From 3910423387cf261613a97630a953e73f03e43291 Mon Sep 17 00:00:00 2001
From: Marcelo Forets <mforets@gmail.com>
Date: Tue, 22 Dec 2020 11:12:56 -0300
Subject: [PATCH] #2453 - Vertices list of IntervalArithmetic types (#2457)

* vertices list of IA types

* typo

* Update unit_Interval.jl
---
 src/Sets/Interval.jl  | 16 ++++++++++++++++
 test/unit_Interval.jl |  8 ++++++++
 2 files changed, 24 insertions(+)

diff --git a/src/Sets/Interval.jl b/src/Sets/Interval.jl
index b67bd3bcf0..0bb526d946 100644
--- a/src/Sets/Interval.jl
+++ b/src/Sets/Interval.jl
@@ -699,3 +699,19 @@ end
         return result
     end
 end
+
+function vertices_list(x::IntervalArithmetic.Interval{N}) where {N}
+    a = IntervalArithmetic.inf(x)
+    b = IntervalArithmetic.sup(x)
+    ST = IntervalArithmetic.SVector{1, N}
+    if _isapprox(a, b)
+        vlist = [ST(a)]
+    else
+        vlist = [ST(a), ST(b)]
+    end
+    return vlist
+end
+
+function vertices_list(H::IntervalArithmetic.IntervalBox)
+    return vertices_list(convert(Hyperrectangle, H))
+end
diff --git a/test/unit_Interval.jl b/test/unit_Interval.jl
index 4145d086c1..b212e16e36 100644
--- a/test/unit_Interval.jl
+++ b/test/unit_Interval.jl
@@ -208,4 +208,12 @@ for N in Ns
     @test rectify(x) == Interval(N(0), N(2))
     x = Interval(N(1), N(2))
     @test rectify(x) == x
+
+    # list of vertices of IA types
+    b = IA.IntervalBox(IA.Interval(0 , 1), IA.Interval(0, 1))
+    vlistIB = vertices_list(b)
+    @test is_cyclic_permutation(vlistIB, [SA[N(1), N(1)], SA[N(0), N(1)], SA[N(1), N(0)], SA[N(0), N(0)]])
+
+    vlistI = vertices_list(b[1])
+    @test is_cyclic_permutation(vlistI, [SA[N(0)], SA[N(1)]])
 end