1 / 10

3D transformations

3D transformations. Dr Nicolas Holzschuch University of Cape Town e-mail: holzschu@cs.uct.ac.za Modified by Longin Jan Latecki latecki@temple.edu Sep. 11, 2002. Map of the lecture. Homogeneous coordinates in 3D Geometric transformations in 3D translations, rotations, scaling,….

selah
Download Presentation

3D transformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3D transformations Dr Nicolas Holzschuch University of Cape Town e-mail: holzschu@cs.uct.ac.za Modified by Longin Jan Latecki latecki@temple.edu Sep. 11, 2002

  2. Map of the lecture • Homogeneous coordinates in 3D • Geometric transformations in 3D • translations, rotations, scaling,…

  3. Homogeneous coordinates in 3D • In order to model all transformations as matrices: • introduce a fourth coordinate, w • two vectors are equal if: x/w = x’/w’, y/w = y’/w’ and z/w=z’/w’ • All transformations are 4x4 matrices

  4. Translations in 3D

  5. Scaling in 3D

  6. Rotations in 3D • One rotation: one axis and one angle • Matrix depends on both axis and angle • direct expression possible, from axis and angle, using cross-products • Rotations about axis have simple expression • other rotations express as composition of these rotations

  7. Rotation around x-axis x-axis is unmodified Sanity check: a rotation of p/2 should change y in z, and z in -y

  8. Rotation around y-axis y-axis is unmodified Sanity check: a rotation of p/2 should change z in x, and x in -z

  9. Rotation about z-axis z-axis is unmodified Sanity check: a rotation of p/2 should change x in y, and y in -x

  10. Any transformation in 3D • All transformations in 3D can be expressed as combinations of translations, rotations, scaling • expressed using matrix multiplication • Transformations can be expressed as 4x4 matrices

More Related