how to rotated a cube 30 deg counterclockwise around the axis that passes through v1 and v8

A = [0 0 500];%v1 axis

B = [5 0 500];

C = [0 5 500];

D = [0 0 505];

E = [0 5 505];

F = [5 0 505];

G = [5 5 500];

H = [5 5 505];%v8 axis

P = [A;B;F;H;G;C;A;D;E;H;F;D;E;C;G;B];

plot3(P(:,1),P(:,2),P(:,3),'b'), hold on

      V6--------------------------v8
    /                             /
   /                             /
  /                             /
V2----------------------------v3
|
|
|
|     V7----------------------------V5
|     /                             /
|   /                              /
|  /                              /
V1---------------------------- v4

Answer 1

[James Tursa]

You can do the following steps:

1) Use v1 and v8 to form a unit rotation axis x
2) Use x and your desired rotation angle to form a rotation quaternion q
3) Convert q to a direction cosine matrix d
4) Multiply all of your points by d

For step 3 you would need a quaterion / dcm conversion routine. You could use quat2dcm from the Aerospace Toolbox, or you could use one of the converters from the FEX. E.g., this submission by John Fuller:

http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm--euler-angles--quaternions--and-euler-vectors