Algorithm for Smoothing Triangulated Surfaces

Automated sequence arrangement of 3D point data for surface fitting in reverse engineering

In reverse engineering, the point cloud data processing is the key, it will directly affect the quality and efficiency of the subsequent reconstruction of the surface. However, the amount of data obtained by three-dimensional laser scanning is often larger and redundant, which will increase the difficulty of the surface reconstruction, therefore, the point cloud data is needed to streamline. Depth analysis of the efficiency and accuracy of curvature grid method, a secondary streamlined algorithm is proposed, which take use of non-uniform grid streamline law based on octree to streamline to the point cloud, and re-use curvature streamline method based on B-spline surface fitting to streamline it. This method, whose streamline ratio is relatively high, can effectively retain the feature point cloud data, providing a great convenience for the follow-up of reverse engineering.

Surface display techniques, including contour mapping, usually use an interpolant when data values are on a rectangular grid; but when values are irregularly located some form of assumed or estimated distance-weighting function is often used to estimate the influence of data points at other locations. If moving average (or some other) techniques are then applied, slopes may be zero at data points; extrema may fall at data points exclusively; or surfaces may not pass through data points.An alternative method is proposed whereby a map is automatically divided into suitable triangular domains with a data point at each vertex. Surface estimation and contour plotting are then performed independently for each triangle using a measured or best-fit plane associated with each data point. The approach requires the utilization of three non-original aspects: 1) the derivation of a local homogeneous area coordinate system for any arbitrary triangle; 2) the construction of a data-structure linking each triangular domain with its three neighbouring triangles and three associated data points, and 3) the use of a conforming triangular finite-element interpolating function.Use of the first two of these concepts permits the economic generation and optimization of a triangular mesh from a set of data points. Optimization criteria used to define the best triangular partition are described in some detail, along with computer timing for this step. Use of the first and third concepts permits the interpolation of a smooth surface over the whole map even though each triangular element is estimated and plotted independently. The requirements for a suitable interpolating function are discussed, and an interpolant is suggested that preserves elevation and slope at each data point as well as elevation and slope continuity between domains. Extrema need not be located at data points but are constrained by their associated planes. Contour line segments are produced by division of each triangle into N2 sub-triangles, elevation estimation at each resulting node, and linear interpolation and plotting withing each sub-triangle. Resolution is then a function of N and local data point density. Extension of the method to higher dimensions is briefly discussed.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

For the current generation of rapid-prototyping models, laser scanners are currently being used more frequently due to rapid first measuring speed and high precision. Direct generation of an STL file from the digitised points has a great of advantage in that it can reduce time and error during the modelling process. A reduction in the number of point data is important while generating the STL file directly from the measured point data and maintaining precision. A new approach is developed in this paper to generate an STL file directly from point clouds by indicating a tolerance e to maintain precision. The STL file can be generated directly from scattered points using a new algorithm that reduces and triangulates digitised point data based on triangulation of 3D parametric surfaces. Two experimental examples are presented to demonstrate the effectiveness and efficiency of the proposed algorithm.

The paper is concerned with path planning for mobile robots. Specifically, the discussion is related to the following problem: Given an ordered sequence of points on the plane, construct a path that fits these points and satisfies certain smoothness requirements. These requirements may be different in different problems and imply basically that the constructed path is to be realizable. Such a problem arises, e.g., when it is required to follow in an automated mode a path stored as a discrete set of points, which, e.g., were collected by a GPS receiver installed on a car when it followed this path for the first time. Due to errors inherent in the data points, the shape of the curve approximating the desired path turns out often inappropriate. The shape of the curve can be improved by applying the so-called fairing, which consists in moving the original data points with the aim to minimize some fairness criterion. Adequate small variations of the data points preserve the proximity of the resulting path to the original data points and make it fairer. In the paper, a new global fairing method is proposed. It reduces the problem of constructing a fair cubic B-spline curve to solving a quadratic programming problem with simple constraints. The fairing criterion is based on minimizing jumps of the spline third derivative. The discussion is illustrated by numerical examples of fairing two actual paths constructed by data points collected by a GPS/GLONASS receiver mounted on a moving vehicle.

Videokeratoscopy is often unable to obtain complete data sets in cases of irregular or asymmetric corneal topography. Subdivision schemes are very common in computer graphics for completion and smoothing of surfaces. Based on a network of triangular facets a smooth and complete surface in a standard coordinate system can be derived from topographic raw data. We examined 88 patients with keratoconus and 40 normal controls. Polygons and polyhedra were defined from videokeratoscopic height data, and a surface was modeled using a modified butterfly subdivision scheme for a nonuniform sampled grid. To assess the model quality topographic raw data were changed to missing values centrally (at the apex of the cone) and in four midperipheral quadrants. The target value was the root mean square error, comparing the remodeled value of the subdivision scheme to the raw data at the position of the missing values for each group. Due to the nonuniform mesh of our Placido-based topographer we used a dynamic adaptive model and the governing dynamic differential equation. With a single missing value, no difference was detected between normals and patients with keratoconus. For a missing area consisting of 13 raw data points, the remodeling error was significantly higher in patients with keratoconus than in normals. With the neighborhood of 13 missing data points, the apex of the cone was remodeled in both groups of patients with less precision than with the peripheral missing data. The locality of the equation systems to be solved and the easy calculation of explicit formulas for the normals may simplify ray-tracing techniques and make subdivision attractive for large datasets in corneal topography even with irregular patterns.

