Multiresolution analysis as an approach for tool path planning in NC machining

Wavelets permit multiresolution analysis of curves and surfaces. A complex curve can be decomposed using wavelet theory into lower resolution curves. The low-resolution (coarse) curves are similar to rough-cuts and high-resolution (fine) curves to finish-cuts in numerical controlled (NC) machining.;In this project, we investigate the applicability of multiresolution analysis using B-spline wavelets to NC machining of contoured 2D objects. High-resolution curves are used close to the object boundary similar to conventional offsetting, while lower resolution curves, straight lines and circular arcs are used farther away from the object boundary.;Experimental results indicate that wavelet-based multiresolution tool path planning improves machining efficiency. Tool path length is reduced, sharp corners are smoothed out thereby reducing uncut areas and larger tools can be selected for rough-cuts

Finding Optimal-Path Maps for Path Planning Across Weighted Regions

This paper appeared in the International Journal of Robotics Research, 19, 2 (February 2000), pp. 83-95, with elaborating additions from [Rowe and Alexander, 1997]. The equations were redone for greatly improved clarity in 2008.Optimal-path maps tell robots or people the best way to reach a goal point from anywhere in a known terrain area, eliminating most of the need to plan during travel. We address the construction of optimal-path maps for twodimensional polygonal weighted-region terrain, terrain partitioned into polygonal areas such that the cost per unit distance traveled is homogeneous and isotropic within each polygon. This is useful for overland route planning across varied ground surfaces and vegetation. We propose a new algorithm that recursively partitions terrain into regions of similar optimal-path behavior, and defines corresponding "path subspaces" for these regions. This process constructs a piecewise-smooth function of terrain position whose gradient direction is everywhere the optimal-path direction, permitting quick finding of optimal paths. Our algorithm is more complicated than the current path-caching and wavefront-propagation algorithms, but gives more accurate maps requiring less space to represent. Experiments with an implementation confirm the practicality of our algorithm.This work was supported in part by the U.S. Army Combat Developments Experimentation Center under MIPR ATEC 88-86. This work was also prepared in part in conjunction with research conducted for the Naval Air Systems Command and funded by the Naval Postgraduate School.supported in part by the U.S. Army Combat Developments Experimentation Center under MIPR ATEC 88-86. This work was also prepared in part in conjunction with research conducted for the Naval Air Systems Command and funded by the Naval Postgraduate School.Approved for public release; distribution is unlimited

Quad Meshing

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing

Geophysical imaging using trans-dimensional trees.

In geophysical inversion, inferences of Earth's properties from sparse data involve a trade-off between model complexity and the spatial resolving power. A recent Markov chain Monte Carlo (McMC) technique formalized by Green, the so-called trans-dimensional samplers, allows us to sample between these trade-offs and to parsimoniously arbitrate between the varying complexity of candidate models. Here we present a novel framework using trans-dimensional sampling over tree structures. This new class of McMC sampler can be applied to 1-D, 2-D and 3-D Cartesian and spherical geometries. In addition, the basis functions used by the algorithm are flexible and can include more advanced parametrizations such as wavelets, both in Cartesian and Spherical geometries, to permit Bayesian multiscale analysis. This new framework offers greater flexibility, performance and efficiency for geophysical imaging problems than previous sampling algorithms. Thereby increasing the range of applications and in particular allowing extension to trans-dimensional imaging in 3-D. Examples are presented of its application to 2-D seismic and 3-D teleseismic tomography including estimation of uncertainty

Spatial relationship based scene analysis and synthesis

In this thesis, we propose a new representation, which we name Interaction Bisector Surface (IBS), that can describe the general nature of spatial relationship. We show that the IBS can be applied in 3D scene analysis, retrieval and synthesis. Despite the fact that the spatial relationship between different objects plays a significant role in describing the context, few works have focused on elaborating a representation that can describe arbitrary interactions between different objects. Previous methods simply concatenate the individual state vectors to produce a joint space, or only use simple representations such as relative vectors or contacts to describe the context. Such representations do not contain detailed information of spatial relationships. They cannot describe complex interactions such as hooking and enclosure. The IBS is a data structure with rich information about the interaction. It provides the topological, geometric and correspondence features that can be used to classify and recognize interactions. The topological features are at the most abstract level and it can be used to recognize spatial relationships such as enclosure, hooking and surrounding. The geometric features encode the fine details of interactions. The correspondence feature describes which parts of the scene elements contribute to the interaction and is especially useful for recognizing character-object interactions. We show examples of successful classification and retrieval of different types of data including indoor static scenes and dynamic scenes which contain character-object interactions. We also conduct an exhaustive comparison which shows that our method outperforms existing approaches. We also propose a novel approach to automatically synthesizing new interactions from example scenes and new objects. Given an example scene composed of two objects, the open space between the objects is abstracted by the IBS. Then, an translation, rotation and scale equivariant feature called shape coverage feature, which encodes how the point in the open space is surrounded by the environment, is computed near the IBS and around the open space of the new objects. Finally, a novel scene is synthesized by conducting a partial matching of the open space around the new objects with the IBS. Using our approach, new scenes can be automatically synthesized from example scenes and new objects without relying on label information, which is especially useful when the data of scenes and objects come from multiple sources