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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center> Poisson disk samples generated via Bridson algorithm </center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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       "<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">\n",
       "<p>The WebIO Jupyter extension was not detected. See the\n",
       "<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/providers/ijulia/\" target=\"_blank\">\n",
       "    WebIO Jupyter integration documentation\n",
       "</a>\n",
       "for more information.\n",
       "</div>\n"
      ],
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       "WebIO._IJuliaInit()"
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      "application/vnd.webio.node+json": {
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      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "using PlotlyJS\n",
    "import StaticArrays:SVector, @SVector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "unif_sampling_annulus (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function distsq(A::SVector{2, T}, B::SVector{2, T}) where T <: Real\n",
    "    return (A[1]-B[1])^2 + (A[2]-B[2])^2\n",
    "end\n",
    "\n",
    "function grid_idxs(point:: SVector{2, T}, cellsize::T) where T <: Real \n",
    "    \"\"\" Returns cell indices, (i,j)=(row, col) for  `point` \"\"\"\n",
    "    return ceil(Int, point[2] / cellsize) + 1, ceil(Int, point[1] / cellsize) + 1\n",
    "end\n",
    "\n",
    "function ispoint_inrectangle(point::SVector{2, T}, rlims::Tuple{T, T}) where T <: Real\n",
    "    \"\"\" \n",
    "    Check whether a point is within the rectangle \n",
    "    [0, rlims[1]] x [0, rlims[2]];\n",
    "    here rlims =(width, height)\n",
    "    \"\"\"\n",
    "    return (0 <= point[1] <= rlims[1]) && (0 <= point[2] <= rlims[2])\n",
    "end    \n",
    "\n",
    "function unif_sampling_annulus(center::SVector{2, T}, inner_rad::T, outer_rad::T; \n",
    "                               k=30) where T <: Real\n",
    "    \"\"\" \n",
    "    Samples  uniformly k points from the annulus of center, `center`, \n",
    "    and radii, inner_radius, outer_radius\n",
    "    \"\"\"\n",
    "    rad = sqrt.(inner_rad^2  .+ (outer_rad^2 - inner_rad^2)*rand(k)) \n",
    "    angle = 2π * rand(k)  \n",
    "    x, y = center[1] .+ rad .* cos.(angle), center[2] .+ rad .*sin.(angle) \n",
    "    return [@SVector([xi, yi]) for (xi, yi) in zip(x,y)]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poisson_disk_sampling (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Poisson_disk_sampling(;width =1.0, height=1.0, radius=0.05, k=30)\n",
    "    \"\"\" \n",
    "    Bridson Algorithm to generate  Poisson disk samples \n",
    "    within a 2D rectangle, [0, width] x [0, height]\n",
    "    Ref: R Bridson, Fast Poisson disk sampling in arbitrary dimensions,\n",
    "    in  SIGGRAPH '07: ACM SIGGRAPH 2007 sketches\n",
    "    https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph07-poissondisk.pdf\n",
    "    \"\"\"\n",
    "    function  is_accepted(point:: SVector{2, T})  where T <: Real\n",
    "        \"\"\" \n",
    "        Check whether the point, `point` can be added to the active_list\n",
    "        \"\"\"\n",
    "        i, j = grid_idxs(point, cellsize)\n",
    "        m, n = maximum([i-2, 1]), maximum([j-2, 1])\n",
    "        p, q = minimum([i+2, grows]), minimum([j+2, gcols])\n",
    "        for k in n:q\n",
    "            for l in m:p\n",
    "                gpoint = grid[(k-1) * grows + l]\n",
    "                if ismissing(gpoint)\n",
    "                    continue\n",
    "                end\n",
    "                if distsq(point, gpoint) <= r2\n",
    "                    return false\n",
