数学图形之鞍面

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