GAM 325/425: Applied 3D Geometry

Instructor Information

Name: André Berthiaume

Preferred Contact:        Berthiaume@cs.depaul.edu

Course Description   

Review of mathematical foundation and techniques needed for the development of 3D graphics and game systems. This class will provide the foundation in linear algebra and 3D geometry required for implementing common tasks in 3D graphics and game systems. Topics include: vectors, matrices, transforms, coordinate changes, projections, intersection. PREREQUISITE(S): CSC 301 or CSC 403

Textbook

Essential Mathematics for Games and Interactive Applications, Third Edition 3rd Edition
by James M. Van Verth, Lars M. Bishop

ISBN-13: 978-1482250923

Software

None required, though access to Microsoft Excel (or any other software with linear algebra package) can be a great asset.

Course Objectives

• To understand several important concepts in linear algebra, including systems of linear equations and their solutions; matrices and their properties; determinants and their properties; vector spaces; linear independence of vectors; subspaces, bases, and dimension of vector spaces; inner product and cross product; linear transformations;
• To apply these concepts to solve basic problems in 3D graphics and game systems such as: movement and rotation of objects, computing collision and intersection of objects, camera matrices, control and operations, interpolation paths, rendering pipeline,etc.

Learning Goals

• Students can solve basic problems involving vectors, transforms and associated operations.
• Students can manipulate points and vectors in 3D space (rotation, translation, scaling, reflection, etc.)
• Students can compute the required transformed for setting up a 3D perspective or orthographic camera.
• Students can solve compute the intersection of lines, planes and simple volumes (spheres, AABB and OBB)
• Students can use different interpolation techniques to approximate curved lines and surfaces.

Graduate students: in addition to the above learning goals, graduate students will also be expected to explain various implementation issues associated with many of the problems listed.

Agenda

This class will be conducted as a mixture of standard lectures and class discussions. Below is a broad outline of the topics to be covered (this list may be modified as needed based on class progression)

• Week 1: Vectors spaces, dot and cross products
• Week 2: Matrices, determinant, and inverse
• Week 3: Affine Transformations and matrix decomposition
• Week 4: Matrix information, coordinate change, orientation representations
• Week 5: General review
• Week 6: Midterm
• Week 7: Camera, view and projections matrices, and general movement
• Week 8: Collision and Intersection Testing Part I
• Week 9: Collision and Intersection Testing, Part II
• Week 10: Interpolation (subject to change)
• Week 11: Final

Grading

The class work will consist regular homework, a midterm exam and a final exam:

• Homework: 30%
• Midterm exam: 35%
• Final exam: 35%

Important notes:

• Homework assignments will generally be due before the beginning of the next lecture through D2L. Late submissions will not be accepted as answers to the previous week's assignment will be discussed and reviewed in class. 
• Exams are taken in person either in class (for students in the live sections) or proctored (for online students). Online student are responsible for making proctoring arrangements.

The final score will be converted to letters based on the following scale: Note: this scale may be adjusted based on overall class performance.

Incompletes

Incompletes will be granted only in the most extreme circumstances and only if the student has already succesfully completed the vast majority of the course work. Students must formally request an incomplete by filling out an Incomplete Grade Request Form.

Academic Integrity and Plagiarism

You are expected to have read and understand DePaul’s policy on Academic Integrity.  It is part of this syllabus; follow it.

Changes to Syllabus

This syllabus is subject to change as necessary to better meet the needs of the students.  Significant changes are unlikely, and will be thoroughly addressed with all students.  Minor changes are possible at any time although you will be informed of all such changes. 

Online Course Evaluations

Evaluations are a way for students to provide valuable feedback regarding their instructor and the course. Detailed feedback will enable the instructor to continuously tailor teaching methods and course content to meet the learning goals of the course and the academic needs of the students. They are a requirement of the course and are key to continue to provide you with the highest quality of teaching. The evaluations are anonymous; the instructor and administration do not track who entered what responses. A program is used to check if the student completed the evaluations, but the evaluation is completely separate from the student’s identity. Since 100% participation is our goal, students are sent periodic reminders over three weeks. Students do not receive reminders once they complete the evaluation. Students complete the evaluation online in CampusConnect.

Academic Policies

All students are required to manage their class schedules each term in accordance with the deadlines for enrolling and withdrawing as indicated in the University Academic Calendar.  Information on enrollment, withdrawal, grading and incompletes can be found at:  cdm.depaul.edu/enrollment.

Students with Disabilities

Students who feel they may need an accommodation based on the impact of a disability should contact the instructor privately to discuss their specific needs. All discussions will remain confidential.
To ensure that you receive the most appropriate accommodation based on your needs, contact the instructor as early as possible in the quarter (preferably within the first week of class), and make sure that you have contacted the Center for Students with Disabilities (CSD) at: csd@depaul.edu.

Lewis Center 1420, 25 East Jackson Blvd.
Phone number: (312)362-8002
Fax: (312)362-6544
TTY: (773)325.7296

Additional Policies

• Class Discussion: Student participation in class discussions will be measured in two ways.  First, students are highly encouraged to ask questions and offer comments relevant to the day’s topic. Secondly, students will be called upon by the instructor to offer comments related to the reading assignments.  Students must keep up with the reading, assignment and project to participate in class discussion.

• Attitude: A professional and academic attitude is expected throughout this course.  Measurable examples of non-academic or unprofessional attitude include but are not limited to: talking to others when the instructor is speaking, mocking another’s opinion, cell phones ringing, emailing, texting or using the internet whether on a phone or computer.  If any issues arise a student may be asked to leave the classroom.  The professor will work with the Dean of Students Office to navigate such student issues.

• Civil Discourse: DePaul University is a community that thrives on open discourse that challenges students, both intellectually and personally, to be Socially Responsible Leaders.  It is the expectation that all dialogue in this course is civil and respectful of the dignity of each student.  Any instances of disrespect or hostility can jeopardize a student’s ability to be successful in the course.  The professor will partner with the Dean of Students Office to assist in managing such issues.