From bd5126d9797102585a5c019c2a6cae290f6d340b Mon Sep 17 00:00:00 2001
From: mforets <marcelo.forets-irurtia@univ-grenoble-alpes.fr>
Date: Sat, 3 Mar 2018 08:28:48 -0300
Subject: [PATCH 1/4] postprocess 2D vertices list with a convex hull

---
 src/plot_recipes.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/plot_recipes.jl b/src/plot_recipes.jl
index 91473391da..b2a3a27c19 100644
--- a/src/plot_recipes.jl
+++ b/src/plot_recipes.jl
@@ -30,7 +30,7 @@ plotting singletons.
                               color="blue", label="", grid=true, alpha=0.5)
 
     P = Approximations.overapproximate(S)
-    vlist = hcat(vertices_list(P)...).'
+    vlist = hcat(convex_hull(vertices_list(P))...).'
     (x, y) = vlist[:, 1], vlist[:, 2]
 
     seriestype := norm(vlist[1, :] - vlist[2, :]) ≈ 0 ? :scatter : :shape

From 5332d9617dacaf86d4caa666bfff8b2da620eeea Mon Sep 17 00:00:00 2001
From: mforets <marcelo.forets-irurtia@univ-grenoble-alpes.fr>
Date: Sat, 3 Mar 2018 08:34:07 -0300
Subject: [PATCH 2/4] explain plot_lazyset algorithm

---
 src/plot_recipes.jl | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/src/plot_recipes.jl b/src/plot_recipes.jl
index b2a3a27c19..acdbeb7fc9 100644
--- a/src/plot_recipes.jl
+++ b/src/plot_recipes.jl
@@ -19,6 +19,13 @@ julia> B = BallInf(ones(2), 0.1)
 julia> plot(2.0 * B)
 ```
 
+### Algorithm
+
+For any 2D lazy set we compute its box overapproximation, followed by the list of
+vertices. A post-processing `convex_hull` is applied to the vertices list;
+this ensures that the shaded area inside the convex hull of the vertices is covered
+correctly.
+
 ### Notes
 
 This recipe detects if the axis-aligned approximation is such that the first two

From 473f06bda1ca4c3b33d3cd417b00b40e23b5dd5d Mon Sep 17 00:00:00 2001
From: mforets <marcelo.forets-irurtia@univ-grenoble-alpes.fr>
Date: Sat, 3 Mar 2018 08:47:48 -0300
Subject: [PATCH 3/4] update vector version too

---
 src/plot_recipes.jl | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/src/plot_recipes.jl b/src/plot_recipes.jl
index acdbeb7fc9..e06c7efbe9 100644
--- a/src/plot_recipes.jl
+++ b/src/plot_recipes.jl
@@ -63,6 +63,13 @@ julia> B1 = BallInf(zeros(2), 0.4)
 julia> B2 = BallInf(ones(2), 0.4)
 julia> plot([B1, B2])
 ```
+
+### Algorithm
+
+For each 2D lazy set in the array we compute its box overapproximation, followed
+by the list of vertices. A post-processing `convex_hull` is applied to the vertices list;
+this ensures that the shaded area inside the convex hull of the vertices is covered
+correctly.
 """
 @recipe function plot_lazyset(arr::Vector{<:LazySet};
                               seriescolor="blue", label="", grid=true,
@@ -72,7 +79,7 @@ julia> plot([B1, B2])
 
     for S in arr
         Pi = Approximations.overapproximate(S)
-        vlist = hcat(vertices_list(Pi)...).'
+        vlist = hcat(convex_hull(vertices_list(P))...).'
         @series (x, y) = vlist[:, 1], vlist[:, 2]
     end
 end

From 2c123d2a55ffc8ff3aac938efe5a0ac01dd03e3a Mon Sep 17 00:00:00 2001
From: mforets <marcelo.forets-irurtia@univ-grenoble-alpes.fr>
Date: Sat, 3 Mar 2018 08:53:00 -0300
Subject: [PATCH 4/4] P -> Pi

---
 src/plot_recipes.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/plot_recipes.jl b/src/plot_recipes.jl
index e06c7efbe9..da807f20c6 100644
--- a/src/plot_recipes.jl
+++ b/src/plot_recipes.jl
@@ -79,7 +79,7 @@ correctly.
 
     for S in arr
         Pi = Approximations.overapproximate(S)
-        vlist = hcat(convex_hull(vertices_list(P))...).'
+        vlist = hcat(convex_hull(vertices_list(Pi))...).'
         @series (x, y) = vlist[:, 1], vlist[:, 2]
     end
 end