CS代考计算机代写 0 Notes

0 Notes
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} .
1

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:
2