數學圖形(1.7)圓內旋輪線

內旋輪線(hypotrochoid)是追蹤附着在圍繞半徑為 R 的固定的圓內側滾轉的半徑為 r 的圓上的一個點得到的轉跡線，這個點到內部滾動的圓的中心的距離是 d。

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圓內旋輪線(隨機圈)

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)

內旋輪線中不同參數設置可以生成一些固定的圖形

三尖瓣線

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)]

星形線

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)]

圓內旋輪線(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)

圓內旋輪線(橢圓)

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)

 橢圓面

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)]

圓內旋輪面(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)]