数学图形(1.7)圆内旋轮线

内旋轮线(hypotrochoid)是追踪附着在围绕半径为 R 的固定的圆内侧滚转的半径为 r 的圆上的一个点得到的转迹线，这个点到内部滚动的圆的中心的距离是 d。

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圆内旋轮线(随机圈)

vertices = 12000
a = rand2(1, 10)
r = rand2(1, 10)
d = rand2(0.5, 10)
t = from 0 to (120*PI)
x = (a - r)*cos(t) + d*cos((a/r - 1)*t)
y = (a - r)*sin(t) - d*sin((a/r - 1)*t)

内旋轮线中不同参数设置可以生成一些固定的图形

三尖瓣线

vertices = 1000
r = 10.0
m = 2
t = from 0 to (5*PI)
x = r*[m*cos(t) + cos(m*t)]
y = r*[m*sin(t) - sin(m*t)]

星形线

vertices = 1000
r = 10.0
m = 1.5
t = from 0 to (5*PI)
x = r*[m*cos(t) + cos(m*t)]
y = r*[m*sin(t) - sin(m*t)]

5角星形

vertices = 1000

r = 10.0
m = 4
t = from 0 to (2*PI)
x = r*[m*cos(t) + cos(m*t)]
y = r*[m*sin(t) - sin(m*t)]

圆内旋轮线(5圈)

vertices = 12000
a = 10
r = 8
d = rand2(0.5, 10)
t = from 0 to (8*PI)
x = (a - r)*cos(t) + d*cos((a/r - 1)*t)
y = (a - r)*sin(t) - d*sin((a/r - 1)*t)

圆内旋轮线(椭圆)

vertices = 12000
a = 10
r = 5
d = rand2(0.5, 10)
t = from 0 to (2*PI)
x = (a - r)*cos(t) + d*cos((a/r - 1)*t)
y = (a - r)*sin(t) - d*sin((a/r - 1)*t)

 椭圆面

vertices = D1:512 D2:100

u = from 0 to (PI*5) D1
v = from 0.0 to 1.0 D2

r = 10.0
m = 1

x = r*[m*cos(u) + v*cos(m*u)]
y = r*[m*sin(u) - v*sin(m*u)]

三尖瓣面

vertices = D1:512 D2:100

u = from 0 to (PI*5) D1
v = from 0.0 to 1.0 D2

r = 10.0
m = 2

x = r*[m*cos(u) + v*cos(m*u)]
y = r*[m*sin(u) - v*sin(m*u)]

五星面

vertices = D1:512 D2:100

u = from 0 to (PI*5) D1
v = from 0.0 to 1.0 D2

r = 10.0
m = 1.5

x = r*[m*cos(u) + v*cos(m*u)]
y = r*[m*sin(u) - v*sin(m*u)]

圆内旋轮面(5角星形)

vertices = D1:512 D2:100

u = from 0 to (PI*5) D1
v = from 0.0 to 1.0 D2

r = 10.0
m = 4

x = r*[m*cos(u) + v*cos(m*u)]
y = r*[m*sin(u) - v*sin(m*u)]