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3D Transformations<br />Same idea as 2D transformations<br />Homogeneous coordinates: (x,y,z,w) <br />4x4 transformation m...
Basic 3D Transformations<br />Identity<br />Scale<br />Translation<br />Mirror about Y/Z plane<br />
Basic 3D Transformations<br />Rotate around Z axis:<br />Rotate around Y axis:<br />Rotate around X axis:<br />
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(...
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3d transformation

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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 />

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