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CSI4130
Review Questions – 3D Transforms University of Ottawa – Universit ́e d’Ottawa
Jochen Lang
These questions are meant as a review of lecture material. The style of these questions is not necessarly a good indication of the style of the midterm (see the midterm examples instead).
1 2D Hierarchy
GivenatriangleABC withtheverticesa= 0 0 T,b= 1 0 T andc= 0 1 T givethe
2D homogeneous transforms TI←ABC and TII←ABC for the following image:
2 3D Transformations 2.1 Object Transformation
Rotate the 3D vector a = −5 4 6 T around the x-axis by α = 30◦ and afterwards translate it by t = 1 3 −2 T . Calculate (numbers!) both, the homogeneous 3D Transformation matrix
T and the vector a after the transformation. 2.2 Frame Transformation
Rotate the 3D frame {0} around its z-axis by α = 90◦ and call the result of the rotation frame {1}. Then translate the frame {1} by t = −2 −2 1 T and call the result frame {2} .
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Find (numbers) the combined frame transformation matrix F{0}→{2}. Sketch the relative posi-
tion of the teapot centered at a{0} = 0 0 0 T and frame {2}.
Calculate the corresponding object transformation which would have resulted in the same
relative position between the teapot at a and the frame {0} (There is always only one reference frame with object transforms).
3 3D Hierarchy
Create the following scene
from a basic square and cylinder with a scenegraph. Give the 3D transformation matrices in homogeneous coordinates taken the gradient color of the blocks into account. Your building blocks are as follows:
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