Vector interpolation for surface normal calculation

The problem of approximating a surface normal by linear interpolation across a surface facet is considered from a geometric point of view. This point of view makes the coordinate independence for triangular facets particularly easy to see, and provides some insight into the problem of non-uniqueness for the non-triangular case.     

Efficient surface reconstruction method for distributed CAD

This paper describes a new fast Reverse Engineering (RE) method for creating a 3D computerized model from an unorganized cloud of points. The proposed method is derived directly from the problems and difficulties currently associated with remote design over the Internet, such as accuracy, transmission time and representation at different levels of abstraction. With the proposed method, 3D models suitable for distributed design systems can be reconstructed in real time. The mesh reconstruction approach is based on aggregating very large scale 3D scanned data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. Then, a Connectivity Graph (CG) is extracted and filled with facets. The HSDM can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the surface reconstruction process becomes robust and stable with respect to sampling noise. Moreover, the data received from different surface/volume sampling devices can be handled naturally. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving significant geometrical features and object topology. As a result, reconstruction and transmission over the network are efficient. Furthermore, the hierarchical representation provides a capability for extracting models at desired levels of detail, thus enabling designers to collaborate at any product development stage: draft or detailed design.     

A new mesh-growing algorithm for fast surface reconstruction

This paper presents a new high-performance method for triangular mesh generation based on a mesh-growing approach. Starting from a seed triangle, the algorithm grows the triangular mesh by selecting a new point based on the Gabriel 2—Simplex criterion. This criterion can be considered to be a good approximation of the 2D Delaunay if the point cloud is well-sampled and not too rough. The performance of the proposed method is compared with that of the Cocone family and that of Ball Pivoting as regards the tessellation rate and the quality of the surface being generated from some benchmark point clouds and artificially noised test cases. The results are analysed and critically discussed.     

A volume-of-fluid interfacial flow solver with advected normals

We presented a new approach to calculating normal vectors to fluid interfaces in [JCP, 2007;226:774-97], by advecting unit normals along with an interface. In this paper, we introduce an implementation of the method in an interfacial flow solver. The advected normals are used to compute the interface curvature for calculating the surface tension force, and for reconstructing the interface in a volume-conserving volume-of-fluid (VOF) method. To improve the performance of the method in under-resolved regions of the flow, where normals vary sharply, a curvature-based criterion is used to detect and correct poorly defined normals. We present two-dimensional results of advection as well as actual flow problems and demonstrate that the new method is well suited for problems that involve large interface deformation and breakup (i.e. problems that involve substantial interface movement).     

Optimization-based approach for curve and surface reconstruction

This paper introduces an optimization-based approach for the curve reconstruction problem, where piecewise linear approximations are computed from sets of points sampled from target curves. In this approach, the problem is formulated as an optimization problem. To be more concrete, at first the Delaunay triangulation for the sample points is computed, and a weight is assigned with each Delaunay edge. Then the problem becomes minimization or maximization of the total weights of the edges that constitute the reconstruction. This paper proposes one exact method and two approximate methods, and shows that the obtained results are improved both theoretically and empirically. In addition, the optimization-based approach is further extended to three dimensions, where surfaces are to be reconstructed, and the quality of the reconstructions is examined.     

一种软件可靠性测试方法研究

为了缩短软件测试周期,本文把马尔可夫链模型运用于软件可靠性测试中,提出了这一技术进行软件可靠性测试的方法。在测试过程中使用了新的评判准则分析测试结果,通过实例证明了该评判准则的实用性和有效性。     

A greedy Delaunay-based surface reconstruction algorithm

In this paper, we present a new greedy algorithm for surface reconstruction from unorganized point sets. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first and in such a way as to prevent the appearance of topological singularities. The output is thus guaranteed to be a piecewise linear orientable manifold, possibly with boundary. Experiments show that this method is very fast and achieves topologically correct reconstruction in most cases. Moreover, it can handle surfaces with complex topology, boundaries, and nonuniform sampling.     

