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Computing Science CMPT 361 Fall 2019

Assignment #2 (30 marks)

Due date: November 4th at 11:59 pm.

Problem 1 (22 marks): 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 once there, look into example1.cpp and associated shaders. You are allowed to use this

code (or parts of it) in your assignment.

(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.

(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. Ensure that the camera always sees the entire board.

(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”

(or “d”) key to increase (or decrease) the angle 𝜃, and the “w” (or “s”) key to increase (or

decrease) the angle 𝜙. If you needed the characters “w”, “a”, “s”, and “d” for block control

Computing Science CMPT 361 Fall 2019

Instructor: Tom Shermer Simon Fraser University

in assignment 1, then use “I”, “j”, “k”, and “l” for the robot arm instead. 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).

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 Fall 2019

Instructor: Tom Shermer Simon Fraser University

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.

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 marks 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.

Prepare a PDF file problems.PDF with your answers to problems 2 and 3.

Submission: All source code, a Makefile to make the executable called FruitTetris3D (the

make command should be simply “make”), a README file that documents any steps not

completed, additional features, and any extra instructions for your TA, and your

problems.PDF file.

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