making a function that translates a point around another point

问题

given an array of points my program should in theory, Find the two furthest points from each other. Then calculate the angle that those two points make with the x axis. Then in rotate all the points in the array around the averaged center of all the points by that angle. For some reason my translation function to rotate all the points around the center is not working it is giving me unexpected values. I am fairly sure the math I am using to do this is accurate since I tested the formula I am using using wolfram alpha and plotted the points on desmos. I am not sure what's wrong with my code because it keeps giving me unexpected output. Any help would greatly be appreciated. This is the code to translate the array:

def translation(array,centerArray):
    array1=array
    maxDistance=0
    point1=[]
    point2=[]
    global angle
    for i in range(len(array1)):
        for idx in range(len(array1)):
            if(maxDistance<math.sqrt(((array1[i][0]-array1[idx][0])**2)+((array1[i][1]-array1[idx][1])**2)+((array1[i][2]-array1[idx][2])**2))):
                maxDistance=math.sqrt(((array1[i][0]-array1[idx][0])**2)+((array1[i][1]-array1[idx][1])**2)+((array1[i][2]-array1[idx][2])**2))
                point1 = array1[i]
                point2 = array1[idx]
    angle=math.atan2(point1[1]-point2[1],point1[0]-point2[0]) #gets the angle between two furthest points and xaxis


    for i in range(len(array1)): #this is the problem here 
        array1[i][0]=((array[i][0]-centerArray[0])*math.cos(angle)-(array[i][1]-centerArray[1])*math.sin(angle))+centerArray[0] #rotate x cordiate around center of all points 
        array1[i][1]=((array[i][1]-centerArray[1])*math.cos(angle)+(array[i][0]-centerArray[0])*math.sin(angle))+centerArray[1] #rotate y cordiate around center of all points 

    return array1   

This is the code I am using to test it. tortose is what I set turtle graphics name as

tortose.color("violet")
testarray=[[200,400,9],[200,-100,9]] #array of 2 3d points but don't worry about z axis it will not be used for in function translation
print("testsarray",testarray)
for i in range(len(testarray)): #graph points in testarray
    tortose.setposition(testarray[i][0],testarray[i][1]) 
    tortose.dot()
testcenter=findCenter(testarray) # array of 1 point in the center of all the points format center=[x,y,z] but again don't worry about z
print("center",testcenter)
translatedTest=translation(testarray,testcenter) # array of points after they have been translated same format and size of testarray

print("translatedarray",translatedTest) #should give the output [[-50,150,9]] as first point but instead give output of [-50,-99.999999997,9] not sure why
tortose.color("green")
for i in range(len(testarray)): #graphs rotated points 
    tortose.setposition(translatedTest[i][0],translatedTest[i][1]) 
    tortose.dot()

print(angle*180/3.14) #checks to make sure angle is 90 degrees because it should be in this case this is working fine



tortose.color("red")
tortose.setposition(testcenter[0],testcenter[1])
tortose.dot()

find center code finds the center of all points in array don't worry about z axis since it is not used in translation:

def findCenter(array):
    sumX = 0
    sumY = 0
    sumZ = 0
    for i in range(len(array)):
        sumX += array[i][0]
        sumY += array[i][1] 
        sumZ += array[i][2]
    centerX= sumX/len(array)
    centerY= sumY/len(array)
    centerZ= sumZ/len(array)
    #print(centerX)
    #print(centerY)
    #print(centerZ)
    centerArray=[centerX,centerY,centerZ]
    return centerArray

import math
import turtle
tortose = turtle.Turtle()
tortose.penup()

my expected output should be a point at (-50,150) but it is giving me a point at (-50,-99.99999999999997)

回答1:

This is a common mistake when doing in-place rotations:

array1[i][0]= ...
array1[i][1]= ... array[i][0] ...

First you update array1[i][0]. Then you update array1[i][1], but you use the new value when you should use the old value. Instead, temporarily store the old value:

x = array1[i][0]
array1[i][0]=((array[i][0]-centerArray[0])*math.cos(angle)-(array[i][1]-centerArray[1])*math.sin(angle))+centerArray[0] #rotate x cordiate around center of all points 
array1[i][1]=((array[i][1]-centerArray[1])*math.cos(angle)+(x-centerArray[0])*math.sin(angle))+centerArray[1] #rotate y cordiate around center of all points 

来源：https://stackoverflow.com/questions/56936429/making-a-function-that-translates-a-point-around-another-point