Question

长话短说，我需要使一堆球在空间中朝随机方向移动。我正在使用带有VRED（3D渲染软件）的python脚本在屏幕上显示球。

我正在尝试使用球坐标，但不知何故，球在空间中的分布偏向Z轴。我真的无法弄清楚哪里出了错。

我正在这样进行：

我生成一个随机的偏航起始方向（-180，180）和一个随机的起始俯仰（0，180）
在每个新帧处，我都会稍微改变偏航角和俯仰角，并沿该新方向移动球。

这是我的Python代码（我希望它不太难读； vrAEBase是与VRED相关的类，它允许loop()每帧更新一次）：

import random
import math

populationsize = 1000
balllist = []

#________________________________________BALL CLASS______________________________________________

class Ball(vrAEBase):

    def __init__(self):
        vrAEBase.__init__(self)
        self.addLoop()
        self.body = createSphere(2,100,1,1,1)  # create sphere
        self.isplaying = false 
        self.steplength = 20      #step length between each frame
        self.yaw = random.uniform(-180, 180)     #set starting yaw
        self.pitch = random.uniform(0, 180)      #set starting pitch
        self.maxsteering = 1 # max angular change for yaw/pitch for each frame
        self.x = 0  #startting X location
        self.y = 0  #startting Y location
        self.z = 0  #startting Z location

    def loop(self):          #loop is executed every frame
        if self.isplaying:

            self.yaw = self.yaw + random.uniform(-1*self.maxsteering, self.maxsteering)       #set new yaw
            self.pitch = self.pitch + random.uniform(-1*self.maxsteering, self.maxsteering)   #set new pitch

            localX = self.steplength * (math.sin(self.pitch)) * (math.cos(self.yaw))  #calculate X step length
            localY = self.steplength * (math.sin(self.pitch)) * (math.sin(self.yaw))  #calculate Y step length
            localZ = self.steplength * (math.cos(self.pitch))                         #calculate Z step length


            self.x += localX
            self.y += localY
            self.z += localZ
            setTransformNodeTranslation(self.body, self.x,self.y,self.z,true)



    def rewind(self):
        self.isplaying = false
        self.x = 0
        self.y = 0
        self.z = 0
        setTransformNodeTranslation(self.body, self.x,self.y,self.z,true)


#__________________________________PLAY__________________________________

def play():
    global balllist
    for ball in balllist:
        if ball.isplaying == false:
            ball.isplaying = true
        else:
            ball.isplaying = false

#__________________________________REWIND_________________________________

def rewind():
    global balllist
    for ball in balllist:
        ball.rewind()


#_______________________________SPAWN BALLS________________________________


for x in range(0, populationsize):
    newball =  Ball()         #create ball
    balllist.append(newball)   #add ball to list

play()

print("end")

这是最终发行的图片：

Answer 1

问题在于，为了在球体周围生成均匀的点分布，您不能进行phi = [0，pi]和theta = [-pi，pi]，因为这将导致表面元素dA = dphi * dtheta代替正确的dA = sin（phi）* dphi * dtheta。

为了实现正确的体积元素变化

def __init__( self):
    ...
    self.yaw = random.uniform(-180, 180)     #set starting yaw
    self.pitch = random.uniform(0, 180)      #set starting pitch
    ...

到

def __init__( self):
    ...
    u = random.uniform(0,1)
    v = random.uniform(0,1)
    self.yaw = 2 * math.pi * u     #set starting yaw
    self.pitch = math.acos( 2*v -1)      #set starting pitch
    ...

有关更多文档，请参见http://mathworld.wolfram.com/SpherePointPicking.html。

还请注意您的时间步例程的行为，截至目前，这些点似乎倾向于朝该分布方向塌陷。我不知道这是否是您的预期行为

Python-球面坐标具有Z轴偏移

1 个答案: