Reconstruction of Sculptured Surface on Reverse Engineering

1997 ◽  
Author(s):  
Gou-Jen Wang ◽  
Chung-Chang Wang
Keyword(s):  
Data Structure ◽  
Reverse Engineering ◽  
Surface Reconstruction ◽  
Sparse Matrix ◽  
Computing Time ◽  
Cubic Spline ◽  
Surface Model ◽  
Two Dimensional ◽  
B Spline ◽  
Spline Curves

Abstract In this article, solutions for redundant measured data elimination and surface reconstruction on reverse engineering are presented. In redundant data elimination, we propose a simple algorithm that can efficiently discard those redundant measured points according to the required degree of accuracy. While in the surface reconstruction, we try first convert all eliminated column or row data into spline (B-Spline, Beizer and Cubic-Spline) curves. Methods for two dimensional spline (u, v directions) curve construction are described. Non-meshed two dimensional spline curves are then blended to a surface model by formatting data points into a sparse matrix data structure. Experimental results show that the proposed characteristic points extraction method can remarkably reduce the reconstruction time only on the cost of a little extracting time and minor modeling errors. Comparisons among B-spline, Beizer and Cubic-spline on data structure, computing time, and accuracy demonstrate that the B-spline algorithm is superior to other algorithms in surface reconstruction.

Automatic Unstructured Mesh Generation Around Two-Dimensional Domains Described by B-Spline Curves

2001 ◽  
Author(s):  
Horacio Flórez Guzmán ◽  
Raúl Manzanilla Morillo
Keyword(s):  
Grid Generation ◽  
Computer Code ◽  
Two Dimensional ◽  
B Spline ◽  
Piecewise Polynomials ◽  
Spline Curves ◽  
Interpolation Problems ◽  
Interpolation Procedure ◽  
Definition Of ◽  
Unstructured Mesh Generation

Abstract A computer code for the generation of unstructured two-dimensional triangular meshes around arbitrary complex geometries has been developed. The code is based on Delaunay triangulation with an automatic point insertion scheme and a smoothing technique. The geometrical definition of the domain to be meshed is prescribed by means of B-spline curves obtained from two approaches of interest in Computer-Aided Geometric Design named inverse design and interpolation problems. The presented scheme is based on an interpolation procedure along a B-spline curve proposed by the author in a recent paper. This technique prevents that the resulting grid may overlap convex portions of the boundaries. The main goal is to study the possibility of extend the methodology of unstructured grid generation beginning with boundaries described by polylines to other in which they are prescribed by piecewise polynomials curves capable to drive more realistic problems. Several figures and examples from Computational Fluid Dynamics have been included to show the various steps of the algorithm. The results show that the code is able to solve the problem of automatic grid generation in a robust manner opening new perspectives for the development of a black-box grid generator.

scholarly journals Synthesis of Spatially and Intrinsically Constrained Curves Using Simulated Annealing

1996 ◽  
Vol 118 (1) ◽  
pp. 53-61 ◽  
Author(s):  
A. Malhotra ◽  
J. H. Oliver ◽  
W. Tu
Keyword(s):  
Simulated Annealing ◽  
Optimization Problem ◽  
Automatic Generation ◽  
Surface Model ◽  
Spatial Constraints ◽  
General Technique ◽  
B Spline ◽  
Model Synthesis ◽  
Spline Curves ◽  
Intrinsic Shape

A general technique is presented for automatic generation of B-spline curves in a spatially constrained environment, subject to specified intrinsic shape properties. Spatial constraints are characterized by a distance metric relating points on the curve to polyhedral models of obstacles which the curve should avoid. The shape of the curve is governed by constraints based on intrinsic curve properties such as parametric variation and curvature. To simultaneously address the independent goals of global obstacle avoidance and local control of intrinsic shape properties, curve synthesis is formulated as a combinatorial optimization problem and solved via simulated annealing. Several example applications are presented which demonstrate the robustness of the technique. The synthesis of both uniform and nonuniform B-spline curves is also demonstrated. An extension of the technique to general sculptured surface model synthesis is briefly described, and a preliminary example of simple surface synthesis presented.

Surface Reconstruction by Alpha Geometric Shape Based on Triangulation

2011 ◽  
Vol 480-481 ◽  
pp. 1536-1541
Author(s):  
Xue Ming He ◽  
Chen Liang Hua ◽  
Cheng Gang Li ◽  
Min Min Ni ◽  
Qing Hua Jin
Keyword(s):  
Data Structure ◽  
Computer Graphics ◽  
Reverse Engineering ◽  
Surface Reconstruction ◽  
Geometric Shape ◽  
Triangle Mesh ◽  
Section Line ◽  
Interactive Selection

Surface reconstruction by alpha geometric shape based on triangulation is a new idea and method in computer graphics and reverse engineering. In the process of Topology reconstruction, the points are reduced and projected to a middle slice plane. The adjacency among slices is established by section line subdivision, and triangle mesh is stored and called by the form of STL. The simplexes are classified and computed in order to obtain α interval by the external-ball radius and center of every simplex, and the data structure is designed to save them. Through the man-machine interactive selection modes, α-shape can be reconstructed by different α parameters. The surface reconstruction is completed.