On surface reconstruction: A priority driven approach

To reconstruct an object surface from a set of surface points, a fast, practical, and efficient priority driven algorithm is presented. The key idea of the method is to consider the shape changes of an object at the boundary of the mesh growing area and to create a priority queue to the advancing front of the mesh area according to the changes. The mesh growing process is then driven by the priority queue for efficient surface reconstruction. New and practical triangulation criteria are also developed to support the priority driven strategy and to construct a new triangle at each step of mesh growing in real time. The quality and correctness of the created triangles will be guaranteed by the triangulation criteria and topological operations. The algorithm can reconstruct an object surface from unorganized surface points in a fast and reliable manner. Moreover, it can successfully construct the surface of the objects with complex geometry or topology. The efficiency and robustness of the proposed algorithm is validated by extensive experiments.     

Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology

In this paper, a novel approach is proposed to reliably reconstruct the geometric shape of a physically existing object based on unorganized point cloud sampled from its boundary surface. The proposed approach is composed of two steps. In the first step, triangle mesh structure is reconstructed as a continuous manifold surface by imposing explicit relationship among the discrete data points. For efficient reconstruction, a growing procedure is employed to build the 2-manifold directly without intermediate 3D representation. Local and global topological operations with ensured completeness and soundness are defined to incrementally construct the 2-manifold with arbitrary topology. In addition, a novel criterion is proposed to control the growing process for ensured geometric integrity and automatic boundary detection with a non-metric threshold. The reconstructed manifold surface captures the object topology with the built-in combinatorial structure and approximates the object geometry to the first order. In the second step, new methods are proposed to efficiently obtain reliable curvature estimation for both the object surface and the reconstructed mesh surface. The combinatorial structure of the triangle mesh is then optimized by changing its local topology to minimize the curvature difference between the two surfaces. The optimized triangle mesh achieves second order approximation to the object geometry and can serve as a basis for many applications including virtual reality, computer vision, and reverse engineering.     

A second order geometric method for ray/parametric surface intersection

In this paper, a new method for computing intersection between a ray and a parametric surface is proposed, which finds many applications in computer graphics, robotics and geometric modeling. The method uses the second order derivative of the surface, which can handle inherent problems that Newton–Raphson and Halley methods have such as instability caused by inappropriate initial conditions and tangential intersection. Case examples are presented to demonstrate the capability of the proposed method.     

A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.     

A method for computation of surface roughness of digital elevation model terrains via multiscale analysis

In this paper, an algorithm to compute surface roughness of digital elevation model (DEM) terrains via multiscale analysis is proposed. The algorithm employs the lifting scheme to generate multiscale DEMs. At each scale, the areas of pixels that are modified are computed. Granulometric analysis is employed to compute the average area of curvature regions in the terrain, and the average roughness of the terrain due the distribution of curvature regions. The selected case studies of the algorithm implementation demonstrated that the proposed algorithm provides a surface roughness parameter that is realistic with respect to the amplitudes and frequencies of the terrain, invariant with respect to rotation and translation, and has intuitive meaning. The algorithm allows for a good quantification of a region’s convexity/concavity over varying scales, distinguishing between shallow and deep incisions of valleys and ridges of the terrain, and hence, provides an accurate surface roughness parameter.     

