De La Salle - College of Saint Benilde
School of Management and Information Technology
Game Design and Development Program
As of 1st Trimester SY 2010-2011
COURSE SYLLABUS
COURSE CODE
COURSE TITLE
COURSE CREDIT
PRE-REQUISITE
PRE-REQUISITE TO
TYPE OF COURSE
FACULTY
TERM /TIME /ROOM
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APLIMAT
Applied Mathematics for Game Programming
3 Units
NONE
NONE
Major Course
COURSE DESCRIPTION:
In this course, students will understand the concepts and mathematics involving collisions of simple
geometries and polygons. The subject is meant to enable the students to implement algorithms for
collision detection for their gaming needs. The subject also teaches concepts and mathematics of physics
with the goal of enabling students to implement them in a program or a gaming application. Finally, the
course also covers advanced topics on 3D orientation and angular displacement representations and
computations.
COURSE OBJECTIVES / COMPETENCY SKILLS:
Upon successful completion of this course, students will be able to:
1.
Understand the concept of collision detection as well as implement a collision detection algorithm
in a 3D game program.
2.
Understand physics concepts as well as implement basic physics algorithms in games.
3.
Understand the advantages and disadvantages of the different methodologies for computing 3D
orientation and angular displacements
4.
Implement a Euler angles and quaternions in 3D programs.
CSB CORE VALUES:
1. Appreciative of the Worth of Each Individual
a. Know one’s strength and weaknesses
b. Confident in the ability of applying Data Structures for creating solutions
c. Able to collaborate with a team and understand each team member’s capabilities and
limitations
d. Adheres to excellence in accomplishing assigned task
2. Socially Responsible
a. Abide by the IT Code of Ethics and
b. Performs assigned task diligently and honestly
3. Professionally Competent
a. Can apply IT and business skills in solving problems
COURSE OUTLINE:
Part I. Points, Lines and Geometries
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Coordinate Systems
o Cartesian coordinate system
o Polar coordinate system
Defining a point
Defining a line
Parabolas
Circles and Spheres
Application in collision detection
Mathematical visualization
2.5 Weeks
APLYMAT Course Syllabus
Page 1 of 4
Part II. Collision Detection Test for Simple 3D Geometries
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Review of related mathematics
Sphere
o Sphere – Sphere Test
o Ray – Sphere Test
o Line Segment – Sphere Test
Aligned-Axis Boxes
o Ray – Box Test
o Sphere – Box Test
Separating Axis
o Line Segment – Box Test
o Triangle – Box Test
o Box – Box Test
Polygons
o Ray – Triangle Test
o Line Segment – Triangle Test
o Ray – Polygon Test
o Triangle – Triangle Test
o Polygon – Polygon Test
o Triangle – Sphere Test
o Polygon – Volume Test
3.5 Weeks
Part III. Physics
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Review of related mathematics
Speed and Velocity
Acceleration
Equations of motion
Visualizing velocity and acceleration
Using vectors
Projectiles and implementation
Forces
Using Newton’s law
Work and kinetic energy
Collision with a stationary object
Momentum and impulse
Modeling collision
Rotational motion
Implementing collision
3.0 Weeks
Part IV. 3D Orientation and Angular Displacement
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Understanding orientation
A review of matrices
Euler Angles
o What are Euler angles?
o Euler angle conventions
o Advantages and disadvantages of Euler angles
o Using Euler angles
Quaternions
o What are quaternions?
o Quaternion operations
Converting angle representations
3.0 Weeks
TEACHING METHODS / STRATEGIES:
The course is delivered mostly through learner-centered methodology with emphasis on individual and
collaborative activities where teachers prepare the environment for learning and guide the learners to
develop the important competencies. These methods are geared towards the belief that students learn
best and retain much of the learning in an atmosphere where they are allowed to apply their creativeness
and self expression.
