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Geometric Modeling and Processing 2000. Theory and Applications. Proceedings

Date 10-12 April 2000

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  • Proceedings Geometric Modeling and Processing 2000. Theory and Applications

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    Freely Available from IEEE
  • Table of contents

    Page(s): V - VIII
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    Freely Available from IEEE
  • Reverse engineering B-rep models from multiple point clouds

    Page(s): 3 - 12
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    The procedure of reconstructing conventional engineering objects from multiple-view 3D point clouds is described. Emphasis is put on producing accurate and topologically consistent B-rep models, ready to be used in computer aided design and manufacture. After describing the basic phases of reverse engineering, related algorithmic difficulties are analyzed. Three particular areas are discussed in more detail: segmenting point data into regions, creating translational and rotational surfaces with smooth, constrained profiles, and finally adding blends. The results of the algorithms are illustrated using a mechanical engineering object, which is a well-known benchmark in the RE community. View full abstract»

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  • A system for constructing boundary representation solid models from a two-dimensional sketch

    Page(s): 13 - 32
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    This paper describes a system which converts a two-dimensional sketch with hidden lines removed of a single polyhedral object into a boundary representation solid model. The system improves on a previous system by Grimstead (1997) by analysing the sketch for symmetry elements and regularities. It uses the results of this analysis to produce a more plausible topological completion of the hidden parts of the object, and to enforce exact constraints on the geometry of the boundary-representation model. View full abstract»

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  • Rapid 3D model acquisition from images of small objects

    Page(s): 33 - 41
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    This paper describes a system for rapid acquisition of 3D models of objects for use in applications such as CAD and VR. The system consists of an image capturing platform, which comprises a PC-controlled turntable and CCD camera, and associated computer vision and graphics algorithms for 3D model acquisition. An algorithm for accurately recovering 3D points from image sequences is described. Experiments performed on synthetic and real data show that the algorithm is accurate in recovering the coordinates of 3D points and is robust against noise in 2D feature location and 3D object rotation. Results of applying the system to acquiring 3D models of real objects are illustrated. View full abstract»

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  • Geometric processing for analysis

    Page(s): 45 - 56
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    Processing geometric models for finite element analysis is a major factor in the time required to develop and optimise a design. Efficient analysis may require simplification of the geometric model by dimensional reduction (replacing thin sheets or slender bars of material with equivalent line or surface elements) or detail suppression (the removal of small features below the scale of interest in the analysis). There are many situations where detailed local models of full dimension could be combined with global models containing reduced dimensional elements, or in which the abstract models used in preliminary design could be used to generate an initial version of the 3D solid model. Furthermore, the most appropriate representation of an object is dependent on the analysis type. These requirements provide significant challenges for future generations of CAE software in feature recognition and the modelling and representation of geometric objects. View full abstract»

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  • A feature-based approach to automatic injection mold generation

    Page(s): 57 - 68
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    This paper presents a feature-based approach to the automatic generation of an injection mold. In the approach, all the molding features of a molded part are recognized first using a universal hint-based feature recognition algorithm, and the optimal parting direction is determined based on the feature model. Then, all the faces related with the parting line are classified into three groups according to the determined parting direction, and two kinds of parting lines are automatically determined by extracting the largest profile of each face group. Finally, the parting surface is generated based on the optimal pacing line, thereafter the mold core and mold cavity are automatically set up by splitting the mold box of the molded part with the generated parting surface. By using recognized molding features, the approach makes it possible to identify all undercuts, to determine internal parting lines and internal parting surfaces, to generate the mold core and cavity of a complex molded part with undercuts as well. View full abstract»

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  • Effect of fabric properties on cloth draping modeling

    Page(s): 69 - 76
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    Cloth draping is of particular interest in the field of garment engineering. Most cloth draping simulation stresses the visual effects of garment design. However, the accuracy of the draping effect should not be overlooked, particularly for garment manufacturing. The accuracy of the draping behaviour is largely affected by the fabric properties. This paper discusses the issue of incorporating the fabric properties into the cloth model, so that its draping behaviour can be realistically simulated. These fabric properties are expressed in terms of a set of measurable mechanical properties. The draping behaviour of the cloth is derived based on elastic theory. Dynamic draping simulation is presented with illustrative examples. View full abstract»

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  • A representation independent geometric modeling kernel

    Page(s): 79 - 89
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    This paper is concerned with "open kernel" geometric modelling systems. It uses industrial needs to identify requirements for the geometric objects of a proposed interface. The necessary mixed-dimension cellular objects are formally defined as the fundamental data abstractions for that interface. Such definitions are imperative for the construction of robust functions and the integrity of data transfer. As an example, formal specifications are provided for "set-like" object combination functions. View full abstract»

