{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "from math import sin, cos, radians\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def interaction(x,y,vx,vy,ax,ay,dt): # ぶつかる処理など\n",
    "    return (False,x,y,vx,vy)         # （後で書くので、今は何もしない）\n",
    "# ボールを投げて、軌跡＝位置（x,y）配列、ゴールしたかを返す\n",
    "def throw(x,y,v0,angle,repeatNum,dt):#位置,初速度,角度,計算回数,計算ステップ\n",
    "    isSuccess = False          # ボールがゴールに入ったか\n",
    "    xarray = []; yarray = []   # 水平=x方向と鉛直=y方向の位置格納配列\n",
    "    vx = v0*cos( radians(angle) ) # ボールの速度（水平=x方向）\n",
    "    vy = v0*sin( radians(angle) ) # ボールの速度（鉛直=y方向）\n",
    "    ax = 0.0  # 水平=x方向に働く加速度はゼロ\n",
    "    ay = -9.8 # 鉛直=x方向に働く加速度＝重力加速度\n",
    "    for i in range(repeatNum): # 時間を細かく進めながら、計算していく\n",
    "        vx = vx + ax*dt      # 水平=x方向加速度で、水平方向速度が変化\n",
    "        vy = vy + ay*dt      # 鉛直=x方向加速度で、鉛直方向速度が変化\n",
    "        x = x + (vx-ax*dt/2)*dt    # 水平(x)方向速度で、水平位置が変化\n",
    "        y = y + (vy-ay*dt/2)*dt    # 鉛直(x)方向速度で、鉛直位置が変化\n",
    "        isPassing,x,y,vx,vy = interaction(x,y,vx,vy,ax,ay,dt) \n",
    "        if isPassing:\n",
    "            isSuccess = True\n",
    "        xarray.append(x) # 水平(x)位置を、水平位置を格納する配列に追加\n",
    "        yarray.append(y) # 鉛直(x)位置を、鉛直位置を格納する配列に追加\n",
    "    return (xarray,yarray,isSuccess)\n",
    "# 描画関数\n",
    "def prepareFigureArea():\n",
    "    plt.figure(figsize=(5,5))         # グラフの大きさを設定\n",
    "    plt.xlim([0,5]); plt.ylim([0,5])  # 描くXY領域(各0から5まで)を設定\n",
    "    plt.xlabel('X - Axis (m)');plt.ylabel('Y - Axis (m)') # 軸説明   \n",
    "    return\n",
    "# ボールを投げ、軌跡・結果を得る。引数：スタート位置,初速度,角度,計算回数,計算ステップ\n",
    "x1,y1,isSuccess  = throw(0,0,6,35,500,0.01)\n",
    "x2,y2,isSuccess2 = throw(0,0,6,45,500,0.01)\n",
    "x3,y3,isSuccess3 = throw(0,0,6,55,500,0.01)\n",
    "# 描画する\n",
    "prepareFigureArea()\n",
    "plt.plot(x1, y1, 'bo-', x2, y2, 'ro-',x3, y3, 'ko-')\n",
    "plt.legend(['35 deg.','45 deg.','55 deg.'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "nx = 50 # 10cm刻みでX,Yに50分割し、10cm×50=5m\n",
    "ny = 50 # の領域を確保する\n",
    "xa = numpy.linspace(0, 5, nx)\n",
    "ya = numpy.linspace(0, 5, ny)\n",
    "X, Y = numpy.meshgrid(xa, ya) # x,yの「平面座標メッシュ」を作る\n",
    "# xyの位置で表される空間に何があるかを、配列として格納しておく\n",
    "obj = numpy.zeros((ny, nx)) # 最初は「空気=0」で埋める\n",
    "obj[0:1,0:49] = 1           # 床は、フラグ値1とする\n",
    "obj[28:42,45:46] = 2        # ゴール板は、フラグ値2とする\n",
    "obj[30:31,42-2:42+2] = 3    #ゴール領域は、フラグ値3とする\n",
    "\n",
    "# ゴールや壁や床を描くよう、描画関数を変更する\n",
    "def prepareFigureArea():\n",
    "    plt.figure(figsize=(5,5))\n",
    "    plt.xlim([0,5]); plt.ylim([0,5]) \n",
    "    plt.xlabel('X - Axis (m)'); plt.ylabel('Y - Axis (m)')    \n",
    "    plt.contourf(X, Y, obj, alpha=0.2) # フラグ値を表示する\n",
    "    plt.tick_params()\n",
    "    return\n",
    "\n",
    "x,y,isSuccess    = throw(0.2,2,8,65,1500,0.01)\n",
    "x2,y2,isSuccess2 = throw(0.2,2,12,34,1500,0.01)\n",
    "prepareFigureArea()\n",
    "plt.plot(x, y, 'bo-', x2, y2, 'ro-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = 1.0  # 反射する時の「跳ね返り（反発）係数」\n",
    "\n",
    "def interaction(x,y,vx,vy,ax,ay,dt):\n",
    "    isPassing = False # ぶつかったか？フラグを「ぶつかってない」にしておく\n",
    "    # ボールの位置が計算領域外なら、ぶつかり・ゴール処理はしない\n",
