SUBJECT
Geometric foundations of 3D graphics
lecture + practical
master
3+3
Semesters 1-4
Autumn/Spring semester
Planar representations of three-dimensional objects by methods of descriptive geometry (parallel and perspective projections). Matrix representations of affine transformations in Euclidean space. Homogeneous coordinates in projective space. Matrix representations of collineations of projective space. Coordinate systems and transformations applied in computer graphics. Position and orientation of a rigid body (in a fixed coordinate system). Approximation of parameterized boundary surfaces by triangulated polyhedral surfaces.
Three primary colors, tristimulus coordinates of a light beam. RGB color model. HLS color model. Geometric and photometric concepts of rendering. Radiance of a surface patch. Basic equation of photometry. Phong interpolation for the radiance of a surface patch illuminated by light sources. Digital description of a raster image. Representation of an object with triangulated boundary surfaces, rendering image by the ray tracing method. Phong shading, Gouraud shading.
J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes: Computer Graphics, Principles and Practice. Addison-Wesley, 1990.