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  • Dimension-driven parameterized design of free form objects

    Page(s): 90 - 100
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    The paper develops a theoretical basis for dimension-driven parameterized design of free form objects. In traditional parametric computer-aided design (CAD) systems, research is focused on the representation of dimension parameters and constraint satisfaction algorithms. Dimension-driven free form object parameterized design is to obtain a new free form object similar in shape to the old one but with different sets of dimension parameter instantiation. In other words, a new member of the master free form object's family will be designed. However, research on dimension-driven parameterized design of free form objects is an unattempted area. Also, there is no commercial CAD system that can deal with dimension-driven free form objects successfully. In this research, we exploit a new concept of similar shape applicable to 3D rational curves and surfaces. Dimension-driven variation of similar free form objects is then explained and illustrated with an example. View full abstract»

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  • On families of objects and their semantics

    Page(s): 101 - 111
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    An approach is presented to define a family of objects in parametric modelling. It avoids an inherent problem of boundary re-evaluation in current parametric modelling systems. Even more important, it offers an effective way to define the properties, or semantics of a family of objects. A family of objects is defined by a prototype feature model, including several types of constraints to precisely specify its semantics. A family membership test is used to check whether an instance corresponding to a particular set of parameter values belongs to a family. The underlying geometric representation is a non-manifold cellular model. View full abstract»

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  • Proximity queries for modeling and manufacturing

    Page(s): 115 - 122
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    Collision detection and distance calculation are two examples of proximity queries between modelled objects. They are interesting both in their own right, and as useful tools to solve other problems (e.g., robot path planning). They also form useful abstractions away from the underlying representation of a geometric model. This paper considers the solution and use of such problems in geometric modeling and robotics, gives examples from our own work, and discusses the possible future of the technology. View full abstract»

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  • Distance computation between non-convex polyhedra at short range based on discrete Voronoi regions

    Page(s): 123 - 128
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    An algorithm for calculating the minimum distance between non-convex polyhedra is described. A polyhedron is represented by a set of triangles. In calculating the distance between two polyhedra, it is important to search efficiently the pair of the triangles which gives the pair of closest points. In our algorithm discrete Voronoi regions are prepared as voxels around a non-convex polyhedron. Each voxel is given the list of triangles which have the possibility of being the closest to the points in the voxel. When a triangle on the other object is intersecting a voxel, the closest triangles can be efficiently searched from this list on the voxel. The algorithm has been implemented, and the results of distance computations show that it can calculate the minimum distance between non-convex polyhedra composed of a thousand triangles at interactive rates. View full abstract»

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  • A sequence of generalized coordinate systems based on Voronoi diagrams and its application to interpolation

    Page(s): 129 - 137
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    This paper presents a general framework for constructing a variety of multi-dimensional interpolants based on Voronoi diagrams. This framework includes previously known methods such as Sibson's interpolant and Laplace's interpolant; moreover it contains infinitely many new interpolants. Computational experiments suggest that the smoothness can be improved by the proposed generalization. In addition, this framework also includes the piecewise linear interpolant over the Delaunay triangulation, which is a finite-element interpolant. This fact suggests that already established techniques in the finite element method might be brought into the research of the Voronoi-based approach. Hence this framework gives a new and promising direction of research on interpolation based on Voronoi diagrams. View full abstract»

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  • Poisson approximation

    Page(s): 141 - 149
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    Poisson approximation extends the Bernstein-Bezier scheme from polynomials to arbitrary analytic functions. A survey of some old and new results in Poisson approximation is presented with special emphasis on algorithmic techniques for analytic functions. View full abstract»

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  • Optimization of knots for the multi curve B-spline approximation

    Page(s): 150 - 161
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    This article presents a method for multi curve approximation with B-splines. The approximation is formulated as a constrained optimization problem with the least squares error as the objective function and the knot vector as the variables. The method presented in this article is designed to eliminate the well-known lethargic behaviour and to maintain the accuracy of control points. The method for fitting skeletal curves was tested on a single-section case and a multi-section case. The tests showed that the method reduces the objective function significantly. The proposed method has potential applications in the shape design of wings, turbine blades and automotive body panels. View full abstract»

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  • Constrained C/sup 1/ piecewise bicubic Bezier surface interpolation

    Page(s): 162 - 171
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    The construction of a C/sup 1/ piecewise bicubic Bezier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials. View full abstract»

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  • Approximating NURBS curves by arc splines

