双曲线绕其对称轴旋转而生成的曲面即为双曲面,上节讲了单叶双曲面,这一节继续讲双叶双曲面.
双叶双曲面的数学公式如下:
x*x/a/a + y*y/b/b - z*z/c/c = -1
在数学里，双曲面是一种二次曲面。采用直角坐标 ，双曲面可以用公式表达为
（单叶双曲面），或
（双叶双曲面）。假若， ，则称为旋转双曲面。
本文将展示几种生成双叶双曲面算法和切图.使用自己定义语法的脚本代码生成数学图形.相关软件参见:数学图形可视化工具,该软件免费开源.QQ交流群: 367752815
(1)
#x*x/a/a + y*y/b/b - z*z/c/c = -1vertices = dimension1:72 dimension2:72u = from 0 to (2*PI) dimension1v = 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 D2:100u = from 0 to (1*PI) D1v = 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)
我之前写过关于双曲线的文章,数学图形(1.10) 双曲线
将双曲线旋转一周即能生成双曲面.
vertices = 360u = from -1 to 1 gap[0]x = uy = 1/xy = limit(y, -50, 50)surface_slices = 72rotate = anchor[0, 0, 0], axis[1, 1, 0], angle[0, 2*PI](4)
双曲面(东西开口)
vertices = 100t = 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 = 72rotate = anchor[0, 0, 0], axis[1, 0, 0], angle[0, 2*PI]双曲面(南北开口)
vertices = 100t = 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 = 72rotate = anchor[0, 0, 0], axis[0, 1, 0], angle[0, 2*PI]