Spring 2018 - MATH 130 D100

Geometry for Computer Graphics (3)

Class Number: 3042

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 3 – Apr 10, 2018: Wed, 1:30–2:20 p.m.
    Surrey

    Jan 3 – Apr 10, 2018: Fri, 12:30–2:20 p.m.
    Surrey

  • Exam Times + Location:

    Apr 21, 2018
    Sat, 12:00–3:00 p.m.
    Surrey

  • Prerequisites:

    Pre-Calculus 12 or Foundations of Mathematics 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C.

Description

CALENDAR DESCRIPTION:

An introductory course in the application of geometry and linear algebra principles to computer graphical representation. Vector and matrix algebra, two and three dimensional transformations, homogeneous coordinates, perspective geometry. Quantitative.

COURSE DETAILS:

The aim of this course is to introduce students to the practical application of mathematical methods to computer graphics representation. While the emphasis is on the mathematical language embedded within computer code, routines and objects rather than on the provision of specific algorithms, every attempt will be made to connect the subject material to applications in disciplines other than mathematics.

Topics:

Trigonometry Review

  • Angles, trig functions, identities, graphs of trig functions, inverse trig functions
  • Tangent Lines and Slope Predictors
Polar Coordinates
  • Plotting points and curves, intersections of curves in polar coordinates, converting polar to rectangular, parametric curves.
Vectors
  • Definition, addition, scalar multiplication, properties, coordinate systems, 3D vectors, left and right orientation, norms and unit vectors, distance, dot product, cross product, projection, determinants, geometric interpretation of dot and cross product.
Lines and common curves
  • Parametric definition of a line (vector, normal, barycentric), uses of various forms, distances, intersections of lines, lines in 3D, planes in 3D, some conic sections (parabola, circle, ellipse, hyperbola) in rectangular and polar coordinates
Matrices
  • Definition, adding, scalar multiplication, multiplication, properties
2D Transformations
  • Definition, standard transformations, combinations of transformations, linking reflections and rotations, transformation of the unit square and the determinant
Homogeneous Coordinates
  • Translations and homogeneous coordinates, rotation about an arbitrary point, reflection in an arbitrary line, the viewing transformation, points at infinity
3D Transformations
  • Extrapolation from 2D transformations, scaling (local, overall shearing), rotations, reflections, combinations, rotations about arbitrary axes, reflections in arbitrary planes
Time Permitting:
Perspective Transformations
  • Orthogonal, axonometric, oblique projections, single, two point and three point perspectives, projectives with rotations
Space curves
  • Slopes of lines and planar curves, practical differentiation, tangents and normals of curves, linear and quadratic interpolation, vector equations of planes.  

Grading

  • Assignments 15%
  • Midterm 1 20%
  • Midterm 2 20%
  • Final Exam 45%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION. 
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. 
Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

REQUIRED READING:

Computer Graphics: Mathematical First Steps
Hall, W.S.
1998; Pearson
ISBN: 9780135995723

Registrar Notes:

SFU’s Academic Integrity web site http://students.sfu.ca/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS