数学图形(1.12) 螺线

在平面极坐标系中，如果极径ρ随极角θ的增加而成比例增加（或减少），这样的动点所形成的轨迹叫做螺线。
最常见的螺线有阿基米德螺线、对数螺线、双曲螺线等。

 

阿基米德螺线

vertices = 1000

t = from 0 to (20*PI)
a = 0.05

r = a*t

x = r*sin(t)
y = r*cos(t)

等角螺线

vertices = 12000

t = from (-20*PI) to (20*PI)
b = 0.05

r = pow(E, b*t)

x = r*sin(t)
y = r*cos(t)

 

对数螺线

vertices = 1000
a = 1.0
b = 1.1
t = from 0 to (15*PI)
p = a*pow(b,t)
x = p*sin(t)
y = p*cos(t)

 

费马螺线

vertices = 12000

r = from -10 to 10
t = r*r

x = r*sin(t)
y = r*cos(t)

 

连锁螺线

vertices = 12000
r = from -10 to 10
k = 1.0
t = k/(r*r)
t = limit(t, -10*PI, 10*PI)
x = r*sin(t)
y = r*cos(t)

 

双曲螺线

#极径与极角成反比的点的轨迹称为双曲螺线。
vertices = 10000
a = 16.0
t = from 0.5 to (200*PI)
x = a*cos(t)/t
y = a*sin(t)/t

 

圆周渐伸线,貌似它与阿基米德螺线是相同的.

vertices = 1000
r = 1.0
t = from 0 to (20*PI)
x = r*[cos(t) + t*sin(t)]
y = r*[sin(t) - t*cos(t)]