Point Set Surfaces Research Articles

Combustion Waves on the Point Set Surface

This paper introduces a combustion model of heat transfer and fuel consumption for the propagation of a fire front on a point cloud surface. The heat transfer includes the heat advection by the airflow as well as diffusion, chemical reaction, and heat loss to generate complex, but controllable heat flows with a designed airflow velocity. For the stable heat advection, we solve a semi-Lagrangian method on point samples using discrete exponential maps to trace the position from which the wind blows while preserving the geodesic distance. We also propose angular Voronoi weights for a discrete Laplace-Beltrami operator that shows better isotropic diffusion on the inhomogeneous distribution of point clouds than the cotangent or moving least-squares schemes. We demonstrate a diversity of burning scenarios by incorporating factors affecting the fire spreading such as buoyancy and object geometries in the airflow velocity fields, or by synthesizing patterns.

Data reduction based on dynamic-threshold uniform grid-algorithm

To reconstruct an object surface from a set of surface points promptly, it is a necessity to reduce the data points. Dynamic-threshold uniform grid-algorithm specifically designed for the needs of CAD/CAM engineering design is proposed. The method builds cubic grids of the original point cloud using uniform grid-algorithm, and chooses the point that is nearest to the center of each cubic grid as a sample. Then, a parametric representation is defined to get the curved surface equation of each cubic grid, and the calculated average curvature of each curved surface is used as the dynamic threshold to decide whether other data points can be the sample. The method is more practical than existing methods because it can process the scattered data points with complex topology and noise effectively, which produces a high-quality data points suited for CAD/CAM. Practical examples given in this paper show that the algorithm can simplify scattered data in a fast and reliable manner.

An integrated CNC accumulation system for automatic building-around-inserts

In this paper a non-layer-based additive manufacturing (AM) process named computer numerically controlled (CNC) accumulation process is presented for applications such as plastic part repairing and modification. To facilitate the CNC accumulation process, a novel three-dimensional (3D) laser scanning system based on a micro-electro-mechanical system (MEMS) device is developed for in situ scanning of inserted components. The integration of the scanning system in the CNC accumulation process enables the building-around-inserts with little human efforts. A point processing method based on the algebraic point set surface (APSS) fitting and layered depth-normal image (LDNI) representation is developed for converting the scanning points into triangular meshes. The newly developed 3D scanning system is compact and has sufficient accuracy for the CNC accumulation process. Based on the constructed surface model, data processing operations including multi-axis tool path planning and motion control are also investigated. Multiple test cases are performed to illustrate the capability of the integrated CNC accumulation process on addressing the requirements of building-around-inserts.

Feature-aware filtering for point-set surface denoising

In this paper, we propose a simple and effective feature-aware filtering for point-set surface denoising, which can achieve a second-order surface approximation of the underlying surface. Our method consists of two stages: robust normal estimation considering sharp features and feature-preserving denoising using a local curvature based projection. The normal clustering based on neighborhood grouping allows the filter to preserve and respect several features during the denoising process. We demonstrate the strength of our method in terms of denoising, feature preservation and computational efficiency.

Contact problem of die regular relief motion over viscoelastic base

The numerical and analytical model is constructed to calculate the deformation friction force component when the regular relief die moves over the viscoelastic base, which is modeled with the Kelvin body with the relation time spectrum. The developed friction model is applicable to both the discrete and full contact between interacting surfaces. The die regular relief is modeled with a set of surface points. The results obtained with the developed model are compared for the case of full contact with the analytic calculation. The sliding velocity and the die regular relief shape are studied to identify the influence on the contact characteristics and the deformation componentof the coefficient of friction.

Nonlinear manifold learning for meshfree finite deformation thin‐shell analysis

SUMMARYCalculations on general point‐set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of a mesh makes it nontrivial to decide if two neighboring points in the three‐dimensional embedding are nearby or rather far apart on the manifold. Furthermore, the topology of surfaces is generally not that of an open two‐dimensional set, ruling out global parametrizations. We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point‐set surface is described by a set of overlapping charts forming a complete atlas. We proceed in four steps: (1) partitioning of the node set into subregions of trivial topology; (2) automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods; (3) parametrization of the surface using smooth meshfree (here maximum‐entropy) approximants; and (4) gluing together the patch representations by means of a partition of unity. Each patch may be viewed as a meshfree macro‐element. We exemplify the generality, flexibility, and accuracy of the proposed approach by numerically approximating the geometrically nonlinear Kirchhoff–Love theory of thin‐shells. We analyze standard benchmark tests as well as point‐set surfaces of complex geometry and topology. Copyright © 2012 John Wiley & Sons, Ltd.

