import three;
size(8cm,0);
real radius=1, theta=37, phi=60;

currentprojection=perspective(4,1,2);

// Planes
pen bg=gray(0.9)+opacity(0.5);
draw(surface((1.2,0,0)--(1.2,0,1.2)--(0,0,1.2)--(0,0,0)--cycle),bg,bg);
draw(surface((0,1.2,0)--(0,1.2,1.2)--(0,0,1.2)--(0,0,0)--cycle),bg,bg);
draw(surface((1.2,0,0)--(1.2,1.2,0)--(0,1.2,0)--(0,0,0)--cycle),bg,bg);

real r=1.5;
draw(Label("$x$",1), O--r*X, Arrow3(HookHead3));
draw(Label("$y$",1), O--r*Y, Arrow3(HookHead3));
draw(Label("$z$",1), O--r*Z, Arrow3(HookHead3));
label("$\rm O$", (0,0,0), W);

triple pQ=radius*dir(theta,phi); // Point Q
// triple pQ=radius*expi(radians(theta),radians(phi)); // Point Q
draw(O--radius*dir(90,phi)^^O--pQ, dashed);
dot("$R*\mathrm{dir}\left(\theta,\phi\right)$",pQ);

// Arcs
draw("$\theta$", reverse(arc(O,0.5*pQ,0.5*Z)), N+0.3E, Arrow3(HookHead2));
draw("$\phi$", arc(O,0.5*X,0.5*(pQ.x,pQ.y,0)), N+0.3E, Arrow3(HookHead2));

path3 p3=O--arc(O,radius,0,phi,90,phi)--cycle;
draw(surface(p3), blue+opacity(0.5));