Implicit Methods for Geometry Creation

1998 ◽  
Vol 08 (05n06) ◽  
pp. 509-536 ◽  
Author(s):  
Mark T. Ensz ◽  
Duane W. Storti ◽  
Mark A. Ganter
Keyword(s):  
Implicit Methods ◽  
Solid Geometry ◽  
Surface Data ◽  
Data Points ◽  
Implicit Geometry ◽  
Sample Set

In this paper, we briefly review the existing direct implicit geometry generation methods, which include creation of blending surfaces, a limited family of sweeps, and reconstruction of solid geometry from a sample set of surface data points. A broader approach is presented, utilizing the properties of the graph of the implicit defining function, to systematically construct swept solids and perform morphing between sections by implicit methods.

Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points

1994 ◽  
Vol 120 (2) ◽  
pp. 165-187 ◽  
Author(s):  
Peter R. Johnston ◽  
Stephen J. Walker ◽  
Jari A.K. Hyttinen ◽  
David Kilpatrick
Keyword(s):  
Body Surface ◽  
Surface Data ◽  
Data Points

Data Process for Reverse Engineering Technology

2012 ◽  
Vol 549 ◽  
pp. 1012-1016
Author(s):  
Hui Guo ◽  
Yan Hui Hu ◽  
Xiao Jing Li
Keyword(s):  
Reverse Engineering ◽  
Coordinate Measuring Machine ◽  
Complex Data ◽  
Practical Application ◽  
Engineering Technology ◽  
Data Process ◽  
Surface Data ◽  
Data Points ◽  
Measuring Machine ◽  
Fitting In

Reverse engineering has become an important tool for CAD model construction from the data points, measured by a coordinate measuring machine (CMM), of an existing part. However, due to special structure and complex topology relation, obtaining full surface data of a prototype is not an easy thing and should carry out complex data process procedure to get global model. The paper presents a method for pre-processing data points for curve fitting in reverse engineering. The proposed method has been developed to process the measured data points before fitting into a B-spline form. The method is implemented and used for a practical application in reverse engineering. The result of the reconstruction proves the viability of the proposed method for integration with current commercial CAD systems.

scholarly journals Visualization Terrain Data Using Cubic Ball Triangular Patches

2018 ◽  
Vol 225 ◽  
pp. 06023 ◽  
Author(s):  
Samsul Ariffin Bin Abdul Karim ◽  
Azizan Saaban
Keyword(s):  
Delaunay Triangulation ◽  
Central Region ◽  
Partial Derivative ◽  
Convex Combination ◽  
Scattered Data ◽  
Sufficient Condition ◽  
Surface Data ◽  
Data Points ◽  
Local Scheme

Scattered data technique is important to visualize the geometrical images of the surface data especially for terrain, earthquake, geochemical distribution, rainfall etc. The main objective of this study is to visualize the terrain data by using cubic Ball triangular patches. First step, the terrain data is triangulated by using Delaunay triangulation. Then partial derivative will be estimated at the data points. Sufficient condition for C1 continuity will be derived for each triangle. Finally, a convex combination comprising three rational local scheme is used to construct the surface. The scheme is tested to visualize the terrain data collected at central region of Malaysia.

Reconstruction Technology on the Surface of Engine Port Based on Reverse Engineering

2011 ◽  
Vol 219-220 ◽  
pp. 1249-1252
Author(s):  
Xiao Zhong Ren ◽  
Ming De Duan ◽  
Jian Xin Su
Keyword(s):  
Reverse Engineering ◽  
Laser Scanner ◽  
Grid Method ◽  
Free Form ◽  
Engineering Technology ◽  
Surface Data ◽  
Fitting Algorithm ◽  
Data Points ◽  
Free Form Surfaces ◽  
Developing Platform

Applying reverse engineering technology to the design of engine port, the reconstruction technology on the free-form surfaces of the engine port were investigated deeply. The data on the 3D surfaces of the engine port sample were collected by means of laser scanner, and the scattered data points were processed in regularization. Triangulation processing of surface data cloud was carried out based on surface grid method. According to the free-form surface technology and curve fitting algorithm used at present, the methods used to reconstruct the port surface were proposed. Taking CATIA software as developing platform, the free-form surfaces of the engine port were reconstructed.

Theoretical Development of a Modified RANSAC Algorithm for Identifying Outliers in Road Surface Data

2017 ◽  
Author(s):  
Savio J. Pereira ◽  
Craig T. Altmann ◽  
John B. Ferris
Keyword(s):  
Road Surface ◽  
Theoretical Development ◽  
Smooth Transition ◽  
Surface Measurement ◽  
Outlier Rejection ◽  
Rejection Algorithm ◽  
Surface Data ◽  
Data Points ◽  
The Cost ◽  
Ransac Algorithm

Modeling and simulation of vehicles can be improved by using actual road surface data acquired by Road Surface Measurement Systems. Due to inherent properties of the sensors used, the data acquired is often ridden with outliers. This work addresses the issue of identifying and removing outliers by extending the robust outlier rejection algorithm, Random Sampling and Consensus (RANSAC). Specifically, this work modifies the cost function utilized in RANSAC in such a way that it provides a smooth transition for the classification of points as inliers or outliers. The modified RANSAC algorithm is applied to neighborhoods of data points, which are defined as subsets of points that are close to each other based on a distance metric. Based on the outcome of the modified RANSAC algorithm in each neighborhood, a novel measure for determining the likelihood of a point being an outlier, defined in this work as its exogeny, is developed. The algorithm is tested on a simulated road surface dataset. In the future this novel algorithm will also be tested on real-world road surface datasets to evaluate its performance.

Producing Follower Motions Through Their Digitized Cam Contours

2002 ◽  
Vol 2 (2) ◽  
pp. 98-105 ◽  
Author(s):  
Der-Min Tsay ◽  
Meng-Hung Huang ◽  
Hui-Chun Ho
Keyword(s):  
Least Squares ◽  
Contact Point ◽  
Spline Approximation ◽  
B Spline ◽  
Theoretical Design ◽  
Analytical Results ◽  
Surface Data ◽  
Cam Follower ◽  
Data Points ◽  
Computing Procedure

A computing procedure that can be used to generate follower motions with a higher degree of accuracy by using their digitized 2-D cam surfaces is presented. Based on the geometric relationships at the contact point between a planar cam and its follower, the reverse functions that can be solved to find the follower motion of the cam-follower mechanism are established. To approximate the digitized cam surfaces and to create their derivatives required in determining the follower motions, a least squares periodic B-spline approximation is also introduced. In comparison with analytical results obtained from a theoretical design, the procedure is verified for its accuracy and reliability. Furthermore, by using the cam surface data points taken from a CMM, a practical example is given to show the effectiveness and usefulness of the proposed techniques.

1518. A theorem in solid geometry.

1941 ◽  
Vol 25 (264) ◽  
pp. 118
Author(s):  
C. V. Dueell
Keyword(s):  
Solid Geometry

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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