Estimating Weak Lensing Convergence Correlation of Type-Ia Supernovae From 5-Year Snls Data by Internal Error Estimate Technique

In the present paper, an algorithm for the discretization of parametric 3D surfaces has been extended to the family of discrete surfaces represented by stereolithography (STL) grids. The STL file format, developed for the rapid prototyping industry, is an attractive alternative to surface representation in solid modeling. Initially, a boundary representation is constructed from the STL file using feature recognition. Then a smooth surface is recovered over the original STL grid using an interpolating subdivision procedure. Finally, the reconstructed surface is subjected to the triangulation accomplished using the advancing front technique operating directly on the surface. The capability of the proposed methodology is illustrated on an example.

On computational geometry by R.-H. Wang Geometry for analysis of corneal shape by B. A. Barsky Approximate implicitization of rational surfaces by C. Falai A geometric approach to $\dim S_2^1(\Delta_{MS})$ by H. Du Subdivision for $C^1$ surface interpolation by N. Dyn, S. Hed, and D. Levin A permanence principle for shape control by G. Farin and D. Hansford Blending several implicit algebraic surfaces with ruled surfaces by G. Feng, T. Wu, K. Yu, S. Zhang, and Y. Zhou Lagrange interpolation by splines on triangulations by G. Numberger and F. Zeilfelder Quantum teleportation and spin echo: A unitary symplectic spinor approach by E. Binz and W. Schempp The generalization of Pascal's theorem and Morgan-Scott's partition by X. Shi and R.-H. Wang 'Optimal' triangulation of surfaces and bodies by C. R. Traas Multivariate spline and geometry by R.-H. Wang Geometric continuous B-spline--A generalization of the approach of $\gamma$-spline by Z. Wu Adaptive and smooth surface construction by triangular A-patches by G. Xu A B-spline function in $s_3^1(R^3,\Delta_2^*)$ by G. Zhao and R.-H. Wang.

Smooth surface interpolation to scattered data using interpolatory subdivision algorithms

We present a new surface representation scheme based on a manifold structure and displacement functions. Given a geometric model represented as a point cloud, we construct a domain manifold which is a smooth surface blended from simple local patches. The original points are then projected on to the local patches and their displacements are adjusted so that the final displaced surface approximates the given point data with high precision. We demonstrate the effectiveness of our approach in various applications, including multi-resolution representations and skeleton-driven shape deformation.KeywordsPoint CloudDisplacement FunctionLocal PatchPoint Cloud DataSubdivision SurfaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A method of constructing smooth tool surfaces for FE prediction of springback in sheet metal forming

Curve and surface representation by iterative B-spine fit to a data point set.

Under the background of intelligent times based on information technology, the analysis and replacement of outliers become particularly critical for databases in the face of massive sequential data streams. In order to improve the effectiveness and practicability of the detection method, this paper determines the abnormal scores of data points in a specific data set by using the K-Sigma algorithm of the Monte Carlo method, adaptively adjusts the k value according to the abnormal scores, and marks the abnormal points.The advantages of the traditional k-sigma algorithm are fast operation speed and theoretical basis, while the disadvantages are that each index dimension is determined independently. However, in industrial production, due to the multi-index dimension of time series data, multiple size indicators of a data set are related to each other. Therefore, it is necessary to comprehensively consider whether an anomaly is abnormal by combining it with the data of other indicators. In addition, when there are no outliers in the data set, the traditional k-sigma algorithm is used to take the mean and variance of the data set as parameters. Due to the limitations of the data set itself, some data points will be mislabeled as outliers. Through the k-sigma algorithm based on the Monte Carlo method, we can effectively solve the above problems.The k-sigma algorithm based on the Monte Carlo method can generate a normal distribution according to the distribution of original data points, and extract a large quantity of data from the distribution to generate Monte Carlo data set. The Mahalanobis distance li from each sample point to the mean in the Monte Carlo data set is calculated and compared with the Mahalanobis distance lj from the samples to be detected to the mean in the original data set. According to the number of sample points satisfying li < lj in the Monte Carlo data set, the value of the parameter kj is determined adaptively, and thus the outliers are determined. We implemented the k-sigma algorithm based on the Monte Carlo method through python, evaluated the effectiveness of the algorithm by accuracy, recall rate, and F1 score, and compared it with some machine learning algorithms. The results verified the feasibility and effectiveness of the algorithm, which can be used for real-time anomaly detection in the energy management database.