3Dwm: Three-Dimensional User Interfaces Using Fast Constructive Solid Geometry

Abstract

Creating 3D objects for use in applications with three-dimensional user interfaces is a non-trivial and time-consuming task, but could be simplified by the ability to combine 3D primitives into complex shapes using constructive solid geometry (CSG). This thesis presents the design and implementation of an algorithm for fast CSG in the context of the 3Dwm user interface platform. During the development of this algorithm, a number of existing algorithms were evaluated, and one based on binary space partitioning (BSP) trees was selected as the basis for this implementation. Here, polyhedra are represented as solids using augmented BSP trees, and regularized Boolean set operations are performed through incremental construction of the resulting BSP trees. A special tree caching mechanism that stores each subtree of a CSG hierarchy has been implemented to minimize tree evaluation when a part of the hierarchy is modified. The algorithm is efficient, elegant, and integrates seamlessly with the rest of the system without breaking the separation between programming interface and implementation, or the network-transparent nature of the system. In addition to this, provisions have been added to 3Dwm to allow for the creation of mathematical 3D primitives such as spheres, cones, and cylinders, that may be used as part of CSG trees.