我正在尝试标记三维中任意向量的法线平面上的角度。我尝试将标签乘以$\omega t$
XY XY()
()、XZ() 和 YZ() 的组合,但没有成功。有什么建议吗?
settings.render=6;
settings.outformat="pdf";
usepackage("bm");
// import modules
import graph3;
import three;
import solids;
// overall settings
currentprojection=orthographic(.25,.5,.1);
viewportmargin=(10,10);
size(6cm);
currentlight=((3,3,0));
// variable parameters
real r=1;
real radio=sqrt(1-(cos(pi/8))^2);
real theta1=0, theta2=112.5;
real phi1=0, phi2=65;
// axes
xaxis3("$\bm{e}_1$",0,r,black,Arrow3);
yaxis3("$\bm{e}_2$",0,r,black,Arrow3);
zaxis3("$\bm{e}_3$",0,r,black,Arrow3);
//This draws a rotated frame theta=pi/8, varphi=pi/8
triple x3=(0.3535533905932738,0.1464466094067262,0.9238795325112868);
triple x2=(-0.3826834323650898,0.9238795325112868,0);
triple x1=(0.8535533905932738,0.3535533905932738,-0.3826834323650898);
triple centro=cos(pi/8)*x3;
triple spinproyxy=(-0.8741514406663723,0.4032814824381883,0.2705980500730985);
draw(O--x2,black+dashed,Arrow3,L=Label("$\bm{e}_2'$",position=EndPoint));
draw(O--x1,black+dashed,Arrow3,L=Label("$\bm{e}_1'$",position=EndPoint));
draw(O--x3, black+dashed,Arrow3,L=Label("$\bm{e}_3'$", position=EndPoint,SE));
//Circle[![enter image description here][1]][1]
path3 mycircleB=circle(c=O,r=1,normal=x3);
draw(surface(mycircleB),gray+opacity(.3));
draw(mycircleB,black+opacity(.3));
//This draws the angle ometa t
draw(arc(c=O,x1*.2,x2*.2, normal=x3), black+linewidth(.5pt),Arrow3(TeXHead2),L=Label("XY()*$\Large\omega t$", position=MidPoint,S));
答案1
我不知道您是如何得出x1
等的表达式的。在粒子数据组的标准约定中,由 形成的正交矩阵(x1,x2,x3)^T
具有 混合角theta1=pi/8
,这与您的评论一致,并且theta2=3*pi/8
,这与您的评论几乎一致。但是,约定可能不同。无论如何,如果我引入一个减号并由 变换,XY()
我rotate(22.5,Y)*rotate(-22.5,Z)
会得到一个看起来合理的结果。这个减号可能是约定问题。或者,更有可能的是,可能会有更好的旋转参数。如果您提供有关如何计算 的更多详细信息,那将有很大帮助(x1,x2,x3)
。
\documentclass{standalone}
\usepackage{asypictureB}
\standaloneenv{asypicture}
\begin{document}
\begin{asypicture}{name=disc}
settings.outformat = "pdf";
settings.prc = false;
settings.render = 0;
usepackage("bm");
// import modules
import graph3;
import three;
import solids;
// overall settings
currentprojection=orthographic(.25,.5,.1);
viewportmargin=(10,10);
size(6cm);
currentlight=((3,3,0));
// variable parameters
real r=1;
real radio=sqrt(1-(cos(pi/8))^2);
real theta1=0, theta2=112.5;
real phi1=0, phi2=65;
// axes
xaxis3("$\bm{e}_1$",0,r,black,Arrow3);
yaxis3("$\bm{e}_2$",0,r,black,Arrow3);
zaxis3("$\bm{e}_3$",0,r,black,Arrow3);
//This draws a rotated frame theta=pi/8, varphi=pi/8
triple x3=(0.3535533905932738,0.1464466094067262,0.9238795325112868);
triple x2=(-0.3826834323650898,0.9238795325112868,0);
triple x1=(0.8535533905932738,0.3535533905932738,-0.3826834323650898);
triple centro=cos(pi/8)*x3;
triple spinproyxy=(-0.8741514406663723,0.4032814824381883,0.2705980500730985);
draw(O--x2,black+dashed,Arrow3,L=Label("$\bm{e}_2'$",position=EndPoint));
draw(O--x1,black+dashed,Arrow3,L=Label("$\bm{e}_1'$",position=EndPoint));
draw(O--x3, black+dashed,Arrow3,L=Label("$\bm{e}_3'$", position=EndPoint,SE));
//Circle
path3 mycircleB=circle(c=O,r=1,normal=x3);
draw(surface(mycircleB),gray+opacity(.3));
draw(mycircleB,black+opacity(.3));
//This draws the angle omega t
draw(arc(c=O,x1*.2,x2*.2, normal=x3), black+linewidth(.5pt),Arrow3(TeXHead2),
L=Label(rotate(22.5,Y)*rotate(-22.5,Z)*XY()*"$\Large\omega t$", position=MidPoint,S));
\end{asypicture}
\end{document}