Rotation of Ellipse to a specific vector

6 次查看（过去 30 天）
Akash V
Akash V 2021-8-22
评论： Akash V 2021-8-22
I have a 3d ellipse which i plotted using ellipsoid(xc,yc,zc,xr,yr,zr) function. You can also see three vectors (blue red and yellow line) which are perpendicular to each other. I want to rotate the ellipsoid such that its x_semi_axis of the ellipse align with blue line, y_semi_axis of the ellipse align with red line and z_semi_axis of the ellipse align with yellow line.Could you please share the code to do so.Thank you
  2 个评论
DGM
DGM 2021-8-22
Not knowing anything about the specifics of your use case, I'd just assume you can use rotate(). There's webdocs, but there's also a few similar questions around. Here's one about using rotate() on an ellipsoid:
https://www.mathworks.com/matlabcentral/answers/582872-how-to-rotate-ellipsoid-correctly-in-matlab?s_tid=answers_rc1-2_p2_MLT
Akash V
Akash V 2021-8-22
I am quite new to matlab. I tried using rotate() but it is not aligning properly at all. Idk whether its the mistake of (roll pitch yaw) angle value itself or whether I have to follow a specific sequence of rotation. Here is the code :
semi_axis_x = 0.085962489000000
semi_axis_y = 0.119483388000000
semi_axis_z = 0.240855299000000
vector_1_x = 0.551221118000000
vector_1_y = 0.832495512000000
vector_1_z = -0.055736010000000
vector_2_x = 0.015328738000000
vector_2_y = 0.056685361000000
vector_2_z = 0.998274411000000
vector_3_x = -0.834218382000000
vector_3_y = 0.551124299000000
vector_3_z = -0.018485062000000
[X,Y,Z] = ellipsoid(0,0,0,semi_axis_x,semi_axis_y,semi_axis_z);
hold on
s = surf(X,Y,Z);
plot3([0 vector_1_x],[0 vector_1_y],[0 vector_1_z],'b');
hold on
plot3([0 vector_2_x],[0 vector_2_y],[0 vector_2_z],'r');
hold on
plot3([0 vector_3_x],[0 vector_3_y],[0 vector_3_z],'y');
axis tight
axis equal
xlabel('My x label')
ylabel('My y label')
zlabel('My z label')

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Wan Ji
Wan Ji 2021-8-22
By following operator you will get what you want
clc;clear
blueLine = [-0.4, 0.8, 0]; % direction of blue line
xc = 1;
yc = 2;
zc = 3;
xr = 1;
yr = 4;
zr = 2;
figure(1)
clf
[x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr);
mesh(x,y,z)
xlabel('x')
ylabel('y')
zlabel('z')
view(30,67)
axis equal
% relative position
x = x - xc;
y = y - yc;
z = z - zc;
t = z; % y,z axis exchange
z = y;
y = t;
figure(2);clf
mesh(x,y,z)
xlabel('x')
ylabel('y')
zlabel('z')
view(30,67)
axis equal
theta = atan2(blueLine(2), blueLine(1)) - pi/2;
x = x*cos(theta) - y*sin(theta); % rotate by theta
y = x*sin(theta) + y*cos(theta);
figure(3);clf
mesh(x,y,z)
xlabel('x')
ylabel('y')
zlabel('z')
view(30,67)
axis equal
% go back to absolute coodinate
x = x + xc;
y = y + yc;
z = z + zc;
  5 个评论
显示 3更早的评论
Wan Ji
Wan Ji 2021-8-22
编辑：Wan Ji 2021-8-22
Yup, I have got your idea, now I believe I achieve my answer. With Axis rotation [x->e1; y->e2; z->cross(e1,e2)]. As follows
% This is an example
% x-axis to e1
% y-axis to e2
% z-axis to e3
P0 = [0,0,0]; % point origin
P1 = [3,0,0]; % point on x-axis
P2 = [0,3,0]; % point on y-axis
P3 = [0,0,3]; % point on z-axis
e1 = [1, 1, 1]/sqrt(3); % e1 vector
e2 = [-1, 0, 1]/sqrt(2); % e2 vector
figure(1); title('Axis rotation [x->e1; y->e2; z->cross(e1,e2)]')
plot3([P0(1), P1(1)], [P0(2), P1(2)], [P0(3), P1(3)],'r-','linewidth',2)
hold on
plot3([P0(1), P2(1)], [P0(2), P2(2)], [P0(3), P2(3)], 'g-','linewidth',2)
plot3([P0(1), P3(1)], [P0(2), P3(2)], [P0(3), P3(3)],'b-','linewidth',2)
text(P1(1), P1(2),P1(3),'x')
text(P2(1), P2(2),P2(3),'y')
text(P3(1), P3(2),P3(3),'z')
P1_rot = rotate3d(e1, e2, P1)*2;
P2_rot = rotate3d(e1, e2, P2)*2;
P3_rot = rotate3d(e1, e2, P3)*2;
plot3([P0(1), P1_rot(1)], [P0(2), P1_rot(2)], [P0(3), P1_rot(3)],'r--','linewidth',2)
hold on
plot3([P0(1), P2_rot(1)], [P0(2), P2_rot(2)], [P0(3), P2_rot(3)], 'g--','linewidth',2)
plot3([P0(1), P3_rot(1)], [P0(2), P3_rot(2)], [P0(3), P3_rot(3)],'b--','linewidth',2)
text(P1_rot(1), P1_rot(2),P1_rot(3),'e1','color','c')
text(P2_rot(1), P2_rot(2),P2_rot(3),'e2','color','c')
text(P3_rot(1), P3_rot(2),P3_rot(3),'e3','color','c')
grid on
[x,y,z] = ellipsoid(0,0,0,2,1,0.5); % with centre at the origin
mesh(x,y,z,'facecolor','m','edgecolor','k', 'facealpha',0.4);
xyz = rotate3d(e1,e2,[x(:),y(:),z(:)]); % rotate the ellipsoid coordinate
xp = reshape(xyz(:,1), size(x)); % recover the coordinate of x-component
yp = reshape(xyz(:,2), size(y)); % recover the coordinate of y-component
zp = reshape(xyz(:,3), size(z)); % recover the coordinate of z-component
mesh(xp,yp,zp,'facecolor','b','edgecolor','w', 'facealpha',0.4); % mesh the rotated ellipsoid
The figure speaks!
rotate3d function is given here
function p = rotate3d(e1, e2, coordinate)
% coordinate must be n*3 matrix
% rotate x-axis to e1 vector
% rotate y-axis to e2 vector
% rotate z-axis to cross(e1,e2) vector
e1 = e1 / norm(e1);
e2 = e2 / norm(e2);
e1 = reshape(e1,1,3);
e2 = reshape(e2,1,3);
e3 = cross(e1, e2);
R = [e1;e2;e3];
p = coordinate*R;
end
Akash V
Akash V 2021-8-22
Thanks a lot for the code and your time :)

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Creating and Concatenating Matrices 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by