written 6.1 years ago by | modified 2.7 years ago by |
Mumbai university > mechanical engineering > sem 7 > cad/cam/cae
Marks: 5M,10M
Difficulty: Medium
written 6.1 years ago by | modified 2.7 years ago by |
Mumbai university > mechanical engineering > sem 7 > cad/cam/cae
Marks: 5M,10M
Difficulty: Medium
written 6.1 years ago by |
3D rotation transformation
Rotation: It is an important geometric transformation. The final position and orientation of a geometric entity is decided by the angle of rotation (θ) and the base point about which the rotation is to be done.
Since we know that, during rotation about z-axis, the z-coordinate of object remains constant. Also during rotation about x-axis and y-axis of object, the x-coordinate and y-coordinate respectively remains constant as x,y,z are mutually perpendicular to each other.It is the property of vector.
Hence for rotation about Z-axis, we can draw the following figure.
To develop the transformation matrix, consider Point P located in XY plane, being rotated in the counter clock wise direction to the new position P’ by an angle θ as shown in above figure.
The position P’ is given by,
P' = [X', Y', Z']
From the figure,
The new position P' is specified by
and z = z remains same.
This can be written in matrix form as :
The above matrix can also be written in Homogeneous form as :
Similarly we can find rotation matrix in 3D about y- axis as well as about x-axis. The rotational matrix are as follows, 1. Rotation about x-axis