Merge pull request #3118 from JuliaReach/schillic/box_approximation

Revise box-/ballinf-approximation and sih code

docs/src/lib/approximations.md

@@ -51,12 +51,11 @@ approximate
 ## Box Approximations
 
 ```@docs
-ballinf_approximation
 box_approximation
 interval_hull
 symmetric_interval_hull
 box_approximation_symmetric
-box_approximation_helper
+ballinf_approximation
 ```
 
 ## Iterative refinement

src/Approximations/ballinf_approximation.jl

@@ -1,9 +1,5 @@
-# ===========================================================
-# Concrete overapproximation with a ball in the infinity norm
-# ===========================================================
-
 """
-    ballinf_approximation(S::ConvexSet)
+    ballinf_approximation(S::LazySet)
 
 Overapproximate a set by a tight ball in the infinity norm.
 
@@ -17,36 +13,26 @@ A tight ball in the infinity norm.
 
 ### Algorithm
 
-The center and radius of the box are obtained by evaluating the support function
-of the given set along the canonical directions.
+The center and radius of the ball are obtained by averaging the low and high
+coordinates of `S` computed with the `extrema` function.
 """
-function ballinf_approximation(S::ConvexSet{N}) where {N}
+function ballinf_approximation(S::LazySet{N}) where {N}
     n = dim(S)
     c = Vector{N}(undef, n)
     r = zero(N)
-    d = zeros(N, n)
-
     @inbounds for i in 1:n
-        d[i] = one(N)
-        htop = ρ(d, S)
-        d[i] = -one(N)
-        hbottom = -ρ(d, S)
-        d[i] = zero(N)
-        c[i] = (htop + hbottom) / 2
-        rcur = (htop - hbottom) / 2
+        lo, hi = extrema(S, i)
+        rcur = (hi - lo) / 2
         if (rcur > r)
             r = rcur
         elseif !_geq(rcur, zero(N))
             # contradicting bounds => set is empty
             return EmptySet{N}(dim(S))
         end
+        c[i] = (hi + lo) / 2
     end
     return BallInf(c, r)
 end
 
-# ===============
-# Specializations
-# ===============
-
 # empty set specialization
 ballinf_approximation(∅::EmptySet) = ∅