3d transformation

2,896 views

Published on

0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
2,896
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
22
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

3d transformation

  1. 1.
  2. 2. 3D Transformations<br />Same idea as 2D transformations<br />Homogeneous coordinates: (x,y,z,w) <br />4x4 transformation matrices<br />
  3. 3. Basic 3D Transformations<br />Identity<br />Scale<br />Translation<br />Mirror about Y/Z plane<br />
  4. 4. Basic 3D Transformations<br />Rotate around Z axis:<br />Rotate around Y axis:<br />Rotate around X axis:<br />
  5. 5. Reverse Rotations<br />Q: How do you undo a rotation of q, R(q)?<br />A: Apply the inverse of the rotation… R-1(q) = R(-q) <br />How to construct R-1(q) = R(-q)<br />Inside the rotation matrix: cos(q) = cos(-q)<br />The cosine elements of the inverse rotation matrix are unchanged<br />The sign of the sine elements will flip<br />Therefore… R-1(q) = R(-q) = RT(q)<br />

×