On-axis triplications in elastic orthorhombic media

SUMMARY Triplicated traveltime curve has three arrivals at a given distance with the bowtie shape in the traveltime-offset curve. The existence of the triplication can cause a lot of problems such as several arrivals for the same wave type, anomalous amplitudes near caustics, anomalous behaviour of rays near caustics, which leads to the structure imaging deviation and redundant signal in the inversion of the model parameters. Hence, triplication prediction becomes necessary when the medium is known. The research of the triplication in transversely isotropic medium with a vertical symmetry axis (VTI) has been well investigated and it has become clear that, apart from the point singularity case, the triplicated traveltime only occurs for S wave. On contrary to the VTI case, the triplication behaviour in the orthorhombic (ORT) medium has not been well focused due to the model complexity. In this paper, we derive the second-order coefficients of the slowness surface for two S waves in the vicinity of three symmetry axes and define the elliptic form function to examine the existence of the on-axis triplication in ORT model. The existence of the on-axis triplication is found by the sign of the defined curvature coefficients. Three ORT models are defined in the numerical examples to analyse the behaviour of the on-axis triplication. The plots of the group velocity surface in the vicinity of three symmetry axes are shown for different ORT models where different shapes: convex or the saddle-shaped (concave along one direction and convex along with another) indicates the existence of the on-axis triplication. We also show the traveltime plots (associated with the group velocity surface) to illustrate the effect of the on-axis triplication.

Five-Axis Freeform Surface Color Printing Technology Based on Offset Curve Path Planning Method

Great progress has been made in 2D color printing with inkjet technology, and mature related products have come out, but there still exists great developmental space in 3D color printing. Therefore, a new path planning method based on the offset curve for 3D inkjet technology is proposed in this paper. Offset curves are generated on a freeform surface with geodesic equidistance, and then points for color printing are generated along the offset curves. In this paper, the principle of color printing technology with a 5-axis platform and the offset curve path planning (OCPP) method are presented. In addition, comparisons between the OCPP and adaptive filling algorithm based on the section method (AFSM) have been implemented. The OCPP significantly increased the rate of the theoretical filling area from 0.89 to 0.99 on a freeform surface.

A LOW-COST MARKERLESS TRACKING SYSTEM FOR TRAJECTORY INTERPRETATION

The tracking abilities of 1^st generation Kinect sensors have been tested over common trajectories of folk dances. Trajectories related errors, including offset, curve shape, noisy points are investigated and mitigated using well-known signal processing filters. Low cost depth trackers can contribute towards the remote tutoring of folk dances, by providing adequate data to instructors and explicit details to the trainees which segments of their dance trajectories need more work.

A Hybrid Approach to Polygon Offsetting Using Winding Numbers and Partial Computation of the Voronoi Diagram

In this paper we present a new, efficient algorithm for computing the “raw offset” curves of 2D polygons with holes. Prior approaches focus on (a) complete computation of the Voronoi Diagram, or (b) pair-wise techniques for generating a raw offset followed by removal of “invalid loops” using a sweepline algorithm. Both have drawbacks in practice. Robust implementation of Voronoi Diagram algorithms has proven complex. Sweeplines take O((n + k)log n) time and O(n + k) memory, where n is the number of vertices and k is the number of self-intersections of the raw offset curve. It has been shown that k can be O(n2) when the offset distance is greater than or equal to the local radius of curvature of the polygon, a regular occurrence in the creation of contour-parallel offset curves for NC pocket machining. Our O(n log n) recursive algorithm, derived from Voronoi diagram algorithms, computes the velocities of polygon vertices as a function of overall offset rate. By construction, our algorithm prunes a large proportion of locally invalid loops from the raw offset curve, eliminating all self-intersections in raw offsets of convex polygons and the “near-circular”, k proportional to O(n2) worst-case scenarios in non-convex polygons.

