FI:PV189 Math for Computer Graphics - Course Information

PV189 Mathematics for Computer Graphics

Extent and Intensity

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

Teacher(s)

doc. RNDr. Pavel Matula, Ph.D. (lecturer)
Mgr. Bc. Roman Solař (assistant)

Guaranteed by

doc. RNDr. Pavel 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 A217

Prerequisites

Completion of MB151 and MB152 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

• Image Processing and Analysis (programme FI, N-VIZ)
• 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 and systems biology (programme FI, N-UIZD)
• Bioinformatics (programme FI, B-AP)
• Bioinformatics (programme FI, N-AP)
• Computer Games Development (programme FI, N-VIZ_A)
• Computer Graphics and Visualisation (programme FI, N-VIZ_A)
• Computer Networks and Communications (programme FI, N-PSKB_A)
• Cybersecurity Management (programme FI, N-RSSS_A)
• Formal analysis of computer systems (programme FI, N-TEI)
• Graphic design (programme FI, N-VIZ)
• Graphic Design (programme FI, N-VIZ_A)
• Hardware Systems (programme FI, N-PSKB_A)
• Hardware systems (programme FI, N-PSKB)
• Image Processing and Analysis (programme FI, N-VIZ_A)
• Information security (programme FI, N-PSKB)
• 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)
• Information Security (programme FI, N-PSKB_A)
• Quantum and Other Nonclassical Computational Models (programme FI, N-TEI)
• 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 visualisation (programme FI, N-VIZ)
• 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 Networks and Communications (programme FI, N-PSKB)
• Computer Systems and Data Processing (programme FI, B-IN)
• Computer Systems (programme FI, N-IN)
• Principles of programming languages (programme FI, N-TEI)
• Embedded Systems (eng.) (programme FI, N-IN)
• Programmable Technical Structures (programme FI, B-IN)
• Embedded Systems (programme FI, N-IN)
• Cybersecurity management (programme FI, N-RSSS)
• Services development management (programme FI, N-RSSS)
• Software Systems Development Management (programme FI, N-RSSS)
• Services Development Management (programme FI, N-RSSS_A)
• 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)
• Software Systems Development Management (programme FI, N-RSSS_A)
• Software Systems (programme FI, N-PSKB_A)
• Software systems (programme FI, N-PSKB)
• Machine learning and artificial intelligence (programme FI, N-UIZD)
• Theoretical Informatics (programme FI, N-IN)
• Teacher of Informatics and IT administrator (programme FI, N-UCI)
• Informatics for secondary school teachers (programme FI, N-UCI) (2)
• 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)
• Computer Games Development (programme FI, N-VIZ)
• Processing and analysis of large-scale data (programme FI, N-UIZD)
• Image Processing (programme FI, N-AP)
• Natural language processing (programme FI, N-UIZD)

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 for 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.
• Interactions of basic objects in 3D (lines, planes, spheres).
• Rotation and quaternions.
• Sampling vs. interpolation of digital signal.
• Interpolation of rotation (LERP, SLERP, SQUAD, etc.).
• Minimization (linear and nonlinear regression).
• Geometrical properties of curves and surfaces (length, tangents, curvature, etc.).

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 with possible oral part.

Language of instruction

English

Further Comments

Study Materials
The course is taught annually.

• Enrolment Statistics (Autumn 2020, recent)
  
• Permalink: https://is.muni.cz/course/fi/autumn2020/PV189