一、背景

点位误差椭圆是一种描述待定点位置在各个方向上误差分布规律的椭圆。

暂无

二、代码

#!/usr/bin/python3
#-*- codng: utf-8 -*-

import numpy as np

import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse

def getErrorEllipsePara(listQxx,drawFigure = None,sigmaZero=None,angle=None):
    Qxx = np.mat(listQxx)
    if Qxx.shape[0] == Qxx.shape[1] and Qxx.shape[0] == 2:
        tan_toubleFia = 2*Qxx[0,1]/(Qxx[0,0]-Qxx[1,1])
        fia = np.arctan(tan_toubleFia)/2
        #fias = np.rad2deg(np.arctan2(2*Qxx[0,1],Qxx[0,0]-Qxx[1,1]))
        print("-fia:{} rad | -fia:{}° | -fiaaddninety:{}°".format(fia,np.rad2deg(fia),np.rad2deg(fia)+90))

        fiaE,fiaF = filter_fiaEF(Qxx,fia)

        if sigmaZero is not None:
            fiaE = np.deg2rad(fiaE)
            fiaF = np.deg2rad(fiaF)
            Q_ff = lambda sitha:(Qxx[0,0]*np.cos(sitha)*np.cos(sitha)+Qxx[1,1]*np.sin(sitha)*np.sin(sitha)+Qxx[0,1]*np.sin(2*sitha))
            sigmaE = np.sqrt(sigmaZero*sigmaZero*Q_ff(fiaE))
            sigmaF = np.sqrt(sigmaZero*sigmaZero*Q_ff(fiaF))

            print("-fiaE:{} 度,-E:{};\n -fiaF:{} 度,-F:{}".format(np.rad2deg(fiaE),sigmaE,np.rad2deg(fiaF),sigmaF))

            # Draw
            if drawFigure is not None:
                drawEllipse(sigmaE,sigmaF,np.rad2deg(fiaE))
                print("- 绘图完成")
            # anlyse
            if angle is not None:
                fia_angle = np.deg2rad(angle)
                newQff = Q_ff(fia_angle)
                print("\n-angle Qff sigma:",np.rad2deg(fia_angle),newQff,sigmaZero*np.sqrt(newQff))
                print("\n*: ",np.sqrt(sigmaE*np.cos(newQff)*np.cos(newQff)+sigmaF*np.sin(newQff)*np.sin(newQff)))
    else:
        print("Error para")

def filter_fiaEF(Qxx,fia):
        fiaE = 0
        fiaF = 0
        if Qxx[0,1] == 0: # 在轴上
            if Qxx[0,0] > Qxx[1,1]:
                fiaE = 0
                fiaF = 90
                print("-fiaE:{} or {},最大位差在x轴上 | -fiaF:{} or {}".format(0,180,90,270))
            else:
                fiaE = 90
                fiaF = 0
                print("-fiaE:{} or {},最大位差在y轴".format(90,270))
        elif Qxx[0,1] > 0:
            # if Qxx[0,1]*np.tan(np.deg2rad(fia))>0:
            print("极大值fiaE位于一、三象限")
            if (fia > 0 and fia < 90) or (fia < 270 and fia > 180):
                fiaE = fia
                fiaF = fia + 90
            # 存疑
            else:
                fiaE = fia + 90
                fiaF = fia

            # else:
            #     if (fia > 0 and fia < 90) or (fia < 270 and fia > 180):
            #         fiaE = fia + 90
            #         fiaF = fia 
            #     else:
            #         fiaE = fia
            #         fiaF = fia + 90
            #     print("极大值位于二、四象限")
        else:
            # if Qxx[0,1]*np.tan(np.deg2rad(fia)) > 0:
            if (fia > 0 and fia < 90) or (fia < 270 and fia > 180):
                fiaE = fia + 90
                fiaF = fia 
            else:
                fiaE = fia
                fiaF = fia + 90
            print("fiaE极大值2、4象限")
            # else:
            #     if (fia > 0 and fia < 90) or (fia < 270 and fia > 180):
            #         fiaE = fia + 90
            #         fiaF = fia
            #     else:
            #         fiaE = fia
            #         fiaF = fia + 90
            #     print("极大值二四象限")
        return fiaE,fiaF

def drawEllipse(E,F,fiaE,x=None,y=None):
    print("-"*20)
    fig = plt.figure(0)
    ax = fig.add_subplot(111, aspect='equal')
    if x is None:
        x = 0
    if y is None:
        y = 0
    e = Ellipse(xy = (x,y), width = E, height = F, angle=fiaE,facecolor= 'green', alpha=0.3)
    ax.add_patch(e)

    ax.plot(x, y, 'ro')
    plt.axis('scaled')
    plt.axis('equal')
    ax.grid(True)
    strInfo = "E:"+str(E)[0:5]+" -F:"+str(F)[0:5]+" -fiaE:"+str(fiaE)[0:6]+"degree"
    plt.title("ErrorEllipse"+strInfo)
    plt.savefig("./ErrorEllipse.png")
    plt.show()

if __name__=="__main__":
    Q = [[5,-1.2],
        [-1.2,4]]
    sigma = 0.81
    getErrorEllipsePara(Q,sigmaZero=sigma,angle=50,drawFigure=True)
    # drawEllipse()

iPad下运行：
[1]

[2]

[3]

[4]amazing

结束