espdev/mirroring-point.ipynb

## mirroring-point.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Отражение точки относительно заданного отрезка"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Задаём отрезок координатами точек начала и конца\n",
    "x1, y1 = 10.5, 11.0\n",
    "x2, y2 = 20.4, 15.6\n",
    "\n",
    "# Задаём точку\n",
    "px = 17.1\n",
    "py = 11.2\n",
    "# px = 12.5\n",
    "# py = 14.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The line equation: -0.4x + 0.9y + -5.6 = 0\n",
      "The perpendicular line equation: -0.9x + -0.4y + 20.2 = 0\n"
     ]
    }
   ],
   "source": [
    "def segment_line_equation(px, py, qx, qy):\n",
    "    \"\"\"Вычисляет общее уравнение прямой Ax + By + C = 0 для отрезка\n",
    "    \"\"\"\n",
    "    A = py - qy\n",
    "    B = qx - px\n",
    "    C = -A * px - B * py\n",
    "\n",
    "    # Нормализация для точности вычислений\n",
    "    z = np.sqrt(A*A + B*B)\n",
    "    A, B, C = [cf / z for cf in (A, B, C)]\n",
    "\n",
    "    return A, B, C\n",
    "\n",
    "\n",
    "# Определяем уравнение прямой для заданного отрезка\n",
    "A, B, C = segment_line_equation(x1, y1, x2, y2)\n",
    "\n",
    "# Определим уравнение прямой, проходящей через заданную точку и перпендикулярной к прямой заданного отрезка\n",
    "Ap, Bp, Cp = segment_line_equation(px, py, (px + A), (py + B))\n",
    "\n",
    "print(f'The line equation: {A:.1f}x + {B:.1f}y + {C:.1f} = 0')\n",
    "print(f'The perpendicular line equation: {Ap:.1f}x + {Bp:.1f}y + {Cp:.1f} = 0')\n",
    "\n",
    "# Проверка\n",
    "# cx = 14.1\n",
    "# cy = (A * cx + C) / -B\n",
    "\n",
    "# cpx = 15.5\n",
    "# cpy = (Ap * cpx + Cp) / -Bp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Определяем проекцию точки на отрезок (точка пересечения прямых)\n",
    "d = (A * Bp - Ap * B)\n",
    "ix = -(C * Bp - Cp * B) / d\n",
    "iy = -(A * Cp - Ap * C) / d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Определяем точку отражения от отрезка (точку, симметричную заданной относительно отрезка)\n",
    "\n",
    "# Вычисляем вектор направления от заданной точки до спроецированной точки на отрезке (точки пересечения)\n",
    "dist = np.sqrt((ix - px)**2 + (iy - py)**2) * 2\n",
    "\n",
    "theta = np.arctan2((iy - py), (ix - px))\n",
    "ux = dist * np.cos(theta)\n",
    "uy = dist * np.sin(theta)\n",
    "\n",
    "mx = px + ux\n",
    "my = py + uy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
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6yal0idWwLAmc3/4WevVSmcvfU6F3UFV1PcvXFbN0dREVR2uZMCiJ/7p1MpeP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15865024c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.plot([x1, x2], [y1, y2], 'o-')\n",
    "plt.plot([px, mx], [py, my], ':b')\n",
    "plt.plot(px, py, 'or')\n",
    "plt.plot(mx, my, 'og')\n",
    "plt.plot(ix, iy, '.m')\n",
    "plt.axis('equal');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Отражение точки относительно заданного отрезка"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 156,
	"metadata": {},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"\n",
	"# Задаём отрезок координатами точек начала и конца\n",
	"x1, y1 = 10.5, 11.0\n",
	"x2, y2 = 20.4, 15.6\n",
	"\n",
	"# Задаём точку\n",
	"px = 17.1\n",
	"py = 11.2\n",
	"# px = 12.5\n",
	"# py = 14.5"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 157,
	"metadata": {},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"The line equation: -0.4x + 0.9y + -5.6 = 0\n",
	"The perpendicular line equation: -0.9x + -0.4y + 20.2 = 0\n"
	]
	}
	],
	"source": [
	"def segment_line_equation(px, py, qx, qy):\n",
	" \"\"\"Вычисляет общее уравнение прямой Ax + By + C = 0 для отрезка\n",
	" \"\"\"\n",
	" A = py - qy\n",
	" B = qx - px\n",
	" C = -A * px - B * py\n",
	"\n",
	" # Нормализация для точности вычислений\n",
	" z = np.sqrt(AA + BB)\n",
	" A, B, C = [cf / z for cf in (A, B, C)]\n",
	"\n",
	" return A, B, C\n",
	"\n",
	"\n",
	"# Определяем уравнение прямой для заданного отрезка\n",
	"A, B, C = segment_line_equation(x1, y1, x2, y2)\n",
	"\n",
	"# Определим уравнение прямой, проходящей через заданную точку и перпендикулярной к прямой заданного отрезка\n",
	"Ap, Bp, Cp = segment_line_equation(px, py, (px + A), (py + B))\n",
	"\n",
	"print(f'The line equation: {A:.1f}x + {B:.1f}y + {C:.1f} = 0')\n",
	"print(f'The perpendicular line equation: {Ap:.1f}x + {Bp:.1f}y + {Cp:.1f} = 0')\n",
	"\n",
	"# Проверка\n",
	"# cx = 14.1\n",
	"# cy = (A * cx + C) / -B\n",
	"\n",
	"# cpx = 15.5\n",
	"# cpy = (Ap * cpx + Cp) / -Bp"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 158,
	"metadata": {},
	"outputs": [],
	"source": [
	"# Определяем проекцию точки на отрезок (точка пересечения прямых)\n",
	"d = (A * Bp - Ap * B)\n",
	"ix = -(C * Bp - Cp * B) / d\n",
	"iy = -(A * Cp - Ap * C) / d"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 159,
	"metadata": {},
	"outputs": [],
	"source": [
	"# Определяем точку отражения от отрезка (точку, симметричную заданной относительно отрезка)\n",
	"\n",
	"# Вычисляем вектор направления от заданной точки до спроецированной точки на отрезке (точки пересечения)\n",
	"dist = np.sqrt((ix - px)2 + (iy - py)2) * 2\n",
	"\n",
	"theta = np.arctan2((iy - py), (ix - px))\n",
	"ux = dist * np.cos(theta)\n",
	"uy = dist * np.sin(theta)\n",
	"\n",
	"mx = px + ux\n",
	"my = py + uy"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 160,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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6yal0idWwLAmc3/4WevVSmcvfU6F3UFV1PcvXFbN0dREVR2uZMCiJ/7p1MpeP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\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x15865024c88>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"%matplotlib inline\n",
	"from matplotlib import pyplot as plt\n",
	"\n",
	"plt.plot([x1, x2], [y1, y2], 'o-')\n",
	"plt.plot([px, mx], [py, my], ':b')\n",
	"plt.plot(px, py, 'or')\n",
	"plt.plot(mx, my, 'og')\n",
	"plt.plot(ix, iy, '.m')\n",
	"plt.axis('equal');"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.6.2"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}