hyperbolic_5_4_scroll.md

adapted from https://github.com/cduck/hyperbolic/blob/master/examples/poincare.ipynb

hyperbolic_test.ipynb

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   "source": [
    "import math\n",
    "import random\n",
    "\n",
    "import drawsvg as draw\n",
    "from drawsvg import Drawing\n",
    "from hyperbolic import euclid, util\n",
    "from hyperbolic.poincare import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1258f18a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hyp_poly_edge_construct(p, q):\n",
    "    pi, pi2 = math.pi, math.pi*2\n",
    "    th = pi2/q\n",
    "    phi = pi2/p\n",
    "    ang1 = pi-phi/2-th/2-pi/2\n",
    "    ang2 = th/2 + pi/2\n",
    "    a = math.sin(ang2)/math.sin(ang1)\n",
    "    b = math.sin(phi/2)/math.sin(ang1)\n",
    "    r_p = math.sqrt(1/(a**2-b**2))\n",
    "    r_c = a*r_p\n",
    "    r_from_c = b*r_p\n",
    "    #return r_c, r_from_c\n",
    "    t1 = pi - math.asin(r_c / (r_from_c / math.sin(phi/2)))\n",
    "    t2 = pi - t1 - phi/2\n",
    "    r = math.sin(t2) * (r_from_c / math.sin(phi/2))\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "250f2d5a",
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   "source": [
    "p = 5\n",
    "corner_deg = 90\n",
    "q = 360 / corner_deg\n",
    "skip = 1.0\n",
    "r = hyp_poly_edge_construct(p, q)\n",
    "p_list = [\n",
    "    Point.from_polar_euclid(r, deg=-skip*i*360/p)\n",
    "    for i in range(p)\n",
    "]\n",
    "print(p_list)\n",
    "\n",
    "n = len(p_list)\n",
    "e_list = [Line.from_points(*p_list[i], *p_list[(i+1)%n]) for i in range(n)]\n",
    "poly = Polygon(e_list, join=True)\n",
    "\n",
    "d = Drawing(2.1, 2.1, origin='center')\n",
    "d.draw(euclid.Circle(0, 0, 1), fill='silver')\n",
    "for edge in e_list:\n",
    "    d.draw(edge, hwidth=0.05, fill='blue')\n",
    "# d.draw(poly, hwidth=(0,-0.15), fill='green')\n",
    "# d.draw(poly, fill='black', opacity=0.3)\n",
    "# for p in p_list:\n",
    "#     d.draw(p, radius=0.05, stroke_width=0.01, stroke='#ccccff',\n",
    "#               fill='none', opacity=0.6)\n",
    "\n",
    "d.set_render_size(w=400)\n",
    "d.save_svg('images/polyRegular.svg')\n",
    "d"
   ]
  },
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   "cell_type": "code",
   "execution_count": 225,
   "id": "a16f9890",
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   "source": [
    "def construct_poly_vertices(p, q, deg_offset=0, skip=1):\n",
    "    r = hyp_poly_edge_construct(p, q)\n",
    "    return [\n",
    "        Point.from_polar_euclid(r, deg=-skip*i*360/p+deg_offset)\n",
    "        for i in range(p)\n",
    "    ]\n",
    "    \n",
    "def construct_poly_from_points(pt_list):\n",
    "    p = len(p_list)\n",
    "    e_list = [Line.from_points(*pt_list[i], *pt_list[(i + 1) % p]) for i in range(p)]\n",
    "    return Polygon(e_list, join=True)\n",
    "\n",
    "def draw_poly(poly, color=\"#ffffff\"):\n",
    "    d.draw(poly, fill=color, opacity=0.25)\n",
    "    d.draw(poly, hwidth=(0.0,0.05), fill='blue')\n",
    "    \n",
    "def draw_points(p_list):\n",
    "    for pt in p_list:\n",
    "        d.draw(pt, hradius=0.15, hwidth=0.02,\n",
    "                   fill='white', opacity=0.9)\n",
    "\n",
