Course detail
Data Visualisation
FSI-SVD Acad. year: 2025/2026 Summer semester
The data that we encounter in practice can be given in different representations, for example, as 3D coordinates, by a function, or by two-dimensional slices. Data visualization is a subject designed to study algorithms and principles of displaying various kinds of these spatial data.
In the first part, students will get acquainted with approximation and interpolation representations of data using mathematical functions. The second and third parts are devoted to imaging algorithms for solid modeling and solid representation of solids. The last part deals with projection, light adjustment, visibility, shadows, texture and the following global imaging methods (e.g. ray tracing) and volumetric rendering.
For algorithms and programming, the Python language or the Matlab environment will be used.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
Department
Entry knowledge
Students are expected to be familiar with basic programming techniques (Python and Matlab) and with basic 2D and 3D graphic algorithms (colour systems, projection, curves and surfaces construction)
Rules for evaluation and completion of the course
Credit is awarded on the basis of the processing and presentation of a semester project.
Missing lessons can be replaced by processing the topic as a homework.
Aims
Students may encounter different kinds of data in their future careers and the need to visualize it correctly. The course covers most of the possible imaging methods applicable to various types of input data. Graduates of this course will have a comprehensive overview and will also get acquainted with the algorithms of selected solutions.
The student will have an overview of various types of 3D data and the possibilities of their representation.
The student will be able to visualize different types of 3D data.
The student will also get acquainted with setting parameters for visualizations such as light, visibility, shadows or texture mapping.
The last lectures deal with neural network usage on image data and point cloud data.
Study aids
Materials are on e-learning.
The study programmes with the given course
Programme N-MAI-P: Mathematical Engineering, Master's, compulsory
Type of course unit
Lecture
13 hours, optionally
Syllabus
The lectures are divided into four thematic blocks related to data visualization.
1. Curves and surfaces in 2D, 3D (B-spline, NURBS, implicit surfaces, subdivision surface)
2. Solid modelling (triangular and boundary representation)
3. Volume representation of solids (voxel, digital topology, isosurface)
4. Data rendering
- basic features of projection, light, visibility, shadows, textures
- global imaging methods – ray tracing
- volumetric rendering
5. Neural network – theoretical background (back-propagation, activation function)
6. Convolutional neural networks – image data
7. Neural networks and point cloud data
Computer-assisted exercise
26 hours, compulsory
Syllabus
The exercises follow the lectures and serve to understand algorithms suitable for various kinds of spatial data representation. Furthermore, selected algorithms are implemented in Python or in the Matlab environment. Each area is devoted to 2-3 weeks of teaching.
1. Curves and areas in 2D, 3D
- Bézier curves and surfaces (algorithm de Casteljau), B-spline, NURBS (algorithm de Boor)
- functions given implicitly and their visualization
- subdivision surfaces
2. Solid modelling (triangular and boundary representation)
3. Solid representation of solids
4. Displaying spatial data
- basic features of projection, light, visibility, shadows, textures
- global imaging methods – ray tracing
- visualization of volume data – volumetric rendering (folding images into the resulting 3D model)
5. Neural network – use on image data and point cloud data
Preparation and consultation of semester work
Participation in the exercises is mandatory.