上一節講的是螺旋管,海螺亦是螺旋管的一種.同樣,貝殼也是有螺旋度的.那么這一節將為大家提供幾種海螺與貝殼的生成算法.提到海螺,讓我想起我的大學是在海邊,出了東校門就是大海,甚至學校宿舍都是海景房.我也很喜歡海螺和貝殼,畢竟它們的肉都很好吃.
相關軟件參見:數學圖形可視化工具,使用自己定義語法的腳本代碼生成數學圖形.
(1)海螺(conchoid)
vertices = dimension1:160 dimension2:160 u = from 0 to (6*PI) dimension1 v = from 0 to (2*PI) dimension2 k = 1.2 a = 1.5 w = (k^u) * (1+cos(v)) x = w*cos(u) y = w*sin(u) z = (k^u)*sin(v) - (k^u)*a
(2)Sea-shell
vertices = dimension1:1000 dimension2:72 u = from 0 to (20*PI) dimension1 v = from 0 to (2*PI) dimension2 m = -0.09 k = 3 a = 1 b = 1 e = pow(E, m*u) w = (a + b*cos(v))*e x = w*cos(u) z = w*sin(u) y = (k*a + b*sin(v))*e
(3)Sea-shell (隨機)
在腳本中使用了隨機數
vertices = dimension1:1000 dimension2:72 u = from 0 to (32*PI) dimension1 v = from 0 to (2*PI) dimension2 m = -1/(rand_int2(2, 100)) k = rand2(1, 100) a = 1 b = rand2(0.5, 2) e = pow(E, m*u) w = (a + b*cos(v))*e x = w*cos(u) z = w*sin(u) y = (k*a + b*sin(v))*e
(4)角螺
這是我自己測試時隨意寫的腳本,角螺的名子也是我隨意取的.
vertices = dimension1:36 dimension2:72 a = from 0 to (2*PI) dimension1 b = from (-PI*0.5) to (PI*0.5) dimension2 r = 10.0 x = r*cos(b)*sin(a) y = r*sin(b)*sqrt(a) z = r*cos(b)*cos(a) u = a v = b*2
(5)鸚鵡螺
vertices = D1:720 D2:72 p = from 0 to (3*PI) D1 q = from 0 to PI D2 r = 1.2^p * sin(q) * 5 x = r * sin(q) * sin(p) y = r * sin(q) * cos(p) z = r * cos(q) u = p v = q*3
(6)貝殼1
vertices = dimension1:100 dimension2:100 u = from 0 to (2*PI) dimension1 v = from 0 to (PI) dimension2 r = sin(v)*pow(E, -u) x = r*sin(v)*sin(u) y = r*cos(v) z = r*sin(v)*cos(u)
(7)貝殼2
vertices = dimension1:100 dimension2:100 u = from 0 to (PI*2) dimension1 v = from 0 to (PI) dimension2 r = sin(v)*sin(v)*pow(E, -u) x = r*sin(v)*sin(u) y = r*cos(v) z = r*sin(v)*cos(u)
