Scalable geometry processing for computer graphics applications

This thesis explores and investigates scalable solutions, grounded on geometry processing and differential geometry concepts, to different computer graphics tasks. My Ph.D. path gave me the opportunity to probe many research topics in the field of computer graphics, as well as delve into mathematical and computational problems. As a summary of my research activity, this thesis echoes my exploration, collecting results from different areas of computer graphics and computational geometry. From novel unified frameworks in spectral geometry to procedural texturing techniques, simulations, and matrix multiplication algorithms, all the discussed topics find their communion in the idea of providing geometry processing solutions made to scale for large volumes of data.