Merge pull request #144 from mforets/mforets/convexhull

Update operations notebook

Author: blegat

examples/operations.ipynb

@@ -186,7 +186,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "On the other hand, `Pint` is contructed from its H-representation hence its V-representation had not been computed yet."
+    "On the other hand, `Pint` is constructed from its H-representation hence its V-representation has not been computed yet."
    ]
   },
   {
@@ -720,25 +720,114 @@
     "hrepiscomputed(P1), hrepiscomputed(P2), hrepiscomputed(Pint)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us note that the `convexhull` of a V-representation contains points and rays and represents the convex hull\n",
+    "of the points together with the conic hull of the rays. So, `convexhull(P1, P2)` does the union of the vertices:"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Polyhedron CDDLib.Polyhedron{Float64}:\n",
+       "15-element iterator of Array{Float64,1}:\n",
+       " [0.965939, -0.408821]\n",
+       " [0.0423453, -2.35475]\n",
+       " [0.445098, 0.496043]\n",
+       " [-0.503593, -0.643319]\n",
+       " [0.275412, 0.958958]\n",
+       " [1.52787, 0.765889]\n",
+       " [2.32907, 0.508292]\n",
+       " [0.976168, -0.213605]\n",
+       " [-1.2088, 0.561409]\n",
+       " [0.0899901, -1.99332]\n",
+       " [-0.436715, -0.0207767]\n",
+       " [-0.915581, -0.307397]\n",
+       " [0.162809, -0.899802]\n",
+       " [1.89527, 0.417177]\n",
+       " [-1.19564, 0.680285]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# each of Q1 and Q2 has 15 vertices\n",
+    "Q1 = polyhedron(vrep(randn(15, 2)), CDDLib.Library())\n",
+    "Q2 = polyhedron(vrep(randn(15, 2)), CDDLib.Library())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "30"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# check that their convex hull has 30 vertices\n",
+    "Qch = convexhull(Q1, Q2)\n",
+    "npoints(Qch)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "However, if we want to remove the redundant points we can use `removevredundancy!`:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "removevredundancy!(Qch)\n",
+    "npoints(Qch)"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.0.1",
+   "display_name": "Julia 1.0.2",
    "language": "julia",
    "name": "julia-1.0"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.0.1"
+   "version": "1.0.2"
   }
  },
  "nbformat": 4,