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)]