Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

CS488/688 Introduction to Computer Graphics 21
9.4 Hierarchical Robot Arm [Last Used: Fall 1992 Final]
We wish to model the robot arm depicted below. You are to design an appropriate display structure.
Show the nodes, their hierarchy, and what purpose each node serves (e.g. rotation about z-axis or
base object).
The base (A) can rotate about the z axis. The post (B) can extend and retract along the z
axis. It moves in and out of the base like a piston in a cylinder. The joint (C) can rotate about
an axis parallel to the x − y plane (orientation depending on how the base has rotated). The angle
that the upper arm (D) makes with the post is determined by the rotation of this joint. The lower
arm (E) slides in and out along the upper arm, like a piston in a cylinder. The grippers (F) pivot
at their ends of attachment to the upper arm.
All components (A through E and both F’s) are formed by scaling a cylinder with unit diameter
and unit height whose base is centered at the origin:
z
y
x
A has height h A and diameter d A , and similarly for all other components. In building your
data structure, do not worry about restrictions on rotations or translations, since that would add
too many complications for the time you have.
z
y
C
B
D
E
F
x
A
9.5 Cube Array [Last Used: Spring 1992 Final]
Below is a data structure that, if properly walked and interpreted, will result in the display of 3
rows each consisting of 3 copies of the cube represented by the node “C”. The nodes with a “T” label
are translations. “T0” is the translation that takes (x, y, z) to (x, y − 4, z). “T1” is the translation
that takes (x, y, z) to (x, y, z). “T2” is the translation that takes (x, y, z) to (x, y + 4, z). “T3” is the
translation that takes (x, y, z) to (x − 4, y, z). “T4” is the translation that takes (x, y, z) to (x, y, z).
“T5” is the translation that takes (x, y, z) to (x + 4, y, z). The “R” node is a rotation, and the “S”
node is a scale.