Feature sensitive re-sampling of point set surfaces with Gaussian spheres

Feature sensitive simplification and re-sampling of point set surfaces is an important and challenging issue for many computer graphics and geometric modeling applications. Based on the regular sampling of the Gaussian sphere and the surface normals mapping onto the Gaussian sphere, an adaptive re-sampling framework for point set surfaces is presented in this paper, which includes a naive sampling step by index propagation and a novel cluster optimization step by normalized rectification. Our proposed re-sampling scheme can generate non-uniformly distributed discrete sample points for the underlying point sets in a feature sensitive manner. The intrinsic geometric features of the underlying point set surfaces can be preserved efficiently due to our adaptive re-sampling scheme. A novel splat rendering technique is adopted to illustrate the efficiency of our re-sampling scheme. Moreover, a numerical error statistics and surface reconstruction for simplified models are also given to demonstrate the effectiveness of our algorithm in term of the simplified quality of the point set surfaces.

Direct Numerical Control (NC) Path Generation: From Discrete Points to Continuous Spline Paths

Spline paths in NC machining are advantageous over linear and circular paths due to their smoothness and compact representation, thus are highly desirable in high-speed machining (HSM) where frequent change of tool position and orientation may lead to inefficient machining, tool wear, and chatter. This paper presents an approach for calculating spline NC paths directly from discrete points with controlled accuracy. Part geometry is represented by discrete points via an implicit point set surface (PSS). Cutter location (CL) points are generated directly from implicit part surfaces and interpolated by B-spline curves. A computing procedure for calculating maximum scallop height is given. The procedure is general and suitable for part surfaces in various surface representations provided that the closest distance from a point to the part surface can be calculated. Our results affirm that the proposed approach can produce high-quality B-spline NC paths directly from discrete points. The resulting spline paths make it possible for directly importing discrete points into Computer Numerical Control (CNC) machines for high-speed machining.

Estimating stacking interaction energy using atom in molecules properties: Homodimers of benzene and pyridine

AbstractAn attempt is presented to infer the stacking interaction energy from the atom in molecules (AIM) properties computed in all critical points of electron density found between interacting molecules. In this study, benzene and pyridine homodimers in coaxial and parallel displaced configurations were used as model structures. We classify the structures and briefly discuss their peculiarities in the AIM theory framework. The maximum absolute error of 2 kcal/mol achieved for 300 potential energy surface point set indicates that a more sophisticated algorithm for estimating atom–atom interactions is needed still. © 2012 Wiley Periodicals, Inc.

Feature-Based Identification and Reconstruction of Regular Curves and Surfaces

Based on the preprocessed measuring data, this paper proposes a method for identification and reconstruction of regular curves and surfaces including straight line(segment), circle(arc), four-sided plane and right cylindrical surface. Considering the geometric feature of each kind of regular curve or surface, the paper studies the corresponding algorithm for identifying the curve or surface point set, reconstructs the curve or surface and gives the parameter equation.

Characterizing the image space of a shape-dependent operator for a potential flow problem

We study the reachability of a shape-dependent operator based on a potential flow and give a complete characterization of the image space. We draw a connection between the structure of the image space and the set of stagnation points, i.e. the set of surface points where the tangential velocity vanishes. We use conformal pull-back to a reference domain and reduce the problem to the question of whether there exists a diffeomorphism which pulls back one top-dimensional differential form to another. For volume forms this question has been answered by Moser 1965, but since we do allow singularities we have to prove a modified version. This leads to a volume condition, which must be fulfilled on every connected component of the nonzero set of the form.

Tracing specular light paths in point-based scenes

Massive point data sets representing meticulous details of various heritage sites and statues are now becoming available due to recent advances in multi-view stereo techniques. Photorealistic rendering of such point sets has not yet, however, matched their polygonal counterparts with respect to the interactivity of applications as well as the quality of light simulations. In this paper, we present a framework for tracing specular light paths in massive point model environments at interactive frame rates on Graphics Processing Units (GPUs). We introduce the Sample Octree (S-Octree), a lightweight data structure for efficient, sampled representation of point set information. The Implicit Surface Octree (ISO), an instance of the S-Octree, provides a compact representation of point set surfaces. The ISO defines a local manifold approximation of the input point data. The Caustic Sample Map (CSM), another instance of the S-Octree, represents contributions of caustic paths. These data structures enable us to further the state of the art by demonstrating reflections, refractions, shadows and caustic effects on massive, complex point models at interactive frame rates.

