Studies On Modeling Techniques Of Swept Volumes

Swept volume has important and wide applications in many areas such as geometry and solid modeling, NC machining simulation and verification, robot workspace analysis and collision detection, where the volume generated by sweeping a geometric entity in space along a trajectory is called the swept volume. The modeling of swept volumes has been studied for four decades of years and there are many precious research achievements. Although the demands for swept volumes get much wider and deeper in many disciplines, the modeling of swept volumes remains to be a challenging problem in terms of simplicity, efficiency and accuracy.Based on the intensive survey and comprehensive analyses of various approaches to the modeling of swept volumes, several algorithms have been designed, implemented and verified to explore the possibility of speeding up the modeling process of swept volumes, generalizing and simplifying the corresponding techniques. Here are these algorithms:A novel modeling algorithm of the swept volume solid of revolved solids is proposed in this thesis. This algorithm consists of the following main steps: First discretization of the trajectory curve and establishments of reference frames; Second extraction and approximation of envelop profiles at each discretized position based on the velocity vector calculated; Third generation of envelop surfaces from the extracted envelop profile curves, and attachment of the ingress and egress surfaces to the envelop surface to form the swept volume solid.A novel algorithm in this paper is presented to fast model a swept volume of a geometric entity which can be either a solid or a polyhedron. This method mainly consists of four stages: firstly analyzing the different types of generators and the swept trajectory; secondly making a superset of primitive curves; thirdly computing a boundary arrangement of the primitives curves, including creating planar slices, intersecting those slices with all primitive curves to obtain special planar meshes, and identifying the outermost boundary contours of the planar meshes; fourthly constructing a non-self-intersecting and manifold boundary of the swept volume through all the planar contours.The self-intersection problem has been solved in different ways in our modeling algorithms of swept volumes. As a complement for the swept volume solid modeling algorithm of revolved solids, the method of trimming self-intersection regions consists of two major steps: firstly roughly detecting self-intersection regions by checking intersections or overlapping of the envelop profiles; secondly splitting the whole envelop surfaces of the swept volume solid into separate non-self-intersecting segments to trim global self-intersections, and to trim local self-intersections, dividing local self-intersecting regions into patches and replacing self-intersecting patches with non-self-intersecting ones. The solutions, to the self-intersection problems in the fast swept-volume-modeling algorithm of a geometric entity, are based on the modeling principle that is the swept envelop is constructed layer by layer, and such solutions vary with the type of the generators.A fast method based on sweeping tracing primitives for collision detection is proposed. In this method, anchor points are sought out from the seed outer boundary vertices, which are further used to create sweeping primitive curves. Then the collision time and area could be detected fast by checking the intersections between the sweeping primitive curves and the environments.