豆粑粑 matlab 欧拉角，旋转矩阵
QL的问题，一开始是想要一个球面上均匀的随机点。查了一下，我靠，真是个挺麻烦的事儿，特别是定义球面上点之间的距离，然后生成对应的点。
另一个，是如果把一个刚体在一个球面坐标上进行旋转。
还是查了一下，一个baidu百科，把本来挺明白事儿给整迷糊了。后来，找了比较官方的书。
《MATHEMATICAL METHODS FOR PHYSICISTS, SIXTH EDITION, George B. Arfken》
基本思路是按水平面转一下，按新的yoz转一下，再按新的xoy转一下，
至于生成随机的点，随机生成一堆alpha, beta, gamma三个角。把初始向量一边一边的转就行。
基本把Euler角怎么转给整明白了。
clear all
clc
clf
%% outline
% illustrate the rot matrix
% according to
% https://baike.baidu.com/item/%E6%97%8B%E8%BD%AC%E7%9F%A9%E9%98%B5/3265181?fr=aladdin
%
%% main
% % define original vector,
% p0_x =1*(sqrt(3)/3);
% p0_y =1*(sqrt(3)/3);
% p0_z =1*(sqrt(3)/3);
% p0_x =1;
% p0_y =0;
% p0_z =0;
phi0 = pi/8;
the0 = pi/2;
r0 = 1;
p0_x = r0 * cos(phi0) * sin(the0);
p0_y = r0 * sin(phi0) * sin(the0);
p0_z = r0 * cos(the0);
%
alp= -pi/4; %% yoz
bet= pi/3; %% xoz
gam= -pi/2; %% xoy
= fun_mm_rot_mat(alp,0,0)
= fun_mm_rot_mat(0,bet,0)
= fun_mm_rot_mat(0,0,gam)
= mat_alp*mat_bet*mat_gam
mat_eul_fun = fun_mm_rot_mat(alp,bet,gam)
% rot alph
tm=mat_alp*;
p_x_alp=tm(1);
p_y_alp=tm(2);
p_z_alp=tm(3);
tm= mat_bet*;
% tm = mat_bet*;
p_x_bet=tm(1);
p_y_bet=tm(2);
p_z_bet=tm(3);
tm = mat_gam*;
% tm = mat_gam*;
p_x_gam=tm(1);
p_y_gam=tm(2);
p_z_gam=tm(3);
tm = mat_eul_fun * ;
p_x_final = tm(1);
p_y_final = tm(2);
p_z_final = tm(3);
%% plot res
=sphere(50);
hold on
% plot orig vec
plot3(,,,'rs-','linewidth',5);
plot3(,,,'gs-','linewidth',5);
plot3(,,,'bs-','linewidth',5);
plot3(,,,'ms-','linewidth',5);
plot3(p_x_final,p_y_final,p_z_final,'o','markersize',10);
% plot sphere
surf(x,y,z,z,'edgecolor',)
plot3(,,,'k','linewidth',3);
plot3(,,,'k','linewidth',3);
plot3(,,,'k','linewidth',3);
% plot xoy
hxoy=surf(x,y,zeros(size(x)),'edgecolor','none')
axis equal
alpha(0.2)
alpha(hxoy,0.5)
xlabel('x')
ylabel('y')
zlabel('z')
view(144,23)
grid on
h_leg=legend('ori vec', '1st vec alpha','2nd vec beta','3rd vec gamma','final point','location','northwest')
%,'sphere','x axis ','y axis ','z axis ','xoy')
axis tight
% legend('boxoff')
h_leg.Color =;
set(h_leg.BoxFace, 'ColorType','truecoloralpha', 'ColorData',uint8(255*[.8;.8;.8;.3]));
function =fun_mm_rot_mat(alpha,beta,gamma);
% =fun_mm_rot_mat(alpha,beta,gamma);
% alph, beta, gamma : three angles
% mat : euler matrix
%
%%
%
% Euler Angles
% Page 202
% MATHEMATICAL
% METHODS FOR
% PHYSICISTS
% SIXTH EDITION
% George B. Arfken
%% main
% three angles
a = alpha;
b = beta;
r = gamma;
% matrix alpha ------------------------------
mat_a = [cos(a)sin(a) 0
-sin(a)cos(a) 0
0 0 1 ];
% matrix beta ------------------------------
mat_b = [cos(b) 0-sin(b)
0 1 0
sin(b) 0 cos(b)];
% matrix gamma ------------------------------
mat_r = [cos(r)sin(r) 0
-sin(r)cos(r) 0
0 0 1];
% euler matrix
mat_eul= mat_r * mat_b * mat_a;
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