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 Generic Approach to Free Form Surface Generation

2002 ◽  
Vol 2 (4) ◽  
pp. 294-301 ◽  
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.

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.

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.

Application of Convex Hull for Tool Interference Avoidance in 5-Axis CNC Machining

1996 ◽  
Author(s):  
Yuan-Shin Lee ◽  
Tien-Chien Chang
Keyword(s):  
Convex Hull ◽  
Tool Path ◽  
Correction Method ◽  
Nc Machining ◽  
Cnc Machining ◽  
Free Form ◽  
Interference Avoidance ◽  
Tool Interference ◽  
Free Form Surface ◽  
Free Form Surfaces

Abstract In this paper, a methodology of applying convex hull property in solving the tool interference problem is presented for 5-axis NC machining of free-form surfaces. Instead of exhausted point-by-point checking for possible tool interference, a quick checking can be done by using the convex hull constructed from the control polygon of free-form surface modeling. Global tool interference in 5-axis NC machining is detected using the convex hull of the free-form surface. A correction method for removing tool interference has also been developed to generate correct tool path for 5-axis NC machining. The inter-surface tool interference can be avoided by using the developed technique.

Research on Digital Modeling about Free-Form Surface with Holes Based on Coordinate Measuring Machine

2011 ◽  
Vol 287-290 ◽  
pp. 2805-2809
Author(s):  
Ming Yu Huang ◽  
Xiu Juan Wu ◽  
Zhong Shi Jia ◽  
Hong Jun Ni ◽  
Jing Jing Lv ◽  
...  
Keyword(s):  
Point Cloud ◽  
Coordinate Measuring Machine ◽  
Free Form ◽  
Model Reconstruction ◽  
Contact Measurement ◽  
Digital Modeling ◽  
Measuring Machine ◽  
Fast Reconstruction ◽  
Free Form Surface ◽  
Free Form Surfaces

Data acquisition and model reconstruction of free-form surfaces with holes were been studied, based on coordinate measuring machines. First, the structural process of the parts was analyzed, the method of combinate contact measurement with non-contact measurement were used to get point cloud; Then the point cloud were been preprocessed, feature curve extracted and solid modeled; Finally, the restructure model was been quality assessed and accuracy assessed. Using the measurement of combinated contact and non-contact can also meet both the precision requirement of key part and the fast reconstruction requirement of non-critical part, which has great significance on that part to fast and accurate reconstruction.

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.

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