DistToPlane.ipynb

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    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "\n",
    "\n",
    "mpl.rcParams['lines.color'] = 'k'\n",
    "mpl.rcParams['axes.prop_cycle'] = mpl.cycler('color', ['k'])"
   ]
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   "cell_type": "code",
   "execution_count": 98,
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   "source": [
    "x = np.linspace(-2, 2, 400)\n",
    "y = np.linspace(-2, 2, 400)\n",
    "x, y = np.meshgrid(x, y)"
   ]
  },
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    "def axes():\n",
    "    plt.axhline(0, alpha=.1)\n",
    "    plt.axvline(0, alpha=.1)\n",
    "def sqdist(a,b,x,y):\n",
    "    part1 = np.square(a-x)\n",
    "    part2 = np.square(b-y)\n",
    "    return part1+part2\n",
    "def relSim(x1,y1,x2,y2,x,y):\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    return (d1-d2)/(d1+d2)\n",
    "def subDist(x1,y1,x2,y2,x,y):\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    return np.abs(d1-d2)\n",
    "def addDist(x1,y1,x2,y2,x,y):\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    return (d1+d2)\n",
    "def relPlaneDist(x1,y1,x2,y2,x,y):\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    dAB = sqdist(x1, y1, x2, y2)\n",
    "    return np.abs(d1-d2)/dAB\n",
    "def planeDist(x1,y1,x2,y2,x,y):\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    dAB = sqdist(x1, y1, x2, y2)\n",
    "    return np.square(d1-d2)/sqdist(x1, y1, x2, y2)/4\n",
    "def ratioDist(x1,y1,x2,y2,x,y):\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    return 1-np.minimum(d1,d2)/np.maximum(d1,d2)\n",
    "def parabolaDist(x1,y1,x2,y2,x,y):\n",
    "    dP = planeDist(x1,y1,x2,y2,x,y)\n",
    "    d1 = sqdist(x1, y1, x, y)\n",
    "    d2 = sqdist(x2, y2, x, y)\n",
    "    return np.minimum(d1,d2)/dP.clip(min=.001)"
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      "text/plain": [
       "<function __main__.myplot>"
      ]
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     "execution_count": 100,
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   "source": [
    "def myplot(x1=-1.0, y1=1.0, x2=1.0, y2=-1.0, d=relSim):\n",
    "    axes()\n",
    "    plt.plot([x1,x2], [y1,y2], 'ro')\n",
    "    cs = plt.contour(x, y, d(x1,y1,x2,y2,x,y), locator=mpl.ticker.LogLocator())#, np.linspace(-5,5,51))\n",
    "    plt.clabel(cs)\n",
    "    plt.show()\n",
    "methods = [relSim,subDist,addDist,relPlaneDist,planeDist,ratioDist, parabolaDist]\n",
    "methods = {f.__name__: f for f in methods}\n",
    "interact(myplot, x1=(-10,10.), y1=(-10,10.), x2=(-10,10.), y2=(-10,10.), d=methods)"
   ]
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   "cell_type": "code",
   "execution_count": 56,
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     "text": [
      "Q:1.0 X1:2.0 X2:-2.0\n",
      "\n",
      "relSim: -0.8\n",
      "relPlaneDist: 0.5\n",
      "dAB: 16.0\n",
      "\n",
      "planeDist1: 1.0\n",
      "planeDist2: 1.0\n",
      "planeDist3: 1.0\n",
      "sqDist: 1.0\n"
     ]
    }
   ],
   "source": [
    "q  = 1.\n",
    "x1 = 2.\n",
    "x2 = -2.\n",
    "\n",
    "print 'Q:%.1f X1:%.1f X2:%.1f'%(q,x1,x2)\n",
    "print ''\n",
    "print 'relSim:',relSim(x1,0,x2,0,q,0)\n",
    "print 'relPlaneDist:',relPlaneDist(x1,0.,x2,0.,q,0.)\n",
    "print 'dAB:',sqdist(x1,0,x2,0)\n",
    "print ''\n",
    "print 'planeDist1:',relPlaneDist(x1,0,x2,0,q,0)**p * sqdist(x1,0,x2,0)/4\n",
    "print 'planeDist2:',(subDist(x1,0,x2,0,q,0)**p / sqdist(x1,0,x2,0))/4\n",
    "print 'planeDist3:',planeDist(x1,0,x2,0,q,0)\n",
    "print 'sqDist:',sqdist((x1+x2)/2.,0,q,0)"
   ]
  }
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