3D transformations

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# 3D transformations - PowerPoint PPT Presentation

3D transformations. Dr Nicolas Holzschuch University of Cape Town e-mail: [email protected] Modified by Longin Jan Latecki [email protected] Sep. 11, 2002. Map of the lecture. Homogeneous coordinates in 3D Geometric transformations in 3D translations, rotations, scaling,….

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## PowerPoint Slideshow about '3D transformations' - selah

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### 3D transformations

Dr Nicolas Holzschuch

University of Cape Town

e-mail: [email protected]

Modified by Longin Jan Latecki

[email protected]

Sep. 11, 2002

Map of the lecture
• Homogeneous coordinates in 3D
• Geometric transformations in 3D
• translations, rotations, scaling,…
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
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
Rotation around x-axis

x-axis is

unmodified

Sanity check: a rotation of p/2

should change y in z, and z in -y

Rotation around y-axis

y-axis is

unmodified

Sanity check: a rotation of p/2

should change z in x, and x in -z