这是一种挺漂亮的曲面图形,可惜没有找到太多的相关解释.
In differential equations, a breather surface is a mathematical surface relating to breathers.
其数学公式很复杂,参数方程为:
where 0 < a < 1.
维基的相关网址为:http://en.wikipedia.org/wiki/Breather_surface
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
#http://xahlee.info/surface/breather_p/breather_p.html vertices = D1:100 D2:100 u = from -13.2 to 13.2 D1 v = from -37.4 to 37.4 D2 b = 0.4 r = 1 - b*b w = sqrt(r) d = b*((w*cosh[b*u])^2 + (b*sin[w*v])^2) y = -u + (2*r*cosh[b*u]*sinh[b*u])/d z = (2*w*cosh[b*u]*(-(w*cos[v]*cos[w*v]) - sin[v]*sin[w*v]))/d x = (2*w*cosh[b*u]*(-(w*sin[v]*cos[w*v]) + cos[v]*sin[w*v]))/d
使用随机数
#http://en.wikipedia.org/wiki/Breather_surface vertices = D1:100 D2:100 u = from -13.2 to 13.2 D1 v = from -37.4 to 37.4 D2 a = rand2(0.1, 0.9) w = sqrt(1 - a*a) d = a*((w*cosh[a*u])^2 + (a*sin[w*v])^2) y = -u + (2*(1 - a*a)*cosh[a*u]*sinh[a*u])/d z = (2*w*cosh[a*u]*(-(w*cos[v]*cos[w*v]) - sin[v]*sin[w*v]))/d x = (2*w*cosh[a*u]*(-(w*sin[v]*cos[w*v]) + cos[v]*sin[w*v]))/d
