数学图形(1.8) 圆外旋轮线

外旋轮线(Epitrochoid) 是追踪附着在围绕半径为 R 的固定的圆外侧滚转的半径 r 的圆上的一个点而得到的转迹线，这个点距离外部滚动的圆的中心的距离是 d

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圆外旋轮线(随机圈)

vertices = 10000
a = rand2(1, 10)
r = rand2(1, 10)
m = a/r
t = from 0 to (160*PI)
x = r*[(m+1)*cos(t) - cos((m+1)*t)]
y = r*[(m+1)*sin(t) - sin((m+1)*t)]

最初版本:这是我没有看数学方面的资源时写的版本.

vertices = 12000
a = rand2(8, 64)
b = rand2(4, 64)
c = a + b
s = c / b
o = rand2(4, b)

i = from 0 to (100*2*PI)
j = mod(i, 2*PI)
k = mod(s*i, 2*PI)

m = a*sin(j)
n = a*cos(j)

x = m + o*sin(k)
y = n + o*cos(k)

圆外旋轮线(N圈)

vertices = 10000
a = 10.3
r = 5.1
m = a/r
t = from 0 to (160*PI)
x = r*[(m+1)*cos(t) - cos((m+1)*t)]
y = r*[(m+1)*sin(t) - sin((m+1)*t)]

圆外旋轮线(10圈)

vertices = 1000

r = 10.0
m = 10
t = from 0 to (2*PI)
x = r*[m*cos(t) - cos(m*t)]
y = r*[m*sin(t) - sin(m*t)]

圆外旋轮面(10圈)

vertices = D1:512 D2:100

u = from 0 to (2*PI) D1
v = from -2.0 to 2.0 D2

r = 10.0
m = 10
x = r*[m*cos(u) - v*cos(m*u)]
y = r*[m*sin(u) - v*sin(m*u)]