A probabilistic task scheduling method for grid environments

This paper presents a probabilistic task scheduling method to minimize the overall mean response time of the tasks submitted to the grid computing environments. Minimum mean response time of a given task can be obtained by finding a subset of appropriate computational resources to service the task. To achieve this, a discrete time Markov chain (DTMC) representing the task scheduling process within the grid environment is constructed. The connection probabilities between the nodes representing the grid managers and resources can be considered as transition probabilities of the obtained DTMC. Knowing the mean response times of the managers and resources, and finding fundamental matrix of the DTMC, the mean response time related to each of the absorbing DTMCs existing inside the overall DTMC can be computed. Minimizing the obtained mean response times and taking into account the probability constraints in each of the absorbing DTMCs, a nonlinear programming (NLP) problem is defined. Solving the NLP problem, the connection probabilities between the managers and resources are obtained. Finally, using the connection probabilities, the best scheduling path within the environment and the minimum mean response time of a particular task can be achieved. In a case in which there is only one optimal scheduling choice within the environment, the proposed method can deterministically find such scheduling by assigning zero or one to the connection probabilities. Results obtained from evaluating the proposed method on the hypothesis and real grid environments show the preference of the proposed method compared to the other methods in minimizing both the overall mean response time of the tasks and total makespan of the environment.     

Novel method for measuring surface tension

It is shown that the observed geometry of an electrostatic deformation of a liquid surface can be used for the measurement of surface tension. Based on simulations and measurements, an empirical formula for the relation between the shape of the deformation and the surface tension is derived and discussed. A novel method for high resolution measurements of the surface tension using interferometry of an electrostatically deformed liquid surface is presented and investigated.     

Surface and normal ensembles for surface reconstruction

The majority of the existing techniques for surface reconstruction and the closely related problem of normal reconstruction are deterministic. Their main advantages are the speed and, given a reasonably good initial input, the high quality of the reconstructed surfaces. Nevertheless, their deterministic nature may hinder them from effectively handling incomplete data with noise and outliers. An ensemble is a statistical technique which can improve the performance of deterministic algorithms by putting them into a statistics based probabilistic setting. In this paper, we study the suitability of ensembles in normal and surface reconstruction. We experimented with a widely used normal reconstruction technique [Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. Surface reconstruction from unorganized points. Computer Graphics 1992;71-8] and Multi-level Partitions of Unity implicits for surface reconstruction [Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel H-P. Multi-level partition of unity implicits. ACM Transactions on Graphics 2003;22(3):463-70], showing that normal and surface ensembles can successfully be combined to handle noisy point sets.     

Reconstructing Curves without Delaunay Computation

A new non-Delaunay-based approach is presented to reconstruct a curve, lying in 2- or 3-space, from a sampling of points. The underlying theory is based on bounding curvature to determine monotone pieces of the curve. Theoretical guarantees are established. The implemented algorithm, based heuristically on the theory, proceeds by iteratively partitioning the sample points using an octree data structure. The strengths of the approach are (a) simple implementation, (b) efficiency-experimental performance compares favorably with Delaunay-based algorithms, (c) robustness-curves with multiple components and sharp corners are reconstructed satisfactorily, and (d) potential extension to surface reconstruction.     

Rolling ball method for 5-axis surface machining

Curvature matching for 5-axis surface machining has been plagued by the complexity of the task. As a result the current tool positioning strategies are likewise computationally complicated. Gouging the surface has been the main concern and has presented the greatest difficulty in the algorithms. Some of the methods perform exhaustive searches of the surface to avoid gouging while others incrementally adjust the tool orientation until gouges are no longer detected. In this paper a new positioning strategy is presented that is simple to implement and is not difficult to compute. The rolling ball method rolls a variable radius ball along the tool path and positions the cutting tool to cut the rolling ball. A small region of the ball's surface is used to approximate a small region of the surface being machined. The radius of each ball is computed by checking a grid of points in the area of the surface that the tool casts a shadow for each tool position. A pseudo-radius is computed for each grid point and the most appropriate radius is selected to be the rolling ball's radius. The selection process follows a hierarchy of surface profiles ranging from convex to concave. Convex, concave, and saddle (mixed) surface regions are all computed in a similar fashion and there are no special cases for which the positioning strategy must be changed to compute a tool position. Local gouge checking is automatically built-in to the positioning computations so that the typical iterative strategy of checking for gouging, then incrementally tilting the tool until no gouges are detected is eliminated. The method is robust and simple to implement and it only requires surface coordinates and surface normals. A simulation of the method and a cutting test were performed and are presented in this document.