    "    if y < 0 or 4.9 < y or x < 0.1 or 4.9 < x: \n",
    "        return (isPassing,x,y,vx,vy)\n",
    "    # ボールが移動する次位置（領域）に「何があるか」を調べる\n",
    "    objAtNextPos = obj[round(y*10), round(x*10)] \n",
    "    if 1 == objAtNextPos or 2 == objAtNextPos: # 床・ゴール板なら\n",
    "        x = x-(vx-ax*dt/2)*dt # 板や床にめりこんだ状態にならないように\n",
    "        y = y-(vy-ay*dt/2)*dt # 位置を「前の瞬間」の位置に戻す\n",
    "    if 1 == objAtNextPos:   # 床なら\n",
    "        vy = -vy*r  # 鉛直方向で跳ね返らせる（方向を反転させる）\n",
    "    elif 2 == objAtNextPos: # ゴール板なら\n",
    "        vx = -vx*r  # 水平方向で跳ね返らせる（方向を反転させる）\n",
    "    elif 3 == objAtNextPos and vy < 0: # ゴールに下向き突入していたら\n",
    "        isPassing = True  # ゴール追加のフラグをTrueとする\n",
    "    return (isPassing,x,y,vx,vy)\n",
    "\n",
    "x,y,isSuccess    = throw(0.2,2,8,65,1500,0.01)\n",
    "x2,y2,isSuccess2 = throw(0.2,2,12,34,1500,0.01)\n",
    "prepareFigureArea()\n",
    "plt.plot(x, y, 'bo-', x2, y2, 'ro-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = 0.8\n",
    "x,y,isSuccess    = throw(0.2,2,8,65,1500,0.01)\n",
    "x2,y2,isSuccess2 = throw(0.2,2,12,34,1500,0.01)\n",
    "prepareFigureArea()\n",
    "plt.plot(x, y, 'bo-', x2, y2, 'ro-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = 0.8\n",
    "angleRange    = numpy.linspace(30, 70, 400) #角度振り条件\n",
    "velocityRange = numpy.linspace(5, 15, 400)  #速度振り条件\n",
    "Xa,Yv = numpy.meshgrid(angleRange,velocityRange)\n",
    "areSuccess = [] # 角度・速度の各条件で成功するか格納する２次元配列\n",
    "for v in velocityRange:             # 角度条件ループ\n",
    "    a = []; for angle in angleRange:# 速度条件ループ\n",
    "        x,y,isSuccess = throw(0.2,2,v,angle,500,0.01)#投げる\n",
    "        a.append( isSuccess )  \n",
    "    areSuccess.append(a) # 上行と合わせ、成功したかを２次元的に格納\n",
    "fig = plt.figure(figsize=(5,5)) # 結果を描く\n",
    "plt.contourf(Xa,Yv,areSuccess,alpha=1.0)  \n",
    "plt.xlabel('Throw Angle(deg)'); plt.ylabel('Throw velocity(m/s)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "angleRange     = numpy.linspace(30, 70, 20) # 角度振り条件\n",
    "velocityRange  = numpy.linspace(5, 15, 30)  # 速度振り条件\n",
    "Xa,Yv = numpy.meshgrid(angleRange,velocityRange)\n",
    "prepareFigureArea() \n",
    "for v in velocityRange:       # 速度ループ\n",
    "    for angle in angleRange:  # 角度ループ\n",
    "        x,y,isSuccess = throw(0.2,2,v,angle,500,0.01)\n",
    "        if isSuccess:# 上行でボールを投げて、成功したら描く\n",
    "            plt.plot(x, y, 'b-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r = 0.8\n",
    "angleRange    = numpy.linspace(30, 70, 400) #角度\n",
    "velocityRange = numpy.linspace(5, 15, 400)  #速度\n",
    "Xa,Yv = numpy.meshgrid(angleRange,velocityRange)\n",
    "areSuccess = [] # 各条件で成功するかどうかを格納する\n",
    "for v in velocityRange: # 角度条件ループ\n",
    "    a = []\n",
    "    for angle in angleRange: # 速度条件ループ\n",
    "        x,y,isSuccess = throw(0.2,1.5,v,angle,500,0.01)\n",
    "        a.append( isSuccess )  \n",
    "    areSuccess.append(a) # 上行と合わせ、成功したかを２次元的に格納する\n",
    "fig = plt.figure(figsize=(5,5)) # 結果を描く\n",
    "plt.contourf(Xa,Yv,areSuccess,alpha=1.0)  \n",
    "plt.xlabel('Throw Angle(deg)'); plt.ylabel('Throw velocity(m/s)');"
   ]
  }
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