Update ConvexHull docstring

src/LazyOperations/ConvexHull.jl

@@ -9,17 +9,23 @@ export ConvexHull, CH,
 """
     ConvexHull{N, S1<:LazySet{N}, S2<:LazySet{N}} <: LazySet{N}
 
-Type that represents the convex hull of the union of two convex sets.
+Type that represents the convex hull of the union of two sets, that is the set
+
+```math
+Z = \\{z ∈ \\mathbb{R}^n : z = λx + (1-λ)y,\\qquad x ∈ X, y ∈ Y,λ ∈ [0, 1] \\}.
+```
 
 ### Fields
 
-- `X` -- convex set
-- `Y` -- convex set
+- `X` -- set
+- `Y` -- set
 
 ### Notes
 
 The `EmptySet` is the neutral element for `ConvexHull`.
 
+This type is always convex.
+
 ### Examples
 
 Convex hull of two 100-dimensional Euclidean balls:
@@ -37,7 +43,7 @@ struct ConvexHull{N, S1<:LazySet{N}, S2<:LazySet{N}} <: LazySet{N}
     X::S1
     Y::S2
 
-    # default constructor with dimension check  
+    # default constructor with dimension check
     function ConvexHull(X::LazySet{N}, Y::LazySet{N}) where {N}
         @assert dim(X) == dim(Y) "sets in a convex hull must have the same dimension"
         return new{N, typeof(X), typeof(Y)}(X, Y)
@@ -67,7 +73,7 @@ Return a new `ConvexHull` object with the arguments swapped.
 
 ### Input
 
-- `ch` -- convex hull of two convex sets
+- `ch` -- convex hull of two sets
 
 ### Output
 
@@ -80,15 +86,15 @@ end
 """
     dim(ch::ConvexHull)
 
-Return the dimension of a convex hull of two convex sets.
+Return the dimension of a convex hull of two sets.
 
 ### Input
 
-- `ch` -- convex hull of two convex sets
+- `ch` -- convex hull of two sets
 
 ### Output
 
-The ambient dimension of the convex hull of two convex sets.
+The ambient dimension of the convex hull of two sets.
 """
 function dim(ch::ConvexHull)
     return dim(ch.X)
@@ -97,13 +103,12 @@ end
 """
     σ(d::AbstractVector, ch::ConvexHull)
 
-Return the support vector of a convex hull of two convex sets in a given
-direction.
+Return the support vector of the convex hull of two sets in a given direction.
 
 ### Input
 
 - `d`  -- direction
-- `ch` -- convex hull of two convex sets
+- `ch` -- convex hull of two sets
 
 ### Output
 
@@ -120,13 +125,12 @@ end
 """
     ρ(d::AbstractVector, ch::ConvexHull)
 
-Return the support function of a convex hull of two convex sets in a given
-direction.
+Return the support function of the convex hull of two sets in a given direction.
 
 ### Input
 
 - `d`  -- direction
-- `ch` -- convex hull of two convex sets
+- `ch` -- convex hull of two sets
 
 ### Output
 
@@ -139,11 +143,11 @@ end
 """
     isbounded(ch::ConvexHull)
 
-Determine whether a convex hull of two convex sets is bounded.
+Determine whether the convex hull of two sets is bounded.
 
 ### Input
 
-- `ch` -- convex hull of two convex sets
+- `ch` -- convex hull of two sets
 
 ### Output
 
@@ -156,7 +160,7 @@ end
 """
     isempty(ch::ConvexHull)
 
-Return if a convex hull of two convex sets is empty or not.
+Return if the convex hull of two sets is empty or not.
 
 ### Input
 
@@ -173,11 +177,11 @@ end
 """
     vertices_list(ch::ConvexHull; apply_convex_hull::Bool=true, backend=nothing)
 
-Return the list of vertices of the convex hull of two convex sets.
+Return the list of vertices of the convex hull of two sets.
 
 ### Input
 
-- `ch`               -- convex hull of two convex sets
+- `ch`                -- convex hull of two sets
 - `apply_convex_hull` -- (optional, default: `true`) if `true`, post-process the
                          vertices using a convex-hull algorithm
 - `backend`           -- (optional, default: `nothing`) backend for computing
@@ -197,6 +201,8 @@ function vertices_list(ch::ConvexHull;
     return vlist
 end
 
+# concretization of a convex hull computes the (concrete) convex hull of the
+# concretization of each wrapped set
 function concretize(ch::ConvexHull)
     return convex_hull(concretize(ch.X), concretize(ch.Y))
 end