Lectures:
Ray tracing. Reducing time complexity of the method. Special effects in ray tracing.
Radiosity method. Determining form factors.
Theoretical foundations of solid modelling:
Topological spaces, topological mappings. n-manifold in Em. Orientability. Euler formula and its application. Regularised boolean operations.
Boundary model of solid and its implementation. Euler operators. Rendering objects represented by a boundary model. Realisation of boolean operations.
CSG model and its implementation. Rendering objects represented by a CSG model.
Another methods of modelling solids: Space enumeration, octant trees, BSP trees. Deformable models.
Uniform and non-uniform, rational and non-rational B-spline curves and surfaces.
Theoretical foundations of the finite element method:
Hilbert's spaces, operators, functionals and their properties. Energetical spaces.
Ritz's method.
Deriving the eqations of FEM for one-dimensional problem.
Deriving the eqations of FEM for more-dimensional problem. Examples of the problems that can be solved by making use of FEM.
Hardware support of 3D rendering pipeline in Silicon Graphics workstations.
Computer labs:
The students are required to work out a program that falls (according to students' choice) into one of the following areas: ray tracing, radiosity method, modelling the curves and surfaces, namely NURBS. Furthermore, tiny tasks falling into boundary representation of solids, Euler's operators, Ritz's method are assigned.
Ray tracing. Reducing time complexity of the method. Special effects in ray tracing.
Radiosity method. Determining form factors.
Theoretical foundations of solid modelling:
Topological spaces, topological mappings. n-manifold in Em. Orientability. Euler formula and its application. Regularised boolean operations.
Boundary model of solid and its implementation. Euler operators. Rendering objects represented by a boundary model. Realisation of boolean operations.
CSG model and its implementation. Rendering objects represented by a CSG model.
Another methods of modelling solids: Space enumeration, octant trees, BSP trees. Deformable models.
Uniform and non-uniform, rational and non-rational B-spline curves and surfaces.
Theoretical foundations of the finite element method:
Hilbert's spaces, operators, functionals and their properties. Energetical spaces.
Ritz's method.
Deriving the eqations of FEM for one-dimensional problem.
Deriving the eqations of FEM for more-dimensional problem. Examples of the problems that can be solved by making use of FEM.
Hardware support of 3D rendering pipeline in Silicon Graphics workstations.
Computer labs:
The students are required to work out a program that falls (according to students' choice) into one of the following areas: ray tracing, radiosity method, modelling the curves and surfaces, namely NURBS. Furthermore, tiny tasks falling into boundary representation of solids, Euler's operators, Ritz's method are assigned.