    "                end\n",
    "            end\n",
    "        end              \n",
    "        return true\n",
    "    end\n",
    "    \n",
    "    cellsize = radius/sqrt(2)\n",
    "    gcols = ceil(Int, width / cellsize) + 1\n",
    "    grows = ceil(Int, height / cellsize) + 1\n",
    "  \n",
    "    grid = Vector{Any}(missing, grows*gcols)\n",
    "    r2 = radius*radius\n",
    "    active_list = SVector{2, Float64}[]\n",
    "    \n",
    "    #generate a random point within the rectangle of interest\n",
    "    # and  insert it into the active_list and grid\n",
    "    point = @SVector([width*rand(1)[1], height*rand(1)[1]])\n",
    "    push!(active_list, point)\n",
    "    i, j = grid_idxs(point, cellsize)\n",
    "    grid[(j-1)*grows+i] = point\n",
    "    \n",
    "    while length(active_list) > 0\n",
    "        i = rand(1:length(active_list), 1)[1]\n",
    "        pt = active_list[i] \n",
    "        active_list  =  active_list[1:end .!= i] #removes the point in pos i\n",
    "        rpoints = unif_sampling_annulus(pt, radius, 2*radius; k=k)\n",
    "        for rp in rpoints\n",
    "            if !ispoint_inrectangle(rp, (width, height)) || !is_accepted(rp)\n",
    "                continue\n",
    "            end    \n",
    "            push!(active_list, rp)    \n",
    "            i, j = grid_idxs(rp, cellsize)\n",
    "            grid[(j-1)*grows+i] = rp\n",
    "        end\n",
    "    end\n",
    "    return filter(x->!ismissing(x), grid)\n",
    "end    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "        {\"editable\":false,\"responsive\":true,\"staticPlot\":false,\"scrollZoom\":true},\n",
       "    )\n",
       "}\n",
       "\n",
       "        });\n",
       "    </script>\n",
       "</div>\n",
       "\n",
       "</body>\n",
       "</html>"
      ],
      "text/plain": [
       "data: [\n",
       "  \"scatter with fields marker, mode, type, x, and y\"\n",
       "]\n",
       "\n",
       "layout: \"layout with fields height, margin, template, width, xaxis, and yaxis\"\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vector_of_samples = Poisson_disk_sampling(;width =5.0, height=3.0, radius=0.045, k=30)\n",
    "xcoords = [p[1] for p in vector_of_samples]\n",
    "ycoords = [p[2] for p in vector_of_samples]\n",
    "fig1 = Plot(scatter(x=xcoords, y=ycoords, mode=\"markers\", marker_size=3), \n",
    "            Layout(width=600, height=400, \n",
    "                   xaxis_showgrid=false, yaxis_showgrid=false))\n",
    "display(fig1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        {\"editable\":false,\"responsive\":true,\"staticPlot\":false,\"scrollZoom\":true},\n",
       "    )\n",
       "}\n",
       "\n",
       "        });\n",
       "    </script>\n",
       "</div>\n",
       "\n",
       "</body>\n",
       "</html>"
      ],
      "text/plain": [
       "data: [\n",
       "  \"scatter with fields marker, mode, type, x, and y\"\n",
       "]\n",
       "\n",
       "layout: \"layout with fields height, margin, template, width, xaxis, and yaxis\"\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vector_of_samples = Poisson_disk_sampling(;width=4.0, height=4.0, radius=0.05, k=30)\n",
    "#perform a translation of the default rectangle [0, width] x [0, height] to [3, 3+]x  [-2, -2+height]\n",
    "xcoords = [p[1] for p in vector_of_samples] .+ 3.0\n",
    "ycoords = [p[2] for p in vector_of_samples] .- 2.0  \n",
    "fig2 = Plot(scatter(x=xcoords, y=ycoords, mode=\"markers\", marker_size=3), \n",
    "            Layout(width=500, height=500, \n",
    "                   xaxis_showgrid=false, yaxis_showgrid=false,\n",
    "                   xaxis_zeroline=false, yaxis_zeroline=false ))\n",
    "display(fig2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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