基于html的个人网站的设计与实现论文,正保建设工程教育网官网,洛阳市App网站开发公司,3网站建设这是一个姓Boy的人发现的,所以取名为Boy surface.该图形与罗马图形有点相似,都是三分的图形.它甚至可以说是由罗马曲面变化而成的. 本文将展示几种Boy曲面的生成算法和切图,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: … 这是一个姓Boy的人发现的,所以取名为Boy surface.该图形与罗马图形有点相似,都是三分的图形.它甚至可以说是由罗马曲面变化而成的. 本文将展示几种Boy曲面的生成算法和切图,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 In geometry, Boys surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901 (he discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space). Unlike the Roman surface and the cross-cap, it has no singularities (i.e. pinch-points), but it does self-intersect. boy surface 01 #http://www.mathcurve.com/surfaces/boy/boy.shtml
vertices D1:100 D2:100
u from 0 to (PI) D1
v from 0 to (PI) D2
a sin(u)
b cos(u)
c sin(v)
d cos(v)
m sqrt(2)
k rand2(0.1, 1.4)
t b/(m - k*sin(2*u)*cos(3*v))
x t*(b*cos(2*v) m*a*d)
y t*(b*sin(2*v) - m*a*c)
z 3*t*b boy surface 02 #http://mathworld.wolfram.com/BoySurface.htmlvertices D1:100 D2:100
u from (-PI/2) to (PI/2) D1
v from 0 to PI D2a SQRT2*pow(cos(v), 2)
d 2 - SQRT2*sin(3*u)*sin(2*v)x a*cos(2*u) cos(u)*sin(2*v)
y a*sin(2*u) - sin(u)*sin(2*v)
z 3*pow(cos(v), 2)x x/d
y y/d
z z/d boy surface 03 我在这套公式上花费的时间最多,因为它最复杂,而且也不完美.它的曲面没能闭合.我研究了很久才发现,当r取无穷大时,该曲面才会闭合. #http://www.ipfw.edu/departments/coas/depts/math/coffman/steinersurface.html
#x (1r^2*cos(t)^2)*(sqrt(2)-sqrt(2)*r^2*cos(t)^22*r*sin(t)) / (3*(1r^2*cos(t)^2)*(1r^2*cos(t)^2r^2*sin(t)^2) 3*sqrt(2)*r^2*cos(t)*sin(t)*(3-r^2*cos(t)^2))
#y 2*(1r^2*cos(t)^2)*(sqrt(2)*r*cos(t) - r^2*cos(t)*sin(t)) / (3*(1r^2*cos(t)^2)*(1r^2*cos(t)^2r^2*sin(t)^2) 3*sqrt(2)*r^2*cos(t)*sin(t)*(3-r^2*cos(t)^2))
#z (1r^2*cos(t)^2)^2 / ((1r^2*cos(t)^2)*(1r^2*cos(t)^2r^2*sin(t)^2) sqrt(2)*r^2*cos(t)*sin(t)*(3-r^2*cos(t)^2))vertices D1:100 D2:100
t from 0 to (PI*2) D1
r from 0 to 10 D2
c cos(t)
s sin(t)
i (r*c) ^ 2
j (r*s) ^ 2
m sqrt(2)
a (1i)*(1ij)
b m*r*r*c*s*(3-i)
x (1i)*(m-m*i2*r*s) / (3*a 3*b)
y 2*(1i)*(m*r*c - r*r*s*c) / (3*a 3*b)
z (1i)*(1i) / (a b) 转载于:https://www.cnblogs.com/WhyEngine/p/3898580.html
