The talk is devoted to different applications of physically accurate simulation of light propagation. Initially efforts were concentrated on visualization of exterior and interior architecture design. The ray tracing technology based on the Monte Carlo approach was elaborated which provided accurate calculations of lighting in real scenes and rendering of images of photorealistic quality. The technology proved to be highly efficient that allowed applying it to simulation of luminaries, car headlights and optical light guiding systems like PLED. The systems of this kind have complicated internal structure including surfaces with complex microrelief where light undergoes billions of interreflections. Practical usability of optical simulation in such applications requires very high accuracy of results. Further elaboration is related with simulation and visualization of materials with complex optical properties like multilayer paint coatings with complex internal microstructure, volume scattering. Newest challenging areas of research which reflect expectations of industry accommodate simulation of light propagation in a media with high concentration of particles (e.g. ink).

Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the final construction. Modern geometric computing provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This opens up new horizons for architecture. On the other hand, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire research area, currently emerging at the border between applied geometry and architecture.

The speaker will report on recent progress in this field, putting special emphasis on the design of architectural freeform structures. Important practical requirements on such structures such as planarity of panels, complexity of nodes in the underlying supporting structure or properties of multilayer-constructions can be elegantly treated within the framework of discrete differential geometry. In fact such architectural applications have also led to advances in mathematical research. The computation of discrete architectural freeform structures is a challenging topic since the underlying mesh geometry needs to be optimized to a much higher aesthetic and functional level than meshes used for typical Computer Graphics applications.