Abstract Carl M. Erikson Hierarchical Levels of Detail to Accelerate the Rendering of Large Static and Dynamic Polygonal Environments (Under the direction of Dinesh Manocha) Interactive visualization of large three-dimensional polygonal datasets is an important topic in the field of computer graphics and scientific visualization. These datasets can be static, such as walkthrough applications, or dynamic, such as CAD scenarios where a designer moves, adds, or deletes parts. In many cases, the number of primitives in these models overwhelms the rendering performance of current graphics systems. One method for accelerating the rendering of these environments is polygonal simplification. This dissertation describes the creation and application of levels of detail, or LODs, and hierarchical levels of detail, or HLODs, to accelerate the rendering of large static and dynamic polygonal environments. The principal idea of this work is that simplification methods should not always treat objects, or collections of polygons, in a scene independently. Instead, they may be able to produce higher quality and drastic approximations by simplifying disjoint regions of a scene together. This idea is applicable to the creation of LODs for individual objects that consist of unconnected polygons, and for the construction of HLODs, or approximations representing groups of static or dynamic objects. We present a polygonal simplification algorithm called General and Automatic Polygonal Simplification, or GAPS, that excels at merging disjoint polygons through the use of an adaptive distance threshold and surface area preservation. We use GAPS to create LODs and HLODs for nodes in the scene graphs of large polygonal environments. These approximations enable two rendering modes, one that allows the user to specify a desired image quality and another that targets a frame-rate. When objects in the scene move, our algorithm updates HLODs that have become inaccurate or invalid using asynchronous simplification processes. Our algorithm currently handles scenes with limited rigid-body dynamic movement. We demonstrate its performance on several large CAD environments including a 13 million polygon power plant model. Our approach has achieved nearly an order of magnitude improvement in average rendering speed with little or no loss in image quality for several viewing paths of complex environments.