Researches on the Measurement Rebuilding and Multi-Axis Flank Milling NC Machining of the Compressor Impeller

The ruled surface of impeller is widely used in the industry of automobile, shipbuilding, aerospace and aeronautics. Researches on the manufacture of blade possess general meaning. The importance of their performance in the certain field and the non-replace ability of their functions in the specified mechanical systems have resulted in that the technology of manufacturing and measurement for ruled surfaces has been a critical research project in the field of dimensional manufacturing and measurements. With the rapid development of the modern science and technology, complex ruled surfaces are employed more and more widely, but their tolerances become narrower and narrower. The common impeller surfaces represented by NURBS are given and then curve and surface interpolation algorithm represented by NURBS are presented. These provide theoretical foundation for NC machining programming of impeller surface. Principals of normal offset curve and inclined offset surface are used to simplify the model. The NC milling method of divide area is presented to raise machining efficiency and to improve quality of machined surface. The machining efficiency is important in line property of rule surface, flank milling rule surface with end-milling, improve surface quality and cutter efficiency. This paper presents a calculate method to generate five-axis flank milling NC code of divide area in the blade of compressor with Vericut simulating the five-axis flank milling NC code and measurement the result of processing that verification the precision of five-axis flank milling. This paper also simulates four-axis machining for comparing cutting efficiency between five-axis machining and four-axis machining and the status of both the great differences in processing efficiency.

Iterative supervirtual refraction interferometry

In refraction tomography, the low signal-to-noise ratio (S/N) can be a major obstacle in picking the first-break arrivals at the far-offset receivers. To increase the S/N, we evaluated iterative supervirtual refraction interferometry (ISVI), which is an extension of the supervirtual refraction interferometry method. In this method, supervirtual traces are computed and then iteratively reused to generate supervirtual traces with a higher S/N. Our empirical results with both synthetic and field data revealed that ISVI can significantly boost up the S/N of far-offset traces. The drawback is that using refraction events from more than one refractor can introduce unacceptable artifacts into the final traveltime versus offset curve. This problem can be avoided by careful windowing of refraction events.

Offsetting obstacles of any shape for robot motion planning

SUMMARYWe present an algorithm for offsetting the workspace obstacles of a circular robot. Our method has two major steps: It finds the raw offset curve for both lines and circular arcs, and then removes the global invalid loops to find the final offset. To generate the raw offset curve and remove global invalid loops, O(n) and O((n+k)log m) computational times are needed respectively, where n is the number of vertices in the original polygon, k is the number of self-intersections and m is the number of segments in the raw offset curve, where m ≤ n. Any local invalid loops are removed before generating the raw offset curve by invoking a pair-wise intersection detection test (PIDT). In the PIDT, two intersecting entities are checked immediately after they are computed, and if the test is positive, portions of the intersecting segments are removed. Our method works for conventional polygons as well as the polygons that contain circular arcs. Our algorithm is simple and very fast, as each sub-process of the algorithm can be completed in linear time except the last one, which is nearly linear. Therefore, the overall complexity of the algorithm is nearly linear. By applying our simple and efficient approach, offsetting obstacles of any shape make it possible to construct a configuration space that ensures optimized motion planning.

Computing Offsets of NURBS Curve and Surface

This paper presents an algorithm for the offsetting of NURBS curve/surface. First the unit normal vectors of the progenitor NURBS curve/surface is computed precisely, then the offset curve/surface can be obtained by offsetting the progenitor curve/surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS curve/surface.

Contour Offset Approach to Generate Tool Path for Polyhedral Surfaces Machining

Polyhedral surfaces are used as representation model for CAM and process planning purposes because of its simplicity for data exchange and geometric computation. However, there is few tool path planning strategies for such surfaces but the iso-plane method. In this paper, contour parallel path are generated for three-axis ball-end milling. This tool path is based on a novel algorithm for offsetting curves on polyhedral surfaces presented in this paper. It reduces the task of removing complex interfering of offset curve from 3D surface to 2D plane by flattening mesh surface, and avoids costly 3D Boolean set operations and expensive distance calculation. This results in an efficient tool-path generation. Empirical examples illustrate the feasibility the proposed method.