Code: 2-MPG-101/00

Continuous assessment: Project work in exercises

Final assessment: Written and oral examination

Learning outcomes: Students will acquire knowledge of algorithmic solutions to fundamental problems in computer graphics.

Course syllabus:

1. Introductory information
2. 2D and 3D transformations
3. 3D rotation and quaternions
4. Representations of 3D objects
5. Determining the visible surface
6. Projections (central and parallel projection)
7. Intersection calculation
8. Clipping
9. Rasterisation and area filling
10. Antialiasing
11. Display pipeline

Exercises are led by Mgr. Marcel Makovník. Further information can be found on the exercise website.

Literature:

Ružický E., Ferko A.: Computer Graphics and Image Processing, Bratislava: Sapientia, 1995
Žára J., Beneš B., Felkel P.: Modern Computer Graphics, Computer Press, 1998
Watt A.: 3D Computer Graphics (3rd edition), Addison Wesley, 1999
Schneider P., Eberly D.: Geometric Tools for Computer Graphics, Morgan Kaufmann, 2003
Hearn D., Baker M, Carithers, W.: Computer Graphics with Open GL (4th Edition), Pearson, 2010
Sederberg T.: Computer Aided Geometric Design, Brigham Young University, 2012
Angel E., Shreiner D.: Interactive Computer Graphics: A Top-Down Approach with WebGL (8th Edition), Pearson, 2020

Supplementary materials for lectures:

• Example of rotation using quaternions, Notes on Quaternions, Quaternions and Rotations, Gimbal lock
• Function-based shape modelling
• Computer Aided Geometric Design - see chapter 3. Polynomial Evaluation and Basis Conversion (pp. 41-44) and 7. Planar Curve Intersection (pp. 83-94)

Additional recommended study literature:

Study material and notes by Dr J. Chalmovianská (pdf + txt):

1. Affine transformations
2. Modelling and representation of 3D objects
3. Determining visible surface
4. Projections (projection) (txt)
5. Intersection calculation
6. Clipping
7. Rasterisation (txt)
8. Antialiasing (txt), antialiasing (scan)
9. Display pipeline

Notes by Assoc. Prof. V. Zaťko (pdf):

1. Essential geometry
2. Overview of geometric object representations
3. Display pipeline
4. Rasterisation
5. Filling
6. Line clipping
7. Visibility

• Exercises for practice

Interesting videos:

• Visualising quaternions - a series of short and engaging videos graphically illustrating the use of quaternions for 3D rotation and stereographic projection
• Gimbal lock - explanation of the Gimbal lock phenomenon (restriction of degrees of freedom) during rotation of objects using Euler angles

Useful websites:

• Computer Graphics - teaching website by Mgr. Kristína Vojtová
• Introduction to Computing - notes for a course on modelling objects with splines and polygonal meshes
• Hyperfun - website dedicated to modelling objects using implicit functions - FRep
• Shadertoy - get inspired and create or share your best shaders
• ImplicitCAD, OpenSCAD - model objects using implicit functions

Source codes of selected algorithms (.py):

• Determining visibility using the horizon envelope method
• Calculation of intersections of a polynomial curve with the x-axis - Bezier clipping