- Numerical solution of nonlinear equations and systems of nonlinear equations. Overview and principles of iterative methods, convergence. Direct methods for solving systems of linear equations, Gauss, Jacobi, Gauss-Seidel, relaxation methods. Application of methods in solving imaging and modeling problems.
- Modeling in computer graphics. Types of models, creation and modification, display. Local and global modifications of models, deformation methods FFD.
PA010, PB009, PA157, PA158
- Principles of surface simplification, LOD models, continuous transition between LOD levels.
- Visibility in image space and object space. Sniper techniques. Algorithms, and their applications.
- Parametric curves, Lagrange, Hermite, Bezier, Coons, NURBS. Continuity, change of degree, conditions for smooth connection.
- Parametric surfaces. Surfaces given by an edge, Bezier surfaces, B-spline surfaces, NURBS. Plating, smooth connection. Implicit surfaces.
- Local and global light models, material properties, BRDF. Surface and volume textures. Global lighting calculation, deterministic and stochastic methods, light path tracking.
- Raster image processing. Histogram, histogram equalization. Thresholding, reduction of brightness levels (colors). Linear and nonlinear filters. Edge detection. Discrete Fourier transform in image editing. Geometric image transformations, filtering, resampling, smoothing.
- Reconstruction of objects and visualization of volume data. Reconstruction from cross sections, volume and spatial data. Direct visualization of volumetric data. Marching dice algorithm.
- Approximation of bodies. Convex packaging, construction in 2D and 3D. Packaging bodies, packaging hierarchy, packaging efficiency.
- Warping and morphing of images and objects.
- Triangulation and constrained triangulation. Voronoi diagrams and Delaunay triangulation.
- Data structures for spatial search. Search by ranges, multidimensional binary trees, line trees.
- OpenGL. Basic characteristics, primitives, types of transformations, work with display lists. Memory layers, use in image creation.
- Visualization of data of various dimensions. Principles, methods, tools.
- Interaction techniques used for visualization in different spaces. Principles and concepts.
- Graphs and graph algorithms. Graph representation. Coherence of a graph, chromaticity, planar graphs. Algorithms: searching the graph in width and depth, the shortest distances, skeletons, flows in networks.
- Object-oriented methods of system design. Design patterns. Software architectures. Component systems and models. Object-oriented methods of software development, RUP.
- Software engineering. SW development process. Unified Process Methodology. Agile SW development. Testing phases and types of tests. Software metrics, code refactoring. Software quality. Estimation of costs and time of SW development. Maintenance and reusability.