Implemented ellipse-rectangle intersection test

src/ConcreteOperations/isdisjoint.jl

@@ -613,6 +613,53 @@ end
     end
 end
 
+"""
+# Extended help
+
+    isdisjoint(H::Hyperrectangle, E::Ellipsoid)
+
+### Algorithm
+
+The sets are disjoint if the ellipse center lies outside the Minkowski sum 
+(rectangle expanded by the ellipsoid). Otherwise, we check one corner using 
+a quadratic form derived from the ellipsoids support function.
+
+### Notes
+It works only for 2D axis-aligned rectangles and ellipsoids.
+
+### Reference
+David Eberly, “Distance Between a Point and an Ellipse, an Ellipsoid, or a Hyperellipsoid”,
+Geometric Tools, 2015. https://www.geometrictools.com/Documentation/DistancePointEllipseEllipsoid.pdf
+"""
+
+@commutative function isdisjoint(H::Hyperrectangle, E::Ellipsoid)
+    @assert dim(H) == dim(E) == 2 "$H and $E must both have 2 dimensions."
+
+    # center to the origin
+    H_trans = translate(H, -H.center)
+    E_trans = translate(E, -H.center)
+    K = E_trans.center 
+
+    bbox = overapproximate(H_trans ⊕ E_trans, Hyperrectangle)
+    if any(abs.(K) .> bbox.radius)
+        return true
+    end
+
+    # find the rectangle corner corresponding to K.
+    s = sign.(K)
+    P = s .* H_trans.radius
+    Δ = K - P
+
+    # support vector on the boundary of E_trans in direction Δ.
+    v = σ(Δ, E_trans)
+    if any(s .* v .<= 0)
+        return false
+    end
+
+    # check the ellipse condition
+    return (ρ(Δ, E_trans))^2 ≤ 1
+end
+
 # ============== #
 # disambiguation #
 # ============== #

test/ConcreteOperations/isdisjoint.jl

@@ -25,3 +25,25 @@ for N in [Float64, Float32, Rational{Int}]
         end
     end
 end
+
+for N in [Float64, Float32]
+    # case 1: ellipse completely outside
+    R1 = Hyperrectangle(N[1.0, -1.0], N[2, 1])
+    El1 = Ellipsoid(N[5.0, 5.0], Matrix{N}(I, 2, 2))
+    @test isdisjoint(R1, El1)
+
+    # case 2: ellipse completely inside
+    R2 = Hyperrectangle(N[0.0, 0.0], N[4.0, 1.0])
+    El2 = Ellipsoid(N[1.0, 0.0], Matrix{N}(I, 2, 2))
+    @test !isdisjoint(R2, El2)
+
+    # case 3: ellipse overlapping
+    R3 = Hyperrectangle(N[0.0, 0.0], N[1.0, 1.0])
+    El3 = Ellipsoid(N[2.0, 0.0], Diagonal(N[2.0, 1.0]))
+    @test !isdisjoint(R3, El3)
+
+    # case 4: ellipse tangent in one point
+    R4 = Hyperrectangle(N[0.0, 0.0], N[1.0, 1.0])
+    El4 = Ellipsoid(N[2.0, 0.0], Diagonal(N[1.0, 1.0]))
+    @test !isdisjoint(R4, El4)
+end