APLYMAT Course Syllabus
Page 2 of 4
REQUIREMENTS / DELIVERABLES:
Individual Activity and Collaborative Work will require any of the following deliverables for a given topic.
1.
2.
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4.
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Preparation and Participation in Lectures / Discussions
Prepared Multimedia Aided Presentations
Exercises and Application Output
Machine Projects
Quizzes and Examinations
Plagiarism Policy
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Using the oral or written words and ideas of others without proper acknowledgment is plagiarism and is
an academic offense. As a form of academic misconduct, students found guilty face serious
consequences as stipulated in the Student’s Handbook.
Submission Policy
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To promote professionalism and competence, submission of requirements and deliverables must always
be on time. The teacher reserves the right NOT to accept late submissions and will rate the requirement
as failed or zero. In case the teacher decides to accept late requirement due to valid reasons, the
teacher will impose point deductions on the score obtained or deduct 10% of the total score per day of
delay. Students must present a letter from their parent or legal guardian appealing for the teacher to
accept the late requirement. Valid proof must be attached to the letter of appeal.
Assessment / Evaluation
To asses the performance and competencies of the learners…
1. Short quizzes will be administered to determine if the learners can remember basic concepts and
principles
2. Exercises will be given as practice sets for students in preparation for future hands on projects
and development requirements as well as to solidify their knowledge on the topics they already
know. Exercises will also be used to illustrate practical and concrete applications to the abstract
concepts taught in class lectures
3. Machine Projects will be required to give the students a first hand experience on implementing
data structures and algorithms in simple programming applications as well as to enable the
students to develop solutions and solve simple problems using data structures.
4. Examinations will be used as tools for validation tools to rate long term memory retention on the
topics at hand. Examinations may also be used as a learning tool to derive how current topics
maybe intertwined to the next area of discussion
Quiz & Exam Policy
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Students must attend all required scheduled quizzes and exams at the designated time and place.
Individual professors may accommodate for illness or personal crisis. Additional accommodation will not
be made unless a written request is sent to and approved by the Chairperson or Dean prior to the
scheduled exam or as prescribed by the student manual. Any student who misses a scheduled quiz or
exam without approval will be given a failing grade for the quiz or exam. Behavior during exams is
expected to conform to College guidelines. No further warnings will be given prior or during the exams,
the penalty for cheating is immediate failure.
GRADING SYSTEM:
Mid-Term Grade
Point
Pre-Final Grade
Distribution
Attendance
10%
Attendance
Exercises and Short Quizzes
20%
Exercises and Short Quizzes
Long Quizzes
25%
Long Quizzes
Machine Project
20%
Machine Project
Mid-Term Examination
25%
Final Examination
Final Grade = 50% of Mid-Term Grade + 50% of Pre-Final Grade
MATERIALS OF INSTRUCTIONS:
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Beginning Math and Physics for Game Programmers – New Riders Publishing
Collision Detection in Interactive 3D Environments – Morgan Kaufmann Publishers
3d Math Primer fro Graphics and Game Development – Wordware Publishing, Inc.
APLYMAT Course Syllabus
Page 3 of 4
PROFESSOR’S CONSULTATION HOURS AND VENUE: ____________________
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COURSE CODE
:
APLIMAT
:
APPLIED MATHEMATICS FOR
ACKNOWLEDGEMENT FORM COURSE TITLE
GAME PROGRAMMING
COURSE CREDIT
:
3 Units
(SUBMIT THIS FORM TO THE TEACHER)
COURSE SCHEDULE :
Days :
Time :
Term :
S.Y. :
SECTION & ROOM
:
Section :
Room :
TEACHER
___________________________________________
COURSE SYLLABUS
This is to certify that I, ___________________________ have read and understood the entire
WRITE YOUR FULL NAME
syllabus and agree with its content, policies and consequences.
___________________
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SIGNATURE
DATE SIGNED
APLYMAT Course Syllabus
Page 4 of 4