PV189 Mathematics for Computer Graphics

Faculty of Informatics
Autumn 2022
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)
Providers of Specific teaching support
Zbyněk Cincibus (přepisovatel)
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
Thu 16:00–17:50 A318
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
there are 69 fields of study the course is directly associated with, display
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.
The course is also listed under the following terms Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2022/PV189