Reference system

Questions
,
1

Hello everyone. I am trying to change the reference system to the system that appears in the image:

1.JPG
1.JPG432Ă—476 13.7 KB

Any idea?

Thank you.

2

I am not sure what you mean. I would consider GeometricTransformation for a general linear change, Translate or Rotate for more specific changes.

3

I’d rather not make assumptions about what you mean by “change the reference system”. Maybe you can provide a before and after comparison so I know what you’re trying to change.

4

I wish to get this transformation:

59621.JPG
59621.JPG914Ă—556 28.9 KB

5

mat = Orthogonalize[RandomReal[{0, 1}, {3, 3}]];
Graphics3D[GeometricTransformation[Cuboid, mat]]

6

Thank you for your response, Gianluca.

I tried to do what you show me, but I couldn’t get the result I am looking for. I show the code and a picture with my code and the result I obtained…maybe
someone find the mistake.

A = {{1, 1, 1}, {1, 6, 8}, {1, 8, 9}};
c = Orthogonalize[Eigenvectors[A]] // N;
c // MatrixForm
Graphics3D[{GeometricTransformation[Cuboid[], c], 
  Arrow[{{0, 0, 0}, {0.09489129421592486, 0.636336138762876, 
     0.7655533689994319}}], 
  Arrow[{{0, 0, 0}, {-0.9918275784421267, 0.005450756929915728, 
     0.12746899187848795}}], 
  Arrow[{{0, 0, 0}, {0.08528597143524745, -0.7713926417546674, 
     0.6306185022048604}}]}, Axes -> True]

2.JPG
2.JPG1253Ă—624 48.7 KB

I’d wish the cuboid coincide with the arrows.

Thank you.

7

You should use the columns of the matrix for the arrows, not the rows:

A = {{1, 1, 1}, {1, 6, 8}, {1, 8, 9}};
c = Orthogonalize[Eigenvectors[A]] // N;
c // MatrixForm
Graphics3D[{GeometricTransformation[Cuboid[], c], 
  Map[Arrow[{{0, 0, 0}, #}] &, Transpose[1.5 c]]}, Axes -> True]

or else

Graphics3D[{GeometricTransformation[{Cuboid[], 
    Map[Arrow[{{0, 0, 0}, #}] &, 1.5 IdentityMatrix[3]]}, c]}, 
 Axes -> True]
8

Thank you very much Gianluca, now the program works like I want!

You helped me a lot, I’m very grateful.

Regards.