超圆是什么?

找了很久也没找到其正式中文定义.

维基上的定义为:

那我用自己的话说吧,

超圆就是方程式x^a+y^b= c所生成的图形.当a==b==2时,为一个圆.

超椭圆是m*x^a+n*y^b= c所生成的图形.当a==b==2时,为一个椭圆.

前面写的就是一种超圆.

 

超圆脚本代码1

vertices = 1000r = 10.0t = from 0 to (2*PI)s = rand2(0.1, 10)x = r*pow_sign(sin(t), s)y = r*pow_sign(cos(t), s)

超圆脚本代码2

vertices = 1000r = 10.0t = from 0 to (2*PI)a = rand2(0.1, 10)b = rand2(0.1, 10)x = r*pow_sign(sin(t), a)y = r*pow_sign(cos(t), b)

超椭圆脚本代码1

vertices = 1000r = 10.0t = from 0 to (2*PI)s = rand2(0.1, 10)w = rand2(0.2, 5)x = r*pow_sign(sin(t), s)y = r*w*pow_sign(cos(t), s)

超椭圆脚本代码2

vertices = 1000r = 10.0t = from 0 to (2*PI)a = rand2(0.1, 10)b = rand2(0.1, 10)w = rand2(0.2, 5)x = r*pow_sign(sin(t), a)y = r*w*pow_sign(cos(t), b)

 

超圆面

vertices = D1:1000 D2:100u = from 0 to (2*PI) D1v = from 0 to (10) D2r = 10.0x = r*pow_sign(sin(u), v)y = r*pow_sign(cos(u), v)

超椭圆面

vertices = D1:1000 D2:100u = from 0 to (2*PI) D1v = from 0 to (10) D2r = 10.0w = rand2(0.2, 5)x = r*pow_sign(sin(u), v)y = r*w*pow_sign(cos(u), v)

 

有种曲线名为kiss curve也是超圆的一种:

#http://www.2dcurves.com/sextic/sextick.htmlvertices = 2000t = from 0 to (2*PI)x = sin(t)y = pow(cos(t), 3)