Computer Science 557

Fall Semester 2011

Section 1: B114 JFSB on T Th at 09:30 am - 10:45 am

Instructor Information

Instructor: Dr. Thomas W. SederbergOffice: N-181 ESCOffice Hours: Office Phone: 801-422-6330Email: tom@byu.eduMobile Phone Number: 801-592-0263


Course Schedule

Date ExportTopics ExportReading ExportAssignments Due Export

T - Aug 30

Overview, Bezier curves, Postscript

Chapter 2


Th - Sep 1

Bezier Curves, CPLOT

Chapter 2

CPLOT Source Code

Description of CPLOT

HW 0 HW 1

T - Sep 6

Bezier Curves, Offsets

Chapter 2

HW 2

Th - Sep 8

Background mathematics

Chapter 1

HW 3

T - Sep 13

Basis Change

Chapter 3

HW 4

Th - Sep 15

Forward Differencing

Chapter 4

Offset Curves

HW 5 Project 1

T - Sep 20

Blending Functions, B-Splines

Chapter 5

HW 6


Th - Sep 22


Chapter 6

HW 7

T - Sep 27


Chapter 6

HW 8

Th - Sep 29

B-spline Basis Functions

Chapter 6

HW 9 Project 2

proj2a.dat proj2b.dat

T - Oct 4

Bernstein root finding Chapter 9

HW 10

Th - Oct 6

Project 3

Chapter 9

HW 11

T - Oct 11

Review for Exam

Review List


Th - Oct 13

Exam: Oct 13-15 in Testing Center

Review List


T - Oct 18

Interval Arithmetic

Chapter 12.1


Th - Oct 20

Interval Arithmetic

Chapter 12.1

Project 3 proj3.dat

T - Oct 25

Algebraic methods

Chapter 16

HW 12

Th - Oct 27

Algebraic methods

Chapter 16

HW 13

T - Nov 1

Algebraic Methods

Chapter 16

HW 14

Th - Nov 3

Free Form Deformation

Chapter 14

HW 15

T - Nov 8

Curve Intersection

Chapter 7

Project 4 proj4.dat

HW 16

Th - Nov 10

Tensor Product Surfaces

Chapter 15

HW 17

T - Nov 15

Tensor Product Surfaces

Chapter 15

HW 18

Th - Nov 17


Chapter 10

HW 19

T - Nov 22

No Class


Project 5 proj5.dat

Th - Nov 24

Thanksgiving BreakNo class-

T - Nov 29


Chapter 10.6

HW 20

Th - Dec 1


Chapter 15

HW 21

T - Dec 6

Subdivision Surfaces


Project 6 proj6.dat

HW 22

Th - Dec 8



HW 23

T - Dec 13

Final Exam

7:00a - 10:00a, B114 JFSB


Devotionals and Forums


T - Sep 6

President and Sister SamuelsonDevotional

T - Sep 13

Elder Neil L. AndersenDevotional

T - Sep 20

Gregg EasterbrookForum

T - Sep 27

Mona HopkinsDevotionalPsychology

T - Oct 18

Greg BurtonDevotionalChemistry/Bio Chemistry

T - Oct 25

Senator Joseph LiebermanForum

T - Nov 1


T - Nov 8

Bill EggingtonDevotionalLinguistics and English Language

T - Nov 15

Damon BahrDevotionalTeacher Education

T - Nov 29

James McPhersonForum

T - Dec 6

Elder Tad R. Callister Devotional

Course Information

Texts & Materials

Required Vendor Price (new) Price (used)
Computer Aided Geometric DesignBy Thomas W. Sederberg Self published (2011)


This course covers the basic principles of curve and surface theory for geometric modeling, particularly the mathematics and algorithms. These concepts are central to several fields such as computer graphics, computer aided design, and animation.


Proficiency in computer programming (C or  C++).

Proficiency in calculus and linear algebra, and sufficient maturity to enjoy new mathematical concepts.

Grading Policies

The final score will be based 15% on homework, 35% on programming projects, 20% on the midterm exam, and 30% on the final exam.


Homework and projects are due at the beginning of class on the due date, unless otherwise noted. Late homework will not be accepted.

Late projects will be penalized 5% for each day late, up to a maximum penalty of 50%.