    "for ind in range(50):\n",
    "    d = Drawing(2.1, 2.1, origin='center')\n",
    "    d.draw(euclid.Circle(0, 0, 1), fill='#f9f9f9')\n",
    "\n",
    "    p = 5\n",
    "    q = 4\n",
    "    # print('Inner angle:', 360/q)\n",
    "\n",
    "    # the central polygon\n",
    "    pt_list = construct_poly_vertices(p, q)\n",
    "    rot_trans = Transform.rotation(deg=270)\n",
    "    offset = Transform.translation(Point(-0.5 + ind * 0.025, -0.0))\n",
    "    trans = Transform.merge(offset, rot_trans)\n",
    "    pt_list = trans.apply_to_list(pt_list)\n",
    "    poly = Polygon.from_vertices(pt_list)\n",
    "    draw_poly(poly)\n",
    "\n",
    "    def ring(p, q, i0, i1, pt_list):\n",
    "        pt_list2 = construct_poly_vertices(p, q)\n",
    "        t0 = pt_list2[0]\n",
    "        t1 = pt_list2[1]\n",
    "        trans_to_origin = Transform.shift_origin(t0, t1)\n",
    "        # print(f\"trans_to_origin: {t0} {t1} -> {trans_to_origin}\")\n",
    "        if False:\n",
    "            px, py = trans_to_origin.apply_to_tuple(p_list2[-1])\n",
    "            # print('Inner angle:', math.degrees(math.atan2(py,px)))\n",
    "\n",
    "        poly_list = []\n",
    "        pt_list_list = []\n",
    "        for i in range(i0, i1):\n",
    "            t0 = pt_list[(i + 1) % p]\n",
    "            t1 = pt_list[i]\n",
    "            trans_to_side = Transform.translation(t0, t1)\n",
    "            # print(f\"{i} t: {tx} {ty} -> {trans_to_side}\")\n",
    "            # offset = Transform.rotation(deg=5)\n",
    "            # offset = Transform.translation(Point(0.1, 0.0))\n",
    "            offset = Transform.translation(Point(0.0, 0.0))\n",
    "            trans = Transform.merge(offset, trans_to_origin, trans_to_side)\n",
    "            pt_list2r = trans.apply_to_list(pt_list2)\n",
    "            poly2 = Polygon.from_vertices(pt_list2r)\n",
    "            pt_list_list.append(pt_list2r)\n",
    "            poly_list.append(poly2)\n",
    "\n",
    "        for poly2 in poly_list:\n",
    "            draw_poly(poly2)\n",
    "        # draw_points(p_list)\n",
    "        # for pt_list2 in pt_list_list:\n",
    "        #     draw_points(pt_list2)\n",
    "\n",
    "        return poly_list, pt_list_list\n",
    "\n",
    "    poly_list, pt_list_list = ring(p, q, i0=0, i1=p, pt_list=pt_list)\n",
    "\n",
    "    # TODO(lucasw) need to avoid drawing the same shape twice\n",
    "    if True:\n",
    "        for poly, pt_list in zip(poly_list, pt_list_list):\n",
    "            poly_list, pt_list_list = ring(p, q, 1, 4, pt_list)\n",
    "            for poly, pt_list in zip(poly_list, pt_list_list):\n",
    "                poly_list, pt_list_list = ring(p, q, 0, 4, pt_list)\n",
    "                for poly, pt_list in zip(poly_list, pt_list_list):\n",
    "                    poly_list, pt_list_list = ring(p, q, 0, 5, pt_list)\n",
    "                    for poly, pt_list in zip(poly_list, pt_list_list):\n",
    "                        poly_list, pt_list_list = ring(p, q, 0, 5, pt_list)\n",
    "\n",
    "    d.set_render_size(w=1080)\n",
    "    name = f'images/poly_tile_{p}_{q}_{ind:05d}'\n",
    "    d.save_png(name + \".png\")\n",
    "    d"
   ]
  }
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