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Pathfinding for commercial games is a challenging problem, and many existing methods use abstractions which lose details of the environment and compromise path quality. Conversely, humans can ignore irrelevant details of an environment that modern search techniques still consider, while maintaining its topography. This thesis describes a technique for extracting features such as dead ends, corridors, and decision points from an environment represented using a constrained Delaunay triangulation. The result is that the pathfinding task is simplified to the point where the search algorithm need only decide to which side of each obstacle to go, while all features of the environment are retained. We present algorithms which search the triangles of the environment (Triangulation A*) and the decision points identified (Triangulation Reduction A*). We also explore a number of techniques which deal with finding paths for circular objects of nonzero radius and enhancements to various aspects of the search.

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Building reconstruction is one of the most difficult and important 3D modelling problems for urban environment. In this paper, we develop an approach using minimum number of basic geometric elements to reconstruct the buildings. The basic element is a number of unstructured 3D points representing the topological identity of a building roof. Such point primitives can be measured by human or computational operators from images either semi-automatically or automatically. The proposed approach reconstructs the roof surface from connecting points to generate line segments and then grouping the line segments to form faces. The outcome is a set of polygons representing the roof surface, i.e., the building model. The first step determines the roof boundary based on the assumptions of angles. The second step finds the roof ridges with conditions of parallelism. The third step reconstructs the roof surface by Delaunay triangulation. The forth step applies the constrained Delaunay triangulation for boundary and roof ridge to be embedded in the triangles. The last step merges coplanar triangles to form roof faces. The outcome is a set of polygons representing the roof surface. Finally, the building will be reconstructed as a polyhedron object expressed by vertices and displayed for 3D visualization and spatial analysis. 1.

We discuss the design and implementation of CAD tools for creating decorative solids that tile 3-space in a regular, isohedral manner. Starting with the simplest case of extruded 2D tilings, we describe geometric algorithms used for maintaining boundary representations of 3D tiles, including a Java implementation of an interactive constrained Delaunay triangulation library and a mesh-cutting algorithm used in layering extruded tiles to create more intricate designs. Finally, we demonstrate a CAD tool for creating 3D tilings that are derived from cubic lattices. The design process for these 3D tiles is more constrained, and hence more difficult, than in the 2D case, and it raises additional user interface issues.

This paper describes a new approach in modeling of sand surface. The terrain model is based on a triangulated irregular network while existing solutions have been based on a regular grid. Memory consumption is significantly reduced without a regular grid at the expense of more complicated algorithms. Our solution allows deforming terrain by a set of virtual tools and erosion simulation. All these simulations run in real time. We want to use haptic devices with our application in the future.