Rotation of Point in 3D Space

1
votes

I have one problem related to rotation of point in 3D-space.

Suppose I have one point with X, Y and Z coordinates.

And now I want to rotate it, by specifying the rotation in one of these three ways:

  1. By user-defined degree
  2. By user-defined axis of rotation
  3. Around (relative to) user-defined point

I found good link over here, but it doesn't address point 3. Can anyone help me solve that?

1
algorithmmathgeometryrotation
Is this an opengl related question? – Kai
@Kai, No it is just a mats related Question......Just Rotation Of Point In 3D Space........ Thanks...... – Pritesh
what is the meaning of point 3? how is it different from a simple axis? – Protostome
@Protostome, where you fine point 3? though i giving answer by my understanding, Point3D means Point with X, Y and Z Co-Ordinate....... – Pritesh
The third question is not well defined. To rotate in 3D you must choose an axis; through the user-defined point there are (infinitely) many axes, and each one will give a different rotation. – Beta

1 Answers

8
votes

All rotations will go around the origin. So you translate to the origin, rotate, then translate back.

T = translate from global coordinates to user-coordinates
R = rotate around the origin (like in your link)
(T^-1) = translate back
point X

X_rotated = (T^-1)*R*T*X

If you have multiple points to rotate then multiply the matrices together:

A = (T^-1)*R*T
X_rotated = A*X