Graduate Program in Systems and Control Engineering.Şahiner, Ali Vahit.Diktaş, Engin Deniz.2023-03-162023-03-162006.SCO 2006 D55https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15627This thesis presents a framework based on spatial subdivision of triangular mesh objects with octrees for virtual reality and haptic applications. For efficient generation of octree representations a method based on Minkowski sums is developed. The calculation of Minkowski sums is achieved geometrically by direct manipulation of planes in 3D-space. For the evaluation of proximity queries a new data structure called the proximity octree is introduced. A technique for tracking of geometric features of convex objects that are in close proximity to a specific point of interest is developed and tested for a number of applications including haptic interaction.30cm.Virtual reality.Minkowski geometry.xiii, 66 leaves;