An Efficient Sensing Localization Algorithm for Free-Form Surface Digitization

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.

Download Full-text

An Efficient Sensing Localization Algorithm for Free-Form Surface Digitization

Volume 2: 27th Computers and Information in Engineering Conference, Parts A and B ◽

10.1115/detc2007-35669 ◽

2007 ◽

Author(s):

Yunbao Huang ◽

Xiaoping Qian

Keyword(s):

High Efficiency ◽

Search Time ◽

Divide And Conquer ◽

Free Form ◽

Point Problem ◽

Localization Algorithm ◽

Efficient Manner ◽

B Spline ◽

On Line ◽

Free Form Surface

This paper presents a divide-and-conquer method that finds a near-optimal distribution of sensing locations in a very efficient manner for the free-form surface digitization process. We formulate the sensing localization issue as a next-best-point problem. We transform the uncertainty of a reconstructed B-spline surface into a higher-dimensional uncertainty surface. This further allows the use of convex hull and subdivision properties of B-spline surfaces in the NBP based sensing localization algorithm. It thus dramatically reduces the search time for determining the next best sensing location. Experimental examples demonstrate that the algorithm compares favorably to existing algorithms and, due to its high efficiency, supports both off-line and on-line sensing planning.

Download Full-text

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

Materials Science Forum ◽

10.4028/www.scientific.net/msf.505-507.547 ◽

2006 ◽

Vol 505-507 ◽

pp. 547-552 ◽

Cited By ~ 2

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.

Download Full-text

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

Journal of Science and Technology Issue on Information and Communications Technology ◽

10.31130/jst.2017.41 ◽

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.

Download Full-text

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

16th Design Automation Conference: Volume 1 — Computer Aided and Computational Design ◽

10.1115/detc1990-0032 ◽

1990 ◽

Author(s):

Joanna M. Brown ◽

Malcolm I. G. Bloor ◽

M. Susan Bloor ◽

Michael J. Wilson

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Spline Approximation ◽

The Finite Element Method ◽

B Spline ◽

B Splines ◽

Spline Surface ◽

Spline Surfaces ◽

Spline Basis ◽

Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

Download Full-text

Sequential B-Spline Surface Construction Using Multiresolution Data Clouds

Journal of Computing and Information Science in Engineering ◽

10.1115/1.4006000 ◽

2012 ◽

Vol 12 (2) ◽

Author(s):

Yuan Yuan ◽

Shiyu Zhou

Keyword(s):

Control Points ◽

Finite Sample ◽

B Spline ◽

Spline Surface ◽

Spline Surfaces ◽

Filtering Technique ◽

Engineering Practices ◽

Asymptotical Convergence ◽

Surface Construction ◽

Fitting Error

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.

Download Full-text

Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

Mathematical Problems in Engineering ◽

10.1155/2014/706247 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

C. H. Garcia-Capulin ◽

F. J. Cuevas ◽

G. Trejo-Caballero ◽

H. Rostro-Gonzalez

Keyword(s):

Genetic Algorithm ◽

Geometric Modeling ◽

Data Set ◽

Surface Approximation ◽

B Spline ◽

B Splines ◽

Spline Surface ◽

Spline Surfaces ◽

Surface Dimension ◽

Hierarchical Genetic Algorithm

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.

Download Full-text

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

Volume 1: Design for Manufacturing Conference ◽

10.1115/96-detc/dfm-1408 ◽

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.

Download Full-text

A Generic Approach to Free Form Surface Generation

Journal of Computing and Information Science in Engineering ◽

10.1115/1.1559579 ◽

2002 ◽

Vol 2 (4) ◽

pp. 294-301 ◽

Cited By ~ 2

Author(s):

J. Cotrina-Navau ◽

N. Pla-Garcia ◽

M. Vigo-Anglada

Keyword(s):

Theoretical Approach ◽

Differentiable Manifold ◽

Surface Generation ◽

Free Form ◽

B Spline ◽

Free Form Surface ◽

Manifold Theory ◽

Free Form Surfaces

A theoretical approach to construct free form surfaces is presented. We develop the concepts that arise when a free form surface is generated by tracing a mesh, using differentiable manifold theory, and generalizing the B-spline scheme. This approach allows us to define a family of practical schemes. Four different applications of the generic approach are also presented in this paper.

Download Full-text

Free-Form Plate Modeling Using Offset Surfaces

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.3257064 ◽

1988 ◽

Vol 110 (3) ◽

pp. 287-294 ◽

Cited By ~ 10

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.

Download Full-text