Topologically Enhanced Slicing of MLS Surfaces

Growing use of massive scan data in various engineering applications has necessitated research on point-set surfaces. A point-set surface is a continuous surface, defined directly with a set of discrete points. This paper presents a new approach that extends our earlier work on slicing point-set surfaces into planar contours for rapid prototyping usage. This extended approach can decompose a point-set surface into slices with guaranteed topology. Such topological guarantee stems from the use of Morse theory based topological analysis of the slicing operation. The Morse function for slicing is a height function restricted to the point-set surface, an implicitly defined moving least-squares (MLS) surface. We introduce a Lagrangian multiplier formulation for critical point identification from the restricted surface. Integral lines are constructed to form Morse-Smale complex and the enhanced Reeb graph. This graph is then used to provide seed points for forming slicing contours, with the guarantee that the sliced model has the same topology as the input point-set surface. The extension of this approach to degenerate functions on point-set surface is also discussed.

Adaptive tool-path generation on point-sampled surfaces

► Tool path generating algorithm on point cloud is proposed via direct projection. ► A reference surface is constructed to plan the points to be projected. ► Curve fitting on projecting points is used to rearrange cutter location points. ► It is a rapid, practical method and inexpensive in calculation. In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.

Computing point-set surfaces with controlled spatial variation of residuals

This paper presents an accurate method for computing point-set surfaces from input data that can suppress the noise effect in the resulting point-set surface. This is accomplished by controlling spatial variation of residual errors between the input data and the resulting point-set surface and offsetting any systematic bias. More specifically, this method first reduces random noise of input data based on spatial autocorrelation statistics: the statistics Z via Moran’s I . The bandwidth of the surface is adjusted until the surface reaches desired value of the statistics Z corresponding to a given significance level. The method then compensates for potential systematic bias of the resultant surface by offsetting along computed normal vectors. Computational experiments on various point sets demonstrate that the method leads to an accurate surface with controlled spatial variation of residuals and reduced systematic bias.

Multi-level partition of unity algebraic point set surfaces

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

MESHFREE ELASTODYNAMIC ANALYSIS OF THREE-DIMENSIONAL SOLIDS USING RADIAL POINT INTERPOLATION METHOD

Meshfree methods are effective tools for solving partial differential equations. The radial point interpolation method, a partial differential equation solver based on a meshfree approach, enables accurate imposition of displacement boundary conditions and has been successfully applied to elastostatic analysis of various kinds of three-dimensional solids. In this method, stiffness matrix construction accounts for the majority of CPU time required for the entire process, resulting in high computational costs, especially when higher-order numerical integration is applied for accurate matrix construction. An alternative method, modified radial point interpolation, was proposed to overcome this shortcoming and has accomplished fast computation of elastostatic solid analysis. The purpose of this study is to develop an algorithm for time-dependent simulation of three-dimensional elastic solids. We show that the modified radial point interpolation method also accelerates the construction of the mass matrix required for time-dependent analysis in addition to that of the stiffness matrix. In our approach, the problem domain is assumed to have an implicit function representation that can be constructed from a set of surface points measured using a three-dimensional scanning system. Several numerical tests for elastodynamic analysis of complex shape models are presented.

Multi-Level Partition of Unity Algebraic Point Set Surfaces

Multi-Level Partition of Unity Algebraic Point Set Surfaces

Point Set Surface Reconstruction for VTK

This document presents a set of classes (vtkPointSetSurfaceReconstruction, vtkVoxelizePolyData) to produce a surface from an oriented point set. These classes are implemented as VTK filters. A Paraview plugin interface is provided to allow extremely easy experimentation with the new functionality. We propose these classes as an addition to the Visualization Toolkit. The code is available here: https://github.com/daviddoria/PointSetSurfaceReconstruction

ℓ 1 -Sparse reconstruction of sharp point set surfaces

We introduce an ℓ 1 -sparse method for the reconstruction of a piecewise smooth point set surface. The technique is motivated by recent advancements in sparse signal reconstruction. The assumption underlying our work is that common objects, even geometrically complex ones, can typically be characterized by a rather small number of features. This, in turn, naturally lends itself to incorporating the powerful notion of sparsity into the model. The sparse reconstruction principle gives rise to a reconstructed point set surface that consists mainly of smooth modes, with the residual of the objective function strongly concentrated near sharp features. Our technique is capable of recovering orientation and positions of highly noisy point sets. The global nature of the optimization yields a sparse solution and avoids local minima. Using an interior-point log-barrier solver with a customized preconditioning scheme, the solver for the corresponding convex optimization problem is competitive and the results are of high quality.