用matlab绘制Roman曲面x = r^2*cos(a)*cos(b)*sin(b) ,y = r^2*sin(a)*cos(b)*sin(b) ,z = r^2*cos(a)*sin(a)*(cos(b) )^2

首先定义参数方程：

syms r a b
x = r^2*cos(a)*cos(b)*sin(b);
y = r^2*sin(a)*cos(b)*sin(b);
z = r^2*cos(a)*sin(a)*(cos(b))^2;

然后选择一组合适的参数范围，这里取r在[0,1]，a在[0,2*pi]，b在[0,pi]：

rvals = linspace(0,1,50);
avals = linspace(0,2*pi,50);
bvals = linspace(0,pi,50);

接下来使用meshgrid生成网格点：

[rgrid,agrid,bgrid] = meshgrid(rvals,avals,bvals);

然后将网格点代入参数方程得到坐标点：

xgrid = eval(subs(x,[r,a,b],[rgrid,agrid,bgrid]));
ygrid = eval(subs(y,[r,a,b],[rgrid,agrid,bgrid]));
zgrid = eval(subs(z,[r,a,b],[rgrid,agrid,bgrid]));

最后使用surf函数绘制曲面：

surf(xgrid,ygrid,zgrid)
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
title('Roman Surface')