Reconstruction approximating method by biquadratic splines of offset surfaces holes

Standard Offset surfaces are defined as locus of the points which are at constant distance along the unit normal direction from the generator surfaces. Offset are widely used in various practical applications, such as tolerance analysis, geometric optics and robot path-planning. In some of the engineering applications, we need to extend the concept of standard offset to the generalized offset where distance offset is not necessarily constant and offset direction are not necessarily along the normal direction. Normally, a generalized offset is functionally more complex than its progenitor because of the square root appears in the expression of the unit normal vector. For this, an approximation method of its construction is necessary. In many situation it is necessary to fill or reconstruct certain function defined in a domain in which there is a lack of information inside one or several sub-domains (holes). In some practical cases, we may have some specific geometrical constrains, of industrial or design type, for example, the case of a specified volume inside each one of these holes. The problem of filling holes or completing a 3D surface arises in all sorts of computational graphics areas, like CAGD, CAD-CAM, Earth Sciences, computer vision in robotics, image reconstruction from satellite and radar information, etc. In this work we present an approximation method of filling holes of the generalized offset of a surface when there is a lack information in a sub-domain of the function that define it. We prove the existence and uniqueness of solution of this problem, we show how to compute it and we establish a convergence result of this approximation method. Finally, we give some graphical and numerical examples.

Virtual Fixture Augmentation of Operator Selection of Non-Contact Material Reduction Task Paths

Decommissioning of nuclear systems and consolidation of resulting waste remains a major hurdle for the industry. The radioactive nature of nuclear waste makes manual handling unfeasible, while teleoperation and inflexible automation also have drawbacks. This effort utilizes virtual fixtures to augment path creation for non-contact material reduction tasks. It builds on previous Nuclear and Applied Robotics Group work with Variable Normal Surface Virtual Fixtures, which generate surfaces offset from task surfaces. Offset surfaces can then provide poses at a set orientation to task surfaces. Once the Variable Normal Surface Virtual Fixture is generated from task information, operators build a list of desired path poses. The Robot Operating System Descartes package takes the pose list and plans a smooth trajectory for task execution. Planar and cylindrical demonstrations based on experimental studies at the United Kingdom’s Sellafield site were performed. This methodology augments waste reduction by allowing flexible laser cutting routes.

Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces

In this study, we give the dual characterizations of Mannheim offsets of ruled surfaces in terms of their integral invariants and obtain a new characterization of the Mannheim offsets of developable surface, i.e., we show that the striction lines of developable Mannheim offset surfaces are Mannheim partner curves. Furthermore, we obtain the relationships between the area of projections of spherical images for Mannheim offsets of ruled surfaces and their integral invariants.