Computation of Voxel Maps Containing Tool Access Directions for Machining Free-Form Shapes

1996 ◽  
Author(s):  
Johan W. H. Tangelder ◽  
Joris S. M. Vergeest ◽  
Mark H. Overmars
Keyword(s):  
Free Form ◽  
Geometric Accuracy ◽  
Surface Sampling ◽  
B Spline ◽  
Spline Surface ◽  
Surface Data

Abstract An algorithm that derives tool access directions for machining free-form shapes is presented. A free-form shape to be machined is given by a preliminary B-spline model. We allow that the B-spline surface data are as inaccurate as the user-selected geometric accuracy of the prototype to be machined. Using surface sampling a visibility voxel map is obtained. From this map a voxel map is derived that contains per voxel a set of tool access directions. From the obtained voxel map regions can be selected that can be machined with a fixed tool access direction per region.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

Comparison of B-Spline Surface and Free-Form Deformation Geometry Control for Aerodynamic Optimization

AIAA Journal ◽  
2017 ◽  
Vol 55 (1) ◽  
pp. 228-240 ◽  
Author(s):  
Christopher Lee ◽  
David Koo ◽  
David W. Zingg
Keyword(s):  
Free Form ◽  
Aerodynamic Optimization ◽  
B Spline ◽  
Spline Surface ◽  
Free Form Deformation

An Efficient Sensing Localization Algorithm for Free-Form Surface Digitization

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Yunbao Huang ◽  
Xiaoping Qian
Keyword(s):  
Search Time ◽  
Divide And Conquer ◽  
Free Form ◽  
Point Problem ◽  
Localization Algorithm ◽  
B Spline ◽  
Divide And Conquer Algorithm ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Free Form Surface

We present a divide-and-conquer method that efficiently finds a near-optimal distribution of sensing locations for free-form surface digitization. We formulate a next-best-point problem and transform the uncertainty of a B-spline surface into a higher-dimensional B-spline surface. This technique allows the use of the convex hull and subdivision properties of B-spline surfaces in the divide-and-conquer algorithm. It thus greatly reduces the search time for determining the next best sensing location.

PB-Spline Hybrid Surface Fitting Technique

2009 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Large Scale ◽  
Free Form ◽  
Rectangular Array ◽  
B Spline ◽  
Large Scale Data ◽  
Spline Surface ◽  
Spline Basis ◽  
Data Points ◽  
Free Form Surfaces ◽  
Scale Data

This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization of tensor product splines, are adopted. The basic idea of this paper is to fit large scale data with a tensorial B-spline surface and to refine the surface until a specified tolerance is met. Since some isolated domains exceeding tolerance may result, detail features on these domains are modeled by a tensorial B-spline basis with a finer resolution, superimposed by employing the PB-spline approach. The present method leads to an efficient model of free form surfaces, since both large scale data and local geometrical details can be efficiently fitted. Two application examples are presented. The first one concerns the fitting of a set of data points sampled from an interior car trim with a central geometrical detail. The second one refers to the modification of the tensorial B-spline surface representation of a mould in order to create a local adjustment. Considerations regarding strengths and limits of the approach then follow.

The Data Exchange of the IGES Cured Surface in Reverse Engineering

2010 ◽  
Vol 426-427 ◽  
pp. 503-506
Author(s):  
Sheng Bing Xiao ◽  
Xue Dong Xie ◽  
Xiang Qian Che
Keyword(s):  
Reverse Engineering ◽  
Data Exchange ◽  
Engineering System ◽  
B Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Cad Cam

The realization of the data exchanges between the reverse engineering system and CAD / CAM system is by Graphics Interchange standards, of which the initial graphics exchanges specification IGES is one of the important ways that data exchanges in systems. At first, the paper introduces the structures of the five parts that composes the IGES file. Secondly, it also introduces the meaning of the parameters that the rational B-spline surface in IGES and gives the method to identify and extract IGES surface data in the reverse engineering system. At last, it uses the OpenGL graphics system to show the surface data. Then, the exchanges of the surface data between the systems can realize easily by the method.

Automatic Polishing of Super Accuracy Mirror Mold with Free-Form Surface by Curvature Analysis

2006 ◽  
Vol 505-507 ◽  
pp. 547-552 ◽  
Author(s):  
Ming June Tsai ◽  
Jing Jing Fang ◽  
Jian Feng Huang
Keyword(s):  
Free Form ◽  
Mold Surface ◽  
B Spline ◽  
Curvature Analysis ◽  
Spline Surface ◽  
Effective Contact ◽  
Automatic Polishing ◽  
Contact Width ◽  
Free Form Surface ◽  
Free Form Surfaces

This paper proposed a polishing path planning method of super accuracy mirror mold with free-form surface by curvature analysis. First, IGES files of free-form surfaces are read and the mold geometry is regenerated as B-spline surface by the Automatic Mold Polishing System (AMPS). By using the derivative properties of B-spline surface, normal vector and principal curvatures at any point of the surface are calculated. In addition, the effective contact width between polishing tool and mold surface based on the grain size and the principal radii of curvature is also determined. The minimum contact width in 3-D is mapped onto the (u, v) parameters of B-spline surface. Then a modified Peano fractal path with weaving function is calculated based on the effective contact width in the (u, v) coordinate. This Peano-weaving path was tested on an optical mold with free-form surface. The polishing result shows the method is very effective and achieves the level of mirror surface with roughness Ra 29nm.

A B-Spline Least-Squares Surface-Fitting Method for Articular Surfaces of Diarthrodial Joints

1993 ◽  
Vol 115 (4A) ◽  
pp. 366-373 ◽  
Author(s):  
G. A. Ateshian
Keyword(s):  
Least Squares ◽  
Articular Surface ◽  
Three Dimensional ◽  
Surface Fitting ◽  
B Spline ◽  
Spline Surface ◽  
Articular Surfaces ◽  
Diarthrodial Joint ◽  
Surface Data ◽  
Fitting Method

The B-spline least-squares surface-fitting method is employed to create geometric models of diarthrodial joint articular surfaces. This method provides a smooth higher-order surface approximation from experimental three-dimensional surface data that have been obtained with any suitable measurement technique. Akima’s method for surface interpolation is used to provide complete support to the B-spline surface. The surface-fitting method is successfully tested on a known analytical surface, and is applied to the human distal femur. Applications to other articular surfaces are also shown. Results show that this method is precise, highly flexible, and can be successfully applied to a large variety of articular surface shapes.

Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme

2017 ◽  
Vol 3 (1) ◽  
pp. 82
Author(s):  
Nga Le-Thi-Thu ◽  
Khoi Nguyen-Tan ◽  
Thuy Nguyen-Thanh
Keyword(s):  
Free Form ◽  
Subdivision Scheme ◽  
B Spline ◽  
Geometric Fitting ◽  
Arbitrary Topology ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Low Degree ◽  
Data Points ◽  
Free Form Surfaces

Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adjusted locally by a simple geometric fitting algorithm to increase the accuracy of the obtained B-spline. The reconstructed B-spline having the low degree along with arbitrary topology is interpolative to most of the given data points after some fitting steps without solving any linear system. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Results show that this approach is simple, fast, flexible and can be successfully applied to a variety of surface shapes.

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