数学图形(1.45)毛雷尔玫瑰(Maurer rose)

毛雷尔玫瑰,也有的翻译是毛瑞尔,它是一种很漂亮的图形.玫瑰线的变异品种.

我没有找到其中文的解释,有兴趣可以看下维基上的相关页面.

A Maurer rose of the rose r = sin(nθ) consists of the 360 lines successively connecting the above 361 points. Thus a Maurer rose is a polygonal curve with vertices on a rose.

A Maurer rose can be described as a closed route in the polar plane. A walker starts a journey from the origin, (0, 0), and walks along a line to the point (sin(nd), d). Then, in the second leg of the journey, the walker walks along a line to the next point, (sin(n·2d), 2d), and so on. Finally, in the final leg of the journey, the walker walks along a line, from (sin(n·359d), 359d) to the ending point, (sin(n·360d), 360d). The whole route is the Maurer rose of the rose r = sin(nθ). A Maurer rose is aclosed curve since the starting point, (0, 0) and the ending point, (sin(n·360d), 360d), coincide.

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vertices = 361

t = from 0 to 360

n = 2
d = 39

k = t*d*0.0174533

x = sin(n*k)*cos(k)
y = sin(n*k)*sin(k)

r = 10
x = x*r
y = y*r
z = z*r

 

vertices = 361

t = from 0 to 360

n = 6
d = 71

k = t*d*0.0174533

x = sin(n*k)*cos(k)
y = sin(n*k)*sin(k)

r = 10
x = x*r
y = y*r
z = z*r

使用随机参数的代码:

vertices = 361

t = from 0 to 360

n = rand_int2(3, 12)
d = rand_int2(1, 100)

k = t*d*0.0174533

x = sin(n*k)*cos(k)
y = sin(n*k)*sin(k)

r = 10
x = x*r
y = y*r
z = z*r