Approximation of generalized offset surfaces by bicubic splines

2019 ◽  
Vol 58 (3) ◽  
pp. 647-662
Author(s):  
R. Akhrif ◽  
A. Kouibia ◽  
M. Pasadas
Keyword(s):  
Offset Surfaces ◽  
Bicubic Splines

Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces

1998 ◽  
Author(s):  
Helmut Pottmann ◽  
Johannes Wallner ◽  
Georg Glaeser ◽  
Bahram Ravani
Keyword(s):  
Motion Planning ◽  
Sculptured Surfaces ◽  
Global Shape ◽  
Be Star ◽  
Offset Surfaces ◽  
Tool Motion ◽  
Curvature Information ◽  
Bivariate Functions

Abstract The paper presents a geometric investigation of collision-free 3-axis milling of surfaces. We consider surfaces with a global shape condition: they shall be interpretable as graphs of bivariate functions or shall be star-shaped with respect to a point. If those surfaces satisfy a local millability criterion involving curvature information, it is proved that this implies globally gouge-free milling. The proofs are based on general offset surfaces. The results can be applied to tool-motion planning and the computation of optimal cutter shapes.

Asymmetric Lens Design Using Bicubic Splines: Application to the Color TV Lighthouse

1971 ◽  
Vol 10 (11) ◽  
pp. 2513 ◽  
Author(s):  
T. P. Vogl ◽  
A. K. Rigler ◽  
B. R. Canty
Keyword(s):  
Lens Design ◽  
Bicubic Splines

Free-Form Plate Modeling Using Offset Surfaces

1988 ◽  
Vol 110 (3) ◽  
pp. 287-294 ◽  
Author(s):  
N. M. Patrikalakis ◽  
P. V. Prakash
Keyword(s):  
Boundary Representation ◽  
Free Form ◽  
Parametric Surfaces ◽  
B Spline ◽  
Spline Surfaces ◽  
Accuracy Criterion ◽  
Offset Surfaces ◽  
Representation Method ◽  
Class Of Functions ◽  
Offset Surface

This paper addresses the representation of plates within the framework of the Boundary Representation method in a Solid Modeling environment. Plates are defined as the volume bounded by a progenitor surface, its offset surface and other, possibly ruled surfaces for the sides. Offset surfaces of polynomial parametric surfaces cannot be represented exactly within the same class of functions describing the progenitor surface. Therefore, if the offset surface is to be represented in the same form as the progenitor surface, approximation is required. A method of approximation relevant to non-uniform rational parametric B-spline surfaces is described. The method employs the properties of the control polyhedron and a recently developed subdivision algorithm to satisfy a certain accuracy criterion. Representative examples are given which illustrate the efficiency and robustness of the proposed method.

Offset Surface Generation and Contouring in Computer-Aided Design

1987 ◽  
Vol 109 (1) ◽  
pp. 133-142 ◽  
Author(s):  
Y. J. Chen ◽  
B. Ravani
Keyword(s):  
Computer Aided Design ◽  
Numerical Control ◽  
Surface Generation ◽  
Computational Techniques ◽  
Computational Technique ◽  
Contour Lines ◽  
Computer Aided ◽  
Offset Surfaces ◽  
Aided Design ◽  
Offset Surface

Two computational techniques are presented for Computer-Aided Design (CAD) and Machining (CAM) of parametrically defined surfaces. One technique deals with construction of offset surfaces. An algorithm is presented that would allow detection and removal of the closed loop on the offset surface due to its self-intersection. The second computational technique presented deals with contouring of parametric surfaces. The technique presented allows for optimal generation of planar contour lines. The results are applied to Numerical Control (NC) machining of surfaces.

scholarly journals Reconstruction approximating method by biquadratic splines of offset surfaces holes

2022 ◽  
Author(s):  
Abdelouahed Kouibia ◽  
Miguel Pasadas
Keyword(s):  
Approximation Method ◽  
Tolerance Analysis ◽  
Convergence Result ◽  
Normal Direction ◽  
Normal Vector ◽  
Practical Applications ◽  
Lack Of Information ◽  
Cad Cam ◽  
Offset Surfaces ◽  
Unit Normal

AbstractStandard 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

2018 ◽  
Author(s):  
Andrew Sharp ◽  
Christina Petlowany ◽  
Mitch Pryor
Keyword(s):  
Experimental Studies ◽  
Waste Reduction ◽  
Contact Material ◽  
Normal Surface ◽  
Virtual Fixtures ◽  
Path Creation ◽  
Virtual Fixture ◽  
Nuclear Systems ◽  
Offset Surfaces ◽  
Selection Of

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.

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