类鸟群Boids——仿真鸟群 （python实现添加个体、驱散、避障等）

工作原理 ：
       模拟类鸟群的三大核心规则如下：
       1）分离：保持类鸟个体之间的最小距离；
       2）列队：让每个类鸟个体指向其局部同伴的平均移动方向；
       3）内聚：让每个类鸟个体朝其局部同伴的质量中心移动。
类鸟群模拟也可以添加其他规则，如避开障碍物，或受到打扰时驱散鸟群等...

分析：
    对于群体中的所有类鸟个体，做以下几件事：
    • 应用三大核心规则；
    • 应用所有附加规则；
    • 应用所有边界条件。
    • 更新类鸟个体的位置和速度。
    • 绘制新的位置和速度。

设置功能：

  1）鼠标点击左键：添加个体鸟

  2）鼠标点击右键：驱散鸟群

  3）避障

代码如下：

import sys, argparse
import math
import numpy as np
import matplotlib.pyplot as plt   
import matplotlib.animation as animation
from scipy.spatial.distance import squareform, pdist, cdist  #计算点之间的距离
from numpy.linalg import norm
from matplotlib.colors import ListedColormap
import matplotlib.patches as patches

width, height = 640, 480   #设置屏幕上模拟窗口的宽度和高度

class Boids:
    def __init__(self, N):
        """ initialize the Boid simulation"""
        #初始化位置和速度
        self.pos = [width/2.0, height/2.0] + 10*np.random.rand(2*N).reshape(N, 2) #'''创建一个 numpy 数组 pos，对窗口中心加上 10 个单位以内的随机偏移。代码np.random.rand（2 * N）创建了一个一维数组，包含范围在[0，1]的 2N 个随机数。然后 reshape()调用将它转换成二维数组的形状（N，2），它将用于保存类鸟群个体的位置。'''
        # normalized random velocities
        angles = 2*math.pi*np.random.rand(N)
        self.vel = np.array(list(zip(np.sin(angles), np.cos(angles))))
        self.N = N         #生成一个数组，包含 N 个随机角度，范围在[0, 2pi]，
        # min dist of approach
        self.minDist = 25.0
        # max magnitude of velocities calculated by "rules"
        self.maxRuleVel = 0.03
        # max maginitude of final velocity
        self.maxVel = 2.0

    def tick(self, frameNum, pts, beak):
        """Update the simulation by one time step."""
        self.distMatrix = squareform(pdist(self.pos))     #用 squareform()和 pdist()方法来计算一组点之间两两的距离
        # apply rules:
        self.vel += self.applyRules()
        self.limit(self.vel, self.maxVel)
        self.pos += self.vel
        self.applyBC()
        # update data
        pts.set_data(self.pos.reshape(2*self.N)[::2], 
                     self.pos.reshape(2*self.N)[1::2])
        vec = self.pos + 10*self.vel/self.maxVel
        beak.set_data(vec.reshape(2*self.N)[::2], 
                      vec.reshape(2*self.N)[1::2])

    def limitVec(self, vec, maxVal):
        """limit magnitide of 2D vector"""
        mag = norm(vec)
        if mag > maxVal:
            vec[0], vec[1] = vec[0]*maxVal/mag, vec[1]*maxVal/mag
    
    def limit(self, X, maxVal):
        """limit magnitide of 2D vectors in array X to maxValue"""
        for vec in X:
            self.limitVec(vec, maxVal)
            
    def applyBC(self):
        """apply boundary conditions"""
        deltaR = 2.0    #该行中的deltaR提供了一个微小的缓冲区，它允许类鸟群个体开始从相反方向回来之前移出小块之外一点，从而产生更好的视觉效果
        for index,coord in enumerate(self.pos):
            if coord[0] > width + deltaR:
                coord[0] = - deltaR
            if coord[0] < - deltaR:
                coord[0] = width + deltaR    
            if coord[1] > height + deltaR:
                coord[1] = - deltaR
            if coord[1] < - deltaR:
                coord[1] = height + deltaR
            if ((coord[1]-225)**2+(coord[0]-225)**2) <=3600:
                self.vel[index] = -self.vel[index]*2
    
    def applyRules(self):
        # apply rule #1 - Separation
        D = self.distMatrix < 25.0
        vel = self.pos*D.sum(axis=1).reshape(self.N, 1) - D.dot(self.pos)
        self.limit(vel, self.maxRuleVel)

        # different distance threshold
        D = self.distMatrix < 50.0

        # apply rule #2 - 列队
        vel2 = D.dot(self.vel)
        self.limit(vel2, self.maxRuleVel)
        vel += vel2;

        # apply rule #1 - 聚集
        vel3 = D.dot(self.pos) - self.pos
        self.limit(vel3, self.maxRuleVel)
        vel += vel3

        return vel

    def buttonPress(self, event):
        """event handler for matplotlib button presses"""
        # left click - add a boid
        if event.button is 1:
            self.pos = np.concatenate((self.pos, 
                                       np.array([[event.xdata, event.ydata]])), 
                                      axis=0)
            # random velocity
            angles = 2*math.pi*np.random.rand(1)
            v = np.array(list(zip(np.sin(angles), np.cos(angles))))
            self.vel = np.concatenate((self.vel, v), axis=0) #拼接
            self.N += 1 
        # right click - scatter
        elif event.button is 3:
            # add scattering velocity 
            self.vel += 0.1*(self.pos - np.array([[event.xdata, event.ydata]]))
        
def tick(frameNum, pts, beak, boids):
    #print frameNum
    """update function for animation"""
    boids.tick(frameNum, pts, beak)
    return pts, beak

# main() function
def main():
  # use sys.argv if needed
    print('starting boids...')

    parser = argparse.ArgumentParser(description="Implementing Craig Reynold's Boids...")
  # add arguments
    parser.add_argument('--num-boids', dest='N', required=False)
    args = parser.parse_args()

  # number of boids
    N = 50
    if args.N:
        N = int(args.N)

  # create boids
    boids = Boids(N)

  # setup plot
    fig = plt.figure(facecolor='pink') 
    ax = plt.axes(xlim=(0, width), ylim=(0, height),facecolor='lightskyblue')
    ax.add_patch(patches.Rectangle((200, 200),50,50,linewidth=1,edgecolor='b',facecolor='b'))
    pts, = ax.plot([], [], markersize=10, 
                    c='k', marker='o', ls='None')
    beak, = ax.plot([], [], markersize=4, 
                  c='r', marker='o', ls='None')
    
    anim = animation.FuncAnimation(fig, tick, fargs=(pts, beak, boids), 
                                 interval=50)

  # add a "button press" event handler
    cid = fig.canvas.mpl_connect('button_press_event', boids.buttonPress)

    plt.show()

# call main
if __name__ == '__main__':
    main()

大概效果如下：