如何平均分割椭圆的周长？

2019年7月28日 563次阅读

类似的问题在此之前是
asked and answered,但没有一个简单到让我理解.下面的代码以相等的角度间隔计算椭圆的点,并将相邻点之间的距离相加以得到近似的周长.然后它将圆周划分为10个假设相等的弧,并输出由分割点产生的角度.

from math import sqrt,cos,sin,radians

def distance(x1,y1,x2,y2):
    return sqrt((x2-x1)**2 + (y2-y1)**2)

a = 5
b = 3
x0 = a
y0 = 0
angle = 0
d = 0
while(angle<=360):
    x = a * cos(radians(angle))
    y = b * sin(radians(angle))
    d += distance(x0,y0,x,y)
    x0 = x
    y0 = y
    angle += 0.25
print "Circumference of ellipse = %f" %d
onetenth = d/10
angle = 0
x0 = a
y0 = 0
angle0 = 0.25
for i in range(10):
    dist = 0
    while(dist<onetenth):
        x = a * cos(radians(angle))
        y = b * sin(radians(angle))
        dist += distance(x0,y0,x,y)
        x0 = x
        y0 = y
        angle += 0.25
    print "%d : angle = %.2f\tdifference = %.2f" %(i+1,angle-0.25, angle-angle0)
    angle0 = angle

它给出了输出：

Circumference of ellipse = 25.526979
1 : angle = 43.00       difference = 43.00
2 : angle = 75.50       difference = 32.50
3 : angle = 105.00      difference = 29.50
4 : angle = 137.50      difference = 32.50
5 : angle = 180.75      difference = 43.25
6 : angle = 223.75      difference = 43.00
7 : angle = 256.00      difference = 32.25
8 : angle = 285.50      difference = 29.50
9 : angle = 318.00      difference = 32.50
10 : angle = 361.50     difference = 43.50

但是这些角度并没有平均分割圆周(picture).我的逻辑/代码出了什么问题,如何改进？

最佳答案 我是问题的OP,我从评论中意识到我做了一个错误的假设.该代码利用椭圆的参数方程来计算x和y坐标.参数方程中的角度不是x轴的角度.我假设它们在代码中是相同的.更正的代码是

from math import sqrt,cos,sin,atan2,radians,degrees

def distance(x1,y1,x2,y2):
    return sqrt((x2-x1)**2 + (y2-y1)**2)

a = 5
b = 3
x0 = a
y0 = 0
angle = 0
d = 0
while(angle<=360):
    x = a * cos(radians(angle))
    y = b * sin(radians(angle))
    d += distance(x0,y0,x,y)
    x0 = x
    y0 = y
    angle += 0.25
print "Circumference of ellipse = %f" %d
onetenth = d/10
angle = 0
x0 = a
y0 = 0
angle0 = 0
for i in range(10):
    dist = 0
    while(dist<onetenth):
        x = a * cos(radians(angle))
        y = b * sin(radians(angle))
        dist += distance(x0,y0,x,y)
        x0 = x
        y0 = y
        angle += 0.25
    xangle = degrees(atan2(y,x))
    print "%d : angle = %.2f\tdifference = %.2f" %(i+1, xangle, xangle-angle0)
    angle0 = xangle

它通过获取点的x和y坐标的反正切来计算与x轴的角度.它给出了输出：

Circumference of ellipse = 25.526979
1 : angle = 29.23       difference = 29.23
2 : angle = 66.68       difference = 37.46
3 : angle = 114.06      difference = 47.38
4 : angle = 151.20      difference = 37.13
5 : angle = -179.55     difference = -330.75
6 : angle = -150.13     difference = 29.42
7 : angle = -112.57     difference = 37.56
8 : angle = -65.19      difference = 47.37
9 : angle = -28.38      difference = 36.81
10 : angle = 0.90       difference = 29.28

这些角度划分椭圆almost equally的圆周.

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