type{<:Real}=Float64,
+              dim::Int=2,
+              rng::AbstractRNG=GLOBAL_RNG,
+              seed::Union{Int, Nothing}=nothing
+             )::HalfSpace{N}
+    rng = reseed(rng, seed)
+    a = randn(rng, N, dim)
+    while iszero(a)
+        a = randn(rng, N, dim)
+    end
+    b = randn(rng, N)
+    return HalfSpace(a, b)
+end
+
 """
     isempty(hs::HalfSpace)::Bool
 
diff --git a/src/Hyperplane.jl b/src/Hyperplane.jl
index 6e5fa20622..b13df55f5b 100644
--- a/src/Hyperplane.jl
+++ b/src/Hyperplane.jl
@@ -1,4 +1,6 @@
-import Base: ∈, isempty
+import Base: rand,
+             ∈,
+             isempty
 
 export Hyperplane,
        an_element
@@ -110,6 +112,45 @@ function ∈(x::AbstractVector{N}, hp::Hyperplane{N})::Bool where {N<:Real}
     return dot(x, hp.a) == hp.b
 end
 
+"""
+    rand(::Type{Hyperplane}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
+         [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing
+        )::Hyperplane{N}
+
+Create a random hyperplane.
+
+### Input
+
+- `Hyperplane` -- type for dispatch
+- `N`          -- (optional, default: `Float64`) numeric type
+- `dim`        -- (optional, default: 2) dimension
+- `rng`        -- (optional, default: `GLOBAL_RNG`) random number generator
+- `seed`       -- (optional, default: `nothing`) seed for reseeding
+
+### Output
+
+A random hyperplane.
+
+### Algorithm
+
+All numbers are normally distributed with mean 0 and standard deviation 1.
+Additionally, the constraint `a` is nonzero.
+"""
+function rand(::Type{Hyperplane};
+              N::Type{<:Real}=Float64,
+              dim::Int=2,
+              rng::AbstractRNG=GLOBAL_RNG,
+              seed::Union{Int, Nothing}=nothing
+             )::Hyperplane{N}
+    rng = reseed(rng, seed)
+    a = randn(rng, N, dim)
+    while iszero(a)
+        a = randn(rng, N, dim)
+    end
+    b = randn(rng, N)
+    return Hyperplane(a, b)
+end
+
 """
     isempty(hp::Hyperplane)::Bool
 
diff --git a/src/Line.jl b/src/Line.jl
index 26cfd0737c..44075ba8c3 100644
--- a/src/Line.jl
+++ b/src/Line.jl
@@ -1,4 +1,6 @@
-import Base: ∈, isempty
+import Base: rand,
+             ∈,
+             isempty
 
 export Line,
        an_element
@@ -175,6 +177,46 @@ function ∈(x::AbstractVector{N}, L::Line{N})::Bool where {N<:Real}
     return dot(L.a, x) == L.b
 end
 
+"""
+    rand(::Type{Line}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
+         [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing
+        )::Line{N}
+
+Create a random line.
+
+### Input
+
+- `Line` -- type for dispatch
+- `N`    -- (optional, default: `Float64`) numeric type
+- `dim`  -- (optional, default: 2) dimension
+- `rng`  -- (optional, default: `GLOBAL_RNG`) random number generator
+- `seed` -- (optional, default: `nothing`) seed for reseeding
+
+### Output
+
+A random line.
+
+### Algorithm
+
+All numbers are normally distributed with mean 0 and standard deviation 1.
+Additionally, the constraint `a` is nonzero.
+"""
+function rand(::Type{Line};
+              N::Type{<:Real}=Float64,
+              dim::Int=2,
+              rng::AbstractRNG=GLOBAL_RNG,
+              seed::Union{Int, Nothing}=nothing
+             )::Line{N}
+    @assert dim == 2 "a Line must have dimension 2"
+    rng = reseed(rng, seed)
+    a = randn(rng, N, dim)
+    while iszero(a)
+        a = randn(rng, N, dim)
+    end
+    b = randn(rng, N)
+    return Line(a, b)
+end
+
 """
     isempty(L::Line)::Bool
 
diff --git a/test/unit_HalfSpace.jl b/test/unit_HalfSpace.jl
index 1e88ee77e6..c782b1930c 100644
--- a/test/unit_HalfSpace.jl
+++ b/test/unit_HalfSpace.jl
@@ -1,4 +1,7 @@
 for N in [Float64, Rational{Int}, Float32]
+    # random half-space
+    rand(HalfSpace)
+
     # normal constructor
     normal = ones(N, 3)
     hs = HalfSpace(normal, N(5))
diff --git a/test/unit_Hyperplane.jl b/test/unit_Hyperplane.jl
index 793c401260..cf91e036bb 100644
--- a/test/unit_Hyperplane.jl
+++ b/test/unit_Hyperplane.jl
@@ -1,4 +1,7 @@
 for N in [Float64, Rational{Int}, Float32]
+    # random hyperplane
+    rand(Hyperplane)
+
     # normal constructor
     a = ones(N, 3)
     hp = Hyperplane(a, N(5))
diff --git a/test/unit_Line.jl b/test/unit_Line.jl
index b40c93686c..c9465a40f7 100644
--- a/test/unit_Line.jl
+++ b/test/unit_Line.jl
@@ -1,4 +1,7 @@
 for N in [Float64, Rational{Int}, Float32]
+    # random line
+    rand(Line)
+
     # construction
     l1 = Line(N[0, 1], N(1))
     l2 = Line(N[1, 0], N(1))