Rotate 3D Shape so Specific Face is Normal to Given Vector

I have a 3D shape made up of faces and vertices. I've been struggling to create code that will respond dynamically to rotate the shape so that the red face is 1. Normal to a given input vector; 2. The red face points in the direction of the vector.

For example, if the above photo is the starting state and I am given an input vector of [-1, 0, 0], I expect an output like this where the red face is: 1. Orthogonal to the vector; 2. The red face is closer to -x than the blue body.

My issue is that I can't figure out how to rotate the red square so that it is normal to the vector while also rotating the blue body to properly maintain the original shape. Enclosed is a copy of the shape, if you'd like to use that as a starting point. Any input is greatly appreciated!

[Dyuman Joshi]

Have you tried rotate?

[Estel]

Rotate works for obvious vectors like [1,0,0] or [0,1,0], but not when given something like [0.707, -0.5, 1]. Or at least I haven't been able to figure out how to incorporate "rotate" + the front face being normal to the vector.

Answer 1

[Matt J]

You can use this to compute the alpha and direction arguments needed for rotate.

function [alpha,direction]=vecrot(vstart,vend)
%Find rotation parameters that rotate one vector into coincidence with another about their
%common perpendicular axis.
%
%    [alpha,direction]=vecrot(vstart,vend)
%           
%IN:         
%            
%    vstart: Initial normal vector
%      vend: Final normal vector
%            
%OUT:        
%
%    alpha:  the rotation angle in degrees
%    direction: the rotation axis



  vstart=vstart(:)/norm(vstart);
  vend=vend(:)/norm(vend);
 
  direction=cross(vstart,vend);
   
  b=vend.'*vstart;
  
  alpha = atan2d(sqrt(1-b^2),b);
  
end

[Estel]

This works great for the figure! Thank you! But I realize now that I wasn't specific about the type of output I expected; I care less about the figure and more about the output of faces and vertices since I need to do further math on this rotated shape.

[Matt J]

This works great for the figure! Thank you!

You're welcome, but please Accept-click the answer to indicate the question was resolved.

But I realize now that I wasn't specific about the type of output I expected; I care less about the figure and more about the output of faces and vertices since I need to do further math on this rotated shape.

Given the direction and rotation angle, you can perform the rotation on a given set of points using AxelRot, in this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis

[Estel]

Thank you! I have questions about the AxelRot:

I know I'd be using the form [XYZnew, R, t] = AxelRot(XYZold, deg, u, x0)

where XYZold = shape.vertices

u = cross(norm_original, norm_desired)

x0 = [0,0,0] %default

but I don't understand the deg value -- is it the same as the Alpha from the vecrot from above?

[Matt J]

You would do,

[alpha,direction]=vecrot(norm_original, norm_desired);

shape.vertices = AxelRot(shape.vertices.', alpha, direction, [0,0,0]).'  ;