在这一节中,将展示几个鞍面图形,或与鞍面类似的图形,如马鞍面,猴鞍面,狗鞍面等.有点奇怪的是马鞍面是让人骑在马上的曲面, 而猴鞍面是让猴骑的曲面,狗鞍面是让狗骑的曲面.此外,还这一节提供了类似沙发,板凳之类的曲面.
使用自己定义语法的脚本代码生成鞍面图形.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)马鞍面
之前我发布过关于双曲抛物面的文章,见:数学图形之双曲抛物面
vertices = dimension1:320 dimension2:320 a =0.7 x = from (-a) to (a) dimension1 z = from (-a) to (a) dimension2 y = x*x - z*z s = 10 x = s*x y = s*y z = s*z
(2)猴鞍面
#http://xuxzmail.blog.163.com/blog/static/25131916200961311531402/ #猴鞍面 （Monkey saddle） 是数学家为猴子量身定做的一种鞍面 vertices = dimension1:320 dimension2:320 a = 1 x = from (-a) to (a) dimension1 z = from (-a) to (a) dimension2 y = x*(x*x - 3*z*z)
(3)狗鞍面
#http://xuxzmail.blog.163.com/blog/static/25131916201232494954783/ #狗鞍面的方程为：z=x*y^3-y*x^3。这是一个4次曲面。 vertices = dimension1:320 dimension2:320 x = from (-2) to (2) dimension1 z = from (-2) to (2) dimension2 y = x*(z^3)-z*(x^3)
(4)Shoe Surface
#http://mathworld.wolfram.com/MennsSurface.html vertices = D1:100 D2:100 u = from -4 to 4 D1 v = from -4 to 4 D2 a = 0.1 x = u z = v y = pow(u, 3)/3 - v*v/2
(5)Quartoid(板凳)
#http://mathworld.wolfram.com/Quartoid.html vertices = D1:100 D2:100 u = from -10 to 10 D1 v = from -10 to 10 D2 x = u z = v y = 40 - pow(u*u + v*v, 2)*0.001
(6)Peninsula Surface(sofa)
#http://mathworld.wolfram.com/PeninsulaSurface.html vertices = D1:100 D2:100 u = from -2 to 2 D1 v = from -2 to 2 D2 a = 0.1 x = u z = v y = pow_sign(1 - u*u - pow(v, 5), 1/3)
(7)Peano Surface
#http://mathworld.wolfram.com/PeanoSurface.html vertices = D1:100 D2:100 u = from -10 to 10 D1 v = from -10 to 10 D2 x = u z = v y = (2*u*u - v)*(v - u*u) * 0.001
(8)Menn's Surface
#http://mathworld.wolfram.com/MennsSurface.html vertices = D1:100 D2:100 u = from -10 to 10 D1 v = from -20 to 20 D2 a = 0.1 x = u z = v y = a*pow(u, 4) + u*u*v - v*v y = y/100
(9)Handkerchief Surface
#http://mathworld.wolfram.com/HandkerchiefSurface.html vertices = D1:100 D2:100 u = from -4 to 4 D1 v = from -4 to 4 D2 a = 0.1 x = u z = v y = pow(u, 3)/3 + u*v*v + 2*(u*u - v*v) y = y*0.1
