From d2ddab15b8af941c4fe1c1fb37b81ff5888d252d Mon Sep 17 00:00:00 2001
From: schillic <christian.schilling@ist.ac.at>
Date: Mon, 20 Jul 2020 12:13:52 +0200
Subject: [PATCH 1/2] specialized box approximation for vertex representation

---
 src/Approximations/overapproximate.jl | 18 ++++++++++++++++++
 test/unit_box_approximation.jl        |  5 +++++
 2 files changed, 23 insertions(+)

diff --git a/src/Approximations/overapproximate.jl b/src/Approximations/overapproximate.jl
index 47648d20e5..cf0a8518d8 100644
--- a/src/Approximations/overapproximate.jl
+++ b/src/Approximations/overapproximate.jl
@@ -1513,6 +1513,24 @@ function overapproximate(am::AbstractAffineMap{N, <:AbstractHyperrectangle{N}},
     return Hyperrectangle(center_MXv, radius_MX)
 end
 
+function overapproximate(P::Union{VPolytope, VPolygon},
+                         ::Type{<:Hyperrectangle}) where {N<:Real}
+    n = dim(P)
+    vlist = vertices_list(P)
+    low = copy(vlist[1])
+    high = copy(vlist[1])
+    @inbounds for v in @view vlist[2:length(vlist)]
+        for i in 1:n
+            if v[i] > high[i]
+                high[i] = v[i]
+            elseif v[i] < low[i]
+                low[i] = v[i]
+            end
+        end
+    end
+    return Hyperrectangle(low=low, high=high)
+end
+
 """
     overapproximate(X::LazySet{N}, ::Type{<:Zonotope},
                     dir::AbstractDirections{N};
diff --git a/test/unit_box_approximation.jl b/test/unit_box_approximation.jl
index 03d7d06fed..11bbf4c043 100644
--- a/test/unit_box_approximation.jl
+++ b/test/unit_box_approximation.jl
@@ -29,6 +29,11 @@ for N in [Float64, Rational{Int}, Float32]
     @test h.center ≈ hexp.center
     @test h.radius ≈ hexp.radius
 
+    # Box approximation of a VPolytope
+    P = VPolytope([N[0, 0], N[2, 1], N[1, 2]])
+    H = box_approximation(P)
+    @test H == Hyperrectangle(N[1, 1], N[1, 1])
+
     # empty set
     E = EmptySet{N}(2)
     @test box_approximation(E) == E

From 34307c7b08e386b0c794455abaa17559fc7540ea Mon Sep 17 00:00:00 2001
From: schillic <christian.schilling@ist.ac.at>
Date: Sun, 2 Aug 2020 10:02:47 +0200
Subject: [PATCH 2/2] faster implementation

---
 src/Approximations/overapproximate.jl | 29 ++++++++++++++++++---------
 1 file changed, 19 insertions(+), 10 deletions(-)

diff --git a/src/Approximations/overapproximate.jl b/src/Approximations/overapproximate.jl
index cf0a8518d8..30e3bb4ed1 100644
--- a/src/Approximations/overapproximate.jl
+++ b/src/Approximations/overapproximate.jl
@@ -1514,21 +1514,30 @@ function overapproximate(am::AbstractAffineMap{N, <:AbstractHyperrectangle{N}},
 end
 
 function overapproximate(P::Union{VPolytope, VPolygon},
-                         ::Type{<:Hyperrectangle}) where {N<:Real}
+                         ::Type{<:Hyperrectangle})
     n = dim(P)
     vlist = vertices_list(P)
-    low = copy(vlist[1])
-    high = copy(vlist[1])
-    @inbounds for v in @view vlist[2:length(vlist)]
-        for i in 1:n
-            if v[i] > high[i]
-                high[i] = v[i]
-            elseif v[i] < low[i]
-                low[i] = v[i]
+    @assert !isempty(vlist) "cannot overapproximate an empty polytope"
+
+    @inbounds v1 = vlist[1]
+    center = similar(v1)
+    radius = similar(v1)
+
+    @inbounds for i in 1:n
+        low_i = v1[i]
+        high_i = v1[i]
+        for v in vlist
+            if v[i] > high_i
+                high_i = v[i]
+            elseif v[i] < low_i
+                low_i = v[i]
             end
         end
+        radius_i = (high_i - low_i) / 2
+        center[i] = low_i + radius_i
+        radius[i] = radius_i
     end
-    return Hyperrectangle(low=low, high=high)
+    return Hyperrectangle(center, radius)
 end
 
 """