Python实现点绕中心点旋转的坐标计算公式与代码示例

Aria

发布时间：2026-10-13 | 3人浏览过

原创

本文介绍了在Python中计算一个点绕另一个中心点旋转后的新坐标方法。详细列出了顺时针和逆时针旋转的数学公式，并提供了基于NumPy和Matplotlib的完整代码示例，展示如何实现旋转计算及可视化结果。

点绕中心点旋转坐标计算方法

具体计算过程如下所示：

假设需要旋转的点坐标为 (x, y)，旋转中心点坐标为 (pointx, pointy)。若旋转方向为顺时针，旋转角度为 angle，则新坐标计算方式如下。

顺时针旋转后的横坐标 srx 计算公式为：srx = (x - pointx) * cos(angle) + (y - pointy) * sin(angle) + pointx

顺时针旋转后的纵坐标 sry 计算公式为：sry = (y - pointy) * cos(angle) - (x - pointx) * sin(angle) + pointy

若旋转方向为逆时针，其他条件不变，即点 (x, y) 绕中心点 (pointx, pointy) 逆时针旋转 angle 角度，则新坐标计算方式如下。

逆时针旋转后的横坐标 nrx 计算公式为：nrx = (x - pointx) * cos(angle) - (y - pointy) * sin(angle) + pointx

逆时针旋转后的纵坐标 nry 计算公式为：nry = (x - pointx) * sin(angle) + (y - pointy) * cos(angle) + pointy


import numpy as np
import math
import matplotlib.pyplot as plt
# 绕pointx,pointy逆时针旋转
def Nrotate(angle,valuex,valuey,pointx,pointy):
 valuex = np.array(valuex)
 valuey = np.array(valuey)
 nRotatex = (valuex-pointx)*math.cos(angle) - (valuey-pointy)*math.sin(angle) + pointx
 nRotatey = (valuex-pointx)*math.sin(angle) + (valuey-pointy)*math.cos(angle) + pointy
 return nRotatex, nRotatey
# 绕pointx,pointy顺时针旋转
def Srotate(angle,valuex,valuey,pointx,pointy):
 valuex = np.array(valuex)
 valuey = np.array(valuey)
 sRotatex = (valuex-pointx)*math.cos(angle) + (valuey-pointy)*math.sin(angle) + pointx
 sRotatey = (valuey-pointy)*math.cos(angle) - (valuex-pointx)*math.sin(angle) + pointy
 return sRotatex,sRotatey
pointx = 1
pointy = 1
sPointx ,sPointy = Nrotate(math.radians(45),pointx,pointy,0,0)
print(sPointx,sPointy)
plt.plot([0,pointx],[0,pointy])
plt.plot([0,sPointx],[0,sPointy])
plt.xlim(-3.,3.)
plt.ylim(-3.,3.)
plt.xticks(np.arange(-3.,3.,1))
plt.yticks(np.arange(-3.,3.,1))
plt.show()


import numpy as np
import math
import matplotlib.pyplot as plt
# 绕pointx,pointy逆时针旋转
def Nrotate(angle,valuex,valuey,pointx,pointy):
 valuex = np.array(valuex)
 valuey = np.array(valuey)
 nRotatex = (valuex-pointx)*math.cos(angle) - (valuey-pointy)*math.sin(angle) + pointx
 nRotatey = (valuex-pointx)*math.sin(angle) + (valuey-pointy)*math.cos(angle) + pointy
 return nRotatex, nRotatey
# 绕pointx,pointy顺时针旋转
def Srotate(angle,valuex,valuey,pointx,pointy):
 valuex = np.array(valuex)
 valuey = np.array(valuey)
 sRotatex = (valuex-pointx)*math.cos(angle) + (valuey-pointy)*math.sin(angle) + pointx
 sRotatey = (valuey-pointy)*math.cos(angle) - (valuex-pointx)*math.sin(angle) + pointy
 return sRotatex,sRotatey
 
x1 = np.array([1,2,3])
y1 = np.array([1,2,3])
x2 = np.array([3,6])
y2 = np.array([2,1])
# x2往x1上拼
disx = x2[0]-x1[0]
disy = y2[0]-y1[0]
removeX2 = x2-disx
removeY2 = y2-disy
tany1 = y1[-1]-y1[0]
tanx1 = x1[-1]-x1[0]
angle1 = math.degrees(np.arctan(tany1/tanx1))
tany2 = y2[-1]-y2[0]
tanx2 = x2[-1]-x2[0]
angle2 = math.degrees(np.arctan(tany2/tanx2))
disAngle = angle2-angle1
print(angle1)
print(angle2)
print(disAngle)
if disAngle<0:
 rotateX,rotateY = Nrotate(math.radians(abs(disAngle)),removeX2,removeY2,x1[0],y1[0])
else:
 rotateX,rotateY = Srotate(math.radians(abs(disAngle)),removeX2,removeY2,x1[0],y1[0])
plt.plot(x1,y1,color='red')
plt.plot(removeX2,removeY2,color='green')
plt.scatter(rotateX,rotateY,color='yellow')
plt.xlim(0.,10.)
plt.ylim(0.,10.)
plt.xticks(np.arange(0.,10.,1))
plt.yticks(np.arange(0.,10.,1))
plt.show()