IAT 261 - Spatial Computing

Download PDF: IAT261-Spring2005.pdf
Credit Hours: 3
Instructors: Daniela Marinescu, Robert Woodbury
Location: SFU Surrey, Room 535
Semester: Spring 2005

Course Description:

An exploration of the major concepts of analytical and computational geometry and an introduction to tools for programming geometric information and displaying the results. Students completing this course will have a basic understanding of how computer graphics systems work; skills in writing programs to display geometric information for graphics display; ability to solve geometric problems using transformations, geometric representations and the basic algorithms of computational geometry; and familiarity with various common mathematical notation for representing spatial objects.

This course is divided into three parts.

1. In Vectors, Points, Lines, Planes and Frames, students learn how to represent simple objects and how to compute properties of these objects using operators such as the dot product, cross product, line operator and plane operator. They learn how to relate objects described in different coordinate systems, through rotation, scaling, shearing and translation transformations.
2. In Curves students learn the systolic array and deCasteljau algorithm as a fundamental representation for curves. This part of the course limits itself to what can be demonstrated directly from the systolic array and from vectors relating to it, including subdivision, degree elevation, hodographs and informal Cn and G n continuity. The systolic array is generalized to a blossom form to demonstrate the B-Spline representation. A sketch of the extension to surfaces is made.
3. In Spatial Sorting students learn algorithms to order objects in space. Algorithms for the convex hull, proximity and maximal line representation are developed.
   

Delivery Method:

Lectures and tutorials

Learning Activities + Evaluation:

Activities consist of class-based discussion, tutorial sessions, weekly problem sets (20%), programming assignments (50%) and an examination (30%).


Texts, Resources + Materials:

Parts of standard texts, such as:
David F. Rogers and J. Alan Adams. (1990) Mathematical Elements for Computer Graphics. Second Edition. McGraw-Hill, New York.
Alyn Rockwood and Peter Chambers, Interactive Curves and Surfaces: A Multimedia Tutorial on CAGD, Morgan-Kaufmann, 1996.
Material from the present online courses ITEC 271, 272 and 273 will be modified for this course.
The following two documents will be refined as course notes:
Daniela Marinescu and Robert Woodbury. (2003). Representing Curves and Surfaces. Simon Fraser University.
Robert Woodbury. (2003). Mathematical Structures for Computing Space. Simon Fraser University.

Prerequisites:

CMPT 125, MATH 232




Last Updated: February 6, 2008

These course outlines are drafts and are subject to change.