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Computing Science CMPT 361
Assignment #2 (30 marks)

, Wednesday at 11:59 pm.
Problem 1 (22 marks + possible 3 bonus): Playing Tetris with a robotic arm
You will upgrade the Tetris-FallingFruits game in assignment 1 into 3D, and control a robot
arm to play this game. Check out the sample code for a robot arm in:
http://www.cs.unm.edu/~angel/BOOK/INTERACTIVE_COMPUTER_GRAPHICS/SIXTH_EDITIO
N/CODE/CHAPTER08/
and look into example1.cpp and associated shaders.
(a) [4 marks] Upgrading Assignment 1 to 3D
Upgrade your Tetris-FallingFruits game to 3D by turning each fruit from a 2D square to a 3D
cuboid. The centers of all fruit cells are constrained in a 2D plane, e.g. 𝑧 = 0. Draw the entire
3D grid–1 by 10 by 20–using faint lines. You can keep the same game logic at this stage.
In case you feel uncomfortable with your implementation of Assignment 1, you can begin
with the sample code (solution) provided for Assignment 1. (This sample code is not yet
available and may take a few days to be ready.)
(b) [4 marks] Viewpoint Changes
The “ctrl” key will be combined with the “left” and “right” key to control the camera’s
movement on a circular orbit that is parallel to the x-z plane with a center on the y axis. The
camera always looks at the center of the Tetris window. Its “up” direction lies in the plane
spanned by the y axis and the camera’s principal axis – the line connecting the camera
center and the “Lookat” point.
(c) [4 marks] Control of the Robot Arm
Put the robot arm in the 3D space of Tetris tiles. The central axes of both lower and upper
arms will be limited in the same plane as fruit cuboids. In this way, the lower arm is
controlled by a rotation angle 𝜃, and the upper arm is controlled by an angle 𝜙. Use the “a”
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
(or “d”) key to increase (or decrease) the angle 𝜃, and the “w” (or “s”) key to increase (or
decrease) the angle 𝜙. Set the arm length and base height appropriately, such that it can
reach every location of the Tetris window.
(d) [4 marks] Game Logic
New Tetris tiles only appear at the tip of the robot arm. Rotate the robot arm to put it at
desired locations. At this stage, it is OK to ignore the collision between the new tile and
existing ones. Use the “space” key to drop a Tetris tile from the robot arm. The tile’s position
should align with the grid, i.e. snapped to the nearest grid position. Once a tile is dropped, it
can either float at the location it is dropped, or keep dropping downward until it hits some
other tiles (like in Assignment 1).
In this assignment, you don’t have to shuffle the fruits, since the “space” key is used for
dropping. If you want to keep this feature, you might use ctrl + ”space” for shuffling. The “up”
key is still reserved to rotate a tile. The “left” and “right” keys are disabled. Press ‘q’ to quit
and ‘r’ to restart. Eliminating full rows and three fruits with the same color is optional and
will not be judged since it is evaluated in Assignment 1.
(e) [4 marks] Collision Detection
The new Tetris tile can only be dropped at places without collision with existing tiles. When
the tile is attached to the robot arm, we allow collision, but will highlight collision cases by
turning the tile to grey color (so that the player knows it cannot be dropped).
Also, if any cell of the tile (when its location is rounded to the nearest cube of the unit grid)
is outside the playing area, turn the tile grey.
(f) [2 marks] Timer
The placement of each tile is limited to a certain amount of seconds. Display the remaining
seconds (as a text message) for the current tile on the top of the window.
When the time is out, the tile on the arm will be automatically dropped at the current
location. If the tile is greyed when the timer expires, then the game is ended. (But not your
application…when a game ends it should be possible to play another game.}
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
(g) [3 marks] Bonus Points
Extend the playing area to n by 10 by 20, where n is a number specified by the user at the
beginning of the game. Also add a parameter to the robot arm model that allows rotation of
the entire arm around the vertical center axis of the base, and user controls for that
parameter. Inform the user what these controls are at the start of the game.
As the robot arm rotates, by default the tile should be translated but not rotated—it stays
oriented the way it started. The user can use the ‘rotate’ key to rotate the tile 90 degrees
around a vertical line through its centerpoint.
Add the tiles consisting of four cubes that vary in x, y, and z. There are three of these, and
two are mirror-reflections of each other. All of them fit in a 2 by 2 by 2 grid. The back slice
is an “L” shape with three cubes, and the front slice is one cube in front of one of the backslice cubes. Which back-slice cube the front-slice cube it is in front of determines the type of
the shape.
Note that the above steps build on top of each other, in order. You need not submit
individual programs to correspond to these steps. If you can implement all the required
parts, a single, complete program is sufficient. Skeleton code for Tetris and Robot Arm are
provided.
Submission: All source codes, a Makefile to make the executable called FruitTetris3D (the
make command should be make), and a README file that documents any steps not
completed, additional features, and any extra instructions for your TA.
Problem 2 (3 marks): Back face culling.
Suppose we have a scene with a single, fully opaque, convex object, which is entirely inside
the view volume. The convex object is specified by a mesh.
Under orthogonal projection, will back face culling alone be guaranteed to produce the
correct set of visible polygons? Why or why not?
Under perspective projection, is it true that back face culling alone is guaranteed to produce
the correct set of visible polygons? Why or why not?
Problem 3 (5 marks): BSP vs. depth-sort.
Show that the back-to-front display order determined by traversing a BSP tree is not
necessarily the same as the back-to-front order determined by depth-sort, even when no
polygons are split. To receive full mark on this problem, the number of polygons you use for
your example must be the smallest possible and you also need to prove that the number of
polygons you used is the smallest possible. Hint: mostly you need an example. The rest is
easy.

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