A New Reverse Engineering Method for the 3D Surface Reconstruction without Contact

2015 ◽  
Vol 1099 ◽  
pp. 140-146
Author(s):  
L. Giraud-Moreau ◽  
R. Slysz ◽  
H. Borouchaki
Keyword(s):  
Reverse Engineering ◽  
Pattern Matching ◽  
Surface Reconstruction ◽  
Delaunay Triangulation ◽  
Three Dimensional ◽  
Engineering Method ◽  
Two Dimensional ◽  
3D Surface Reconstruction ◽  
3D Surface ◽  
Structure Light

In this paper, a new reverse engineering method is proposed for 3d surface reconstruction without contact. This method is based on the combination of stereovision and structure light methods. The originality of the proposed technique is that the pattern is a two-dimensional Delaunay triangulation. A key characterizing the vertices is computed for each vertex. The pattern matching between two images is reduced to the comparison of two meshes. The three dimensional triangulation of the surface can then be obtained by using the geometric properties of the acquisition devices.

Research on Spiral Bevel Gear Tooth Surface Reconstruction Based on NURBS

2011 ◽  
Vol 130-134 ◽  
pp. 701-705
Author(s):  
Lin Yang ◽  
Shuai Nan Ren ◽  
Zhen Yu Wang ◽  
Peng Zhang
Keyword(s):  
Surface Reconstruction ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Surface Shape ◽  
Tooth Surface ◽  
Surface Model ◽  
Spiral Bevel Gear ◽  
Surface Sampling ◽  
B Spline ◽  
Spiral Bevel

The tooth surface shape of spiral bevel gear is complex. In the detection process of errors tooth surface model is constructed based on coordinate data of limited the actual tooth surface sampling points. The model is used to analysis and manufacture of gear to meet the processing requirements. NURBS (non-uniform rational B-Spline) method is the most effective reconstruction method for geometry there are both freedom and analytic curves and surfaces. NURBS method is used to calculate non-uniform knot vector, NURBS control points and B-Spline inverse and reconstruct tooth surface. Reconstructionof spiral bevel gears in using NURBS is achieved and the tooth surface reconstruction is drawn out in Open GL in VC environment. And then reconstruction error on the tooth surface is analyzed. It proves that using the method of NURBS to reconstruct spiral bevel gear tooth surface is correct and feasible.

Collision-Free Trajectory Planning for a Two-Dimensional Mobile Robot by Optimizing Continuous Curves

1998 ◽  
Vol 10 (4) ◽  
pp. 364-369 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Chang-jun Lin
Keyword(s):  
Mobile Robot ◽  
Trajectory Planning ◽  
Performance Index ◽  
Nonlinear Problems ◽  
Complex Method ◽  
Control Points ◽  
Two Dimensional ◽  
B Spline ◽  
Spline Curves ◽  
Continuous Curves

We propose a new algorithm for planning collision-free trajectories for a mobile robot. The trajectories of the mobile robot are described by uniform B-spline curves and these control points are optimized using the complex method. The complex method is very effective for this type of optimization of nonlinear problems because it does not require any computation of the gradient of performance index. B-spline curves have advantages for trajectory generation in that they guarantee the continuity of trajectories and the order of trajectories can be changed easily. Effectiveness is also confirmed by trajectory planning simulation of a two-dimensional mobile robot.

scholarly journals Synthesis of Spatially and Intrinsically Constrained Curves Using Simulated Annealing

1991 ◽  
Author(s):  
Alok Malhotra ◽  
James H. Oliver ◽  
Weizhen Tu
Keyword(s):  
Simulated Annealing ◽  
Optimization Problem ◽  
Automatic Generation ◽  
Surface Model ◽  
Spatial Constraints ◽  
General Technique ◽  
B Spline ◽  
Model Synthesis ◽  
Spline Curves ◽  
Intrinsic Shape

Abstract A general technique is presented for automatic generation of B-spline curves in a spatially constrained environment, subject to specified intrinsic shape properties. Spatial constraints are characterized by a distance metric relating points on the curve to polyhedral models of obstacles which the curve should avoid. The shape of the curve is governed by constraints based on intrinsic curve properties such as parametric variation and curvature. To simultaneously address the independent goals of global obstacle avoidance and local control of intrinsic shape properties, curve synthesis is formulated as a combinatorial optimization problem and solved via simulated annealing. Several example applications are presented which demonstrate the robustness of the technique. The synthesis of both uniform and non-uniform B-spline curves is also demonstrated. An extension of the technique to general sculptured surface model synthesis is briefly described, and a preliminary example of simple surface synthesis presented.

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