雙曲線繞其對稱軸旋轉而生成的曲面即為雙曲面,上節講了單葉雙曲面,這一節繼續講雙葉雙曲面.
雙葉雙曲面的數學公式如下:
x*x/a/a + y*y/b/b - z*z/c/c = -1
在數學里，雙曲面是一種二次曲面。采用直角坐標 
，雙曲面可以用公式表達為
-
（單葉雙曲面），
或
-
（雙葉雙曲面）。
假若，
，則稱為旋轉雙曲面。
本文將展示幾種生成雙葉雙曲面算法和切圖.使用自己定義語法的腳本代碼生成數學圖形.相關軟件參見:數學圖形可視化工具,該軟件免費開源.QQ交流群: 367752815
(1)
#x*x/a/a + y*y/b/b - z*z/c/c = -1 vertices = dimension1:72 dimension2:72 u = from 0 to (2*PI) dimension1 v = from (-5) to (5) dimension2 a = rand2(1, 5) b = rand2(1, 5) c = rand2(1, 5) x = a*sqrt(v*v - 1)*cos(u) z = b*sqrt(v*v - 1)*sin(u) y = c*v
(2)
vertices = D1:100 D2:100 u = from 0 to (1*PI) D1 v = from (0) to (2*PI) D2 gap[PI*0.5, PI*1.5] a = rand2(1, 10) b = rand2(1, 10) c = rand2(1, 10) x = a*tan(v)*sin(u) y = b*sec(v) z = c*tan(v)*cos(u)
(3)
我之前寫過關於雙曲線的文章,數學圖形(1.10) 雙曲線
將雙曲線旋轉一周即能生成雙曲面.
vertices = 360 u = from -1 to 1 gap[0] x = u y = 1/x y = limit(y, -50, 50) surface_slices = 72 rotate = anchor[0, 0, 0], axis[1, 1, 0], angle[0, 2*PI]
(4)
雙曲面(東西開口)
vertices = 100 t = from 0 to (2*PI) gap[PI*0.5, PI, PI*1.5] a = rand2(0.1, 10) b = rand2(0.1, 10) x = a*sec(t) y = b*tan(t) x = limit(x, -50, 50) y = limit(y, -50, 50) surface_slices = 72 rotate = anchor[0, 0, 0], axis[1, 0, 0], angle[0, 2*PI]
雙曲面(南北開口)
vertices = 100 t = from 0 to (2*PI) gap[PI*0.5, PI, PI*1.5] a = rand2(0.1, 10) b = rand2(0.1, 10) x = a*tan(t) y = b*sec(t) x = limit(x, -50, 50) y = limit(y, -50, 50) surface_slices = 72 rotate = anchor[0, 0, 0], axis[0, 1, 0], angle[0, 2*PI]
