Vectorized Solution to Rotate Multiple Points each at a Different Angle
조회 수: 13 (최근 30일)
이전 댓글 표시
I want to rotate a matrix of points, i.e. column vectors. However, I want to rotate each vector in the matrix by a different angle. For example:
pointMatrix = [v1,v2,v3,v4]; %vi is a column vector
rotateAngles = [10,20,30,40]; %degrees
Say I want to rotate these points around the z-axis. Therefore, for one point I could do something like the following:
Rz = [[cos(rotateAngles(1)) -sin(rotateAngles(1)) 0];...
[sin(rotateAngles(1)) cos(rotateAngles(1)) 0];...
[ 0 0 1]];
v1Rotated = Rz*v1;
Is there a non-loop way to rotate all the vectors in my pointMatrix by each one's unique rotation angle? Something like this...
allRotatedPoints = superRotationMatrix*pointMatrix;
where the superRotationMatrix "magically" rotates each column by the corresponding angle.
Thanks!
댓글 수: 0
채택된 답변
Teja Muppirala
2013년 3월 8일
편집: Teja Muppirala
2013년 3월 8일
This vectorized solution uses complex exponentials and works about 2 orders of magnitude faster for large vectors.
M = exp(rotateAngles*1i) .* ([1 1i 0]*pointMatrix);
allRotatedPoints = [real(M); imag(M); pointMatrix(3,:)];
댓글 수: 1
Fvieira
2021년 4월 30일
Notice that this works for 3 coordinate vectors (p = x,y,z).
For 2d one must consider this variation:
M = exp(rotateAngles*1i) .* ([1 1i]*pointMatrix);
allRotatedPoints = [real(M); imag(M)].'
Here is a full example that I did based on Muppirala's answer regarding some small details (angle in radians, for example):
v1 = [1;1]; v2 = [2;2]; v3 = [3;0]; v4 = [4;2];
pointMatrix = [v1 v2 v3 v4] %vi is a column vector
rotateAngles = [90 90 90 90] *pi/180 % radians
M = exp(rotateAngles*1i) .* ([1 1i]*pointMatrix);
allRotatedPoints = [real(M); imag(M)].'
pointMatrix = pointMatrix.'
figure(1)
plot(pointMatrix(:,1),pointMatrix(:,2),'o')
axis([-5 5 -5 5])
grid on, hold on
plot(allRotatedPoints(:,1),allRotatedPoints(:,2),'x')
Here are the plots: Circles are the points, crosses are them rotated by 90 degrees.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/602480/image.jpeg)
참고 항목
카테고리
Help Center 및 File Exchange에서 Surface and Mesh Plots에 대해 자세히 알아보기
제품
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!