Learning Outcomes

  • Bezier Curves

    Understand the theory, properties, and algorithms for Bezier curves: de Casteljau algorithm, degree elevation, hodographs, curve intersection algorithms, convex hull property, variationa diminishing property, rational Bezier curves, explicit Bezier curves.

  • B-Spline Curves

    Understand polar form, the de Boor algorithm, the Boehm algorithm, knot intervals.

  • Tensor product surfaces

    Understand tensor product Bezier and B-Spline surfaces, including the de Casteljau algorithm, partial derivatives, parametric continuity, tesselation.

  • Computational Practice

    A student who completes this course will be able to implement algorithms for Bezier or B-Spline curves and surfaces.

University Policies

BYU Honor Code

In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. Adherence demonstrates respect for yourself and others and ensures an effective learning and working environment. It is the university's expectation, and my own expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office at 422-2847 if you have questions about those standards.

Preventing Sexual Discrimination and Harassment

Title IX of the Education Amendments of 1972 prohibits sex discrimination against any participant in an educational program or activity that receives federal funds. The act is intended to eliminate sex discrimination in education. Title IX covers discrimination in programs, admissions, activities, and student-to-student sexual harassment. BYU's policy against sexual harassment extends not only to employees of the university, but to students as well. If you encounter unlawful sexual harassment or gender-based discrimination, please talk to your professor; contact the Equal Employment Office at 422-5895 or 367-5689 (24-hours); or contact the Honor Code Office at 422-2847.

Students with Disabilities

Brigham Young University is committed to providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. If you have any disability which may impair your ability to complete this course successfully, please contact the Services for Students with Disabilities Office (422-2767). Reasonable academic accommodations are reviewed for all students who have qualified, documented disabilities. Services are coordinated with the student and instructor by the SSD Office. If you need assistance or if you feel you have been unlawfully discriminated against on the basis of disability, you may seek resolution through established grievance policy and procedures by contacting the Equal Employment Office at 422-5895, D-285 ASB.

Academic Honesty Policy

The first injunction of the BYU Honor Code is the call to be honest. Students come to the university not only to improve their minds, gain knowledge, and develop skills that will assist them in their life's work, but also to build character. President David O. McKay taught that 'character is the highest aim of education' (The Aims of a BYU Education, p. 6). It is the purpose of the BYU Academic Honesty Policy to assist in fulfilling that aim. BYU students should seek to be totally honest in their dealings with others. They should complete their own work and be evaluated based upon that work. They should avoid academic dishonesty and misconduct in all its forms, including but not limited to plagiarism, fabrication or falsification, cheating, and other academic misconduct.

Plagiarism Policy

Writing submitted for credit at BYU must consist of the student's own ideas presented in sentences and paragraphs of his or her own construction. The work of other writers or speakers may be included when appropriate (as in a research paper or book review), but such material must support the student's own work (not substitute for it) and must be clearly identified by appropriate introduction and punctuation and by footnoting or other standard referencing.

Respectful Environment Policy

"Sadly, from time to time, we do hear reports of those who are at best insensitive and at worst insulting in their comments to and about others... We hear derogatory and sometimes even defamatory comments about those with different political, athletic, or ethnic views or experiences. Such behavior is completely out of place at BYU, and I enlist the aid of all to monitor carefully and, if necessary, correct any such that might occur here, however inadvertent or unintentional."
"I worry particularly about demeaning comments made about the career or major choices of women or men either directly or about members of the BYU community generally. We must remember that personal agency is a fundamental principle and that none of us has the right or option to criticize the lawful choices of another." President Cecil O. Samuelson, Annual University Conference, August 24, 2010

"Occasionally, we ... hear reports that our female faculty feel disrespected, especially by students, for choosing to work at BYU, even though each one has been approved by the BYU Board of Trustees. Brothers and sisters, these things ought not to be. Not here. Not at a university that shares a constitution with the School of the Prophets." Vice President John S. Tanner, Annual University Conference, August 24, 2010

Devotional and Forum Attendance Policy

Brigham Young University's devotional and forum assemblies are an important part of your BYU experience. As Elder Dallin H. Oaks stated, 'You neglect your education and fail to use a unique resource of this university if you miss a single one' (from the address 'Challenges for the Year Ahead', 6 September, 1973). Your attendance at each forum and devotional is strongly encouraged.