FI:PV189 Math for Computer Graphics - Course Information

PV189 Mathematics for Computer Graphics

Extent and Intensity

2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Pavel Matula, Ph.D. (lecturer)
Dmitry Sorokin, Ph.D. (assistant)

Guaranteed by

doc. RNDr. Petr Matula, Ph.D.
Department of Visual Computing – Faculty of Informatics
Supplier department: Department of Visual Computing – Faculty of Informatics

Timetable

Fri 8:00–9:50 C511

Prerequisites

Completion of MB101 and MB102 is the precondition.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Applied Informatics (programme FI, B-AP)
• Applied Informatics (programme FI, N-AP)
• Information Technology Security (eng.) (programme FI, N-IN)
• Information Technology Security (programme FI, N-IN)
• Bioinformatics (programme FI, B-AP)
• Bioinformatics (programme FI, N-AP)
• Information Systems (programme FI, N-IN)
• Informatics with another discipline (programme FI, B-EB)
• Informatics with another discipline (programme FI, B-FY)
• Informatics with another discipline (programme FI, B-GE)
• Informatics with another discipline (programme FI, B-GK)
• Informatics with another discipline (programme FI, B-CH)
• Informatics with another discipline (programme FI, B-IO)
• Informatics with another discipline (programme FI, B-MA)
• Informatics with another discipline (programme FI, B-TV)
• Mathematical Informatics (programme FI, B-IN)
• Parallel and Distributed Systems (programme FI, B-IN)
• Parallel and Distributed Systems (programme FI, N-IN)
• Computer Graphics and Image Processing (programme FI, B-IN)
• Computer Graphics (programme FI, N-IN)
• Computer Networks and Communication (programme FI, B-IN)
• Computer Networks and Communication (programme FI, N-IN)
• Computer Systems and Data Processing (programme FI, B-IN)
• Computer Systems (programme FI, N-IN)
• Embedded Systems (eng.) (programme FI, N-IN)
• Programmable Technical Structures (programme FI, B-IN)
• Embedded Systems (programme FI, N-IN)
• Service Science, Management and Engineering (eng.) (programme FI, N-AP)
• Service Science, Management and Engineering (programme FI, N-AP)
• Social Informatics (programme FI, B-AP)
• Theoretical Informatics (programme FI, N-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, N-SS) (2)
• Artificial Intelligence and Natural Language Processing (programme FI, B-IN)
• Artificial Intelligence and Natural Language Processing (programme FI, N-IN)
• Image Processing (programme FI, N-AP)

Course objectives

This lecture aims to enhance the mathematical foundations acquired through the previous studies. We focus on practical utilization of mathematics in the computer graphics area. The students gain an insight into the practical mathematics necessary to implementation of many computer graphics algorithms.

Learning outcomes

After finishing the course the student will be able to: understand the common mathematics being used for solving computer graphics tasks; solve the typical tasks

Syllabus

• Revision of linear algebra. Vectors, matrices, linear transformations.
• Afinne geometry, homogeneous coordinates.
• Eigen values, eigen vectors and their geometric meaning.
• Principal component analysis.
• Conics.
• Interactions of basic objects in 3D (lines, planes, spheres).
• Rotation and quaternions.
• Sampling vs. interpolation of digital signal.
• Interpolation of rotation.
• Minimization (linear and nonlinear regression).
• Geometric and topological properties of curves and surfaces.

Literature

• GLASSNER, Andrew S. Principles of digital image synthesis. Volume 1. San Francisco: Morgan Kaufmann Publishers, 1995, xx, 540 s. ISBN 1-55860-276-31. info

Teaching methods

Lectures. Electronic revision during semester.

Assessment methods

Written examination.

Language of instruction

Czech

Further Comments

Study Materials
The course is taught annually.

• Enrolment Statistics (Autumn 2017, recent)
  
• Permalink: https://is.muni.cz/course/fi/autumn2017/PV189