    Page(s): 175 - 183
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    It is desirable to approximate a smooth curve by arc splines with the fewest segments within a prescribed tolerance. We present an efficient algorithm for fitting planar smooth curves by arc splines. The main idea is that we construct the optimal arc spline by optimizing the interpolating biarc curve. The scheme consists of three steps: sampling the curve based on consecutive tangent deviation; construct the interpolating arc spline; and reduce the arc number to the minimum within a prescribed tolerance. The algorithm can control the approximating error efficiently and results in the fewest number of arc segments. View full abstract»

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  • A method of shape control of curve design

    Page(s): 184 - 189
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    Constraining an interpolating curve to be bounded in a given region is an important task in curve design. In (Qi Duan et al., 1999) the rational cubic spline with a linear denominator has been used to control the interpolating curves to be bounded in the given region, but it does not work in some cases. This paper deals with the weighted rational cubic spline with a linear denominator for this kind of constraint, the sufficient condition for controlling the interpolating curves to be bounded in the given region are derived. An example is given which shows that the constraint which cannot be done by the rational spline defined in (Qi Duan et al., 1999) could be achieved by the weighted rational spline. View full abstract»

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  • Recursive formulae for Hermite polynomial approximations to rational Bezier curves

    Page(s): 190 - 197
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    This paper presents the algorithms for calculating the control points of Hermite polynomial approximation to rational Bezier curves and the recursive formulae between different degree Hermite polynomial approximations based on the close relationship between hybrid polynomial approximation and Hermite polynomial approximation. The error bound for the Hermite polynomial approximation is also obtained. View full abstract»

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  • Robust watermarking of polygonal meshes

    Page(s): 201 - 208
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    This paper presents two variations of a robust watermarking method for general polygonal meshes of arbitrary topology which can be used for copyright protection, tamper proofing or content annotation purposes. The proposed watermark is immune to translation, rotation, scaling or affine transformation of the mesh and is hard to detect unless the exact encoding parameters are disclosed. Several examples demonstrate the effectiveness of the algorithm. View full abstract»

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  • On-line polygon refining using a low computation subdivision algorithm

    Page(s): 209 - 219
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    Subdivision algorithms have been extensively used in computer graphics to produce a more accurate geometry model. For the purpose of integration into the context of a standard graphics pipeline for real-time display, we can only make use of the available information of one triangle. We propose a low computation cost algorithm to subdivide a polygon using vertex coordinates and vertex normal vectors of one triangle. Compared with other suitable algorithms, our algorithm produces decent results with lowest computational complexity. We also consider the generation of interpolated normal vectors and texture mapping parameters. Detailed comparisons among other suitable algorithms are presented. View full abstract»

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  • Using most isometric parameterizations for remeshing polygonal surfaces

    Page(s): 220 - 228
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    The importance of triangle meshes with a special kind of connectivity, the so-called subdivision connectivity is still growing. Therefore it is important to develop efficient algorithms for converting a given mesh with arbitrary connectivity into one with subdivision connectivity. We focus on 2-manifold triangle meshes with a boundary and no holes. We discuss the importance of a parametrization with minimal distortion for the process of remeshing. Based on the concept of most isometric parameterizations we have developed a remeshing algorithm for the given class of triangle meshes. A series of examples shows the advantages of our approach. View full abstract»

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  • Polyhedral surface smoothing with simultaneous mesh regularization

    Page(s): 229 - 237
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    A computer graphics object reconstructed from real-world data often contains undesirable noise and small-scale oscillations. An important problem is how to remove the noise and oscillations while preserving desirable geometric features of the object. We develops methods for polyhedral surface smoothing and denoising with simultaneous increasing mesh regularity. We also propose an adaptive smoothing method allowing to reduce possible oversmoothing. Roughly speaking, our smoothing schemes consist of moving every vertex in the direction defined by the Laplacian flow with speed equal to a properly chosen function of the mean curvature at the vertex. View full abstract»

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  • Approximate shortest path on a polyhedral surface based on selective refinement of the discrete graph and its applications

    Page(s): 241 - 250
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    A new algorithm is proposed for calculating the approximate shortest path on a polyhedral surface. The method mainly uses Dijkstra's algorithm and is based on selective refinement of the discrete graph of a polyhedron. Although the algorithm is an approximation, it has the significant advantages of being fast, easy to implement, high approximation accuracy, and numerically robust. The approximation accuracy and computation time are compared between this approximation algorithm and the extended Chen and Han (1990) (ECH) algorithm that can calculate the exact shortest path for non-convex polyhedra. The approximation algorithm can calculate shortest paths within 0.4% accuracy to roughly 100-1000 times faster than the ECH algorithm in our examples. Two applications are discussed of the approximation algorithm to geometric modeling. View full abstract»

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