Punctuated simplification of man-made objects

We present a simplification algorithm for manifold polygonal meshes of plane-dominant models. Models of this type are likely to appear in man-made environments. While traditional simplification algorithms focus on generality and smooth meshes, the approach presented here considers a specific class of man-made models. By detecting and classifying edge loops on the mesh and providing a guided series of binary mesh partitions, our approach generates a series of simplified models, each of which better respects the semantics of these kinds of models than conventional approaches do. A guiding principle is to eliminate simplifications that do not make sense in constructed environments. This, coupled with the concept of “punctuated simplification”, leads to an approach that is both efficient and delivers high visual quality. Comparative results are given.     

User-assisted simplification method for triangle meshes preserving boundaries

This paper proposes a user-assisted mesh simplification method applied to CAD models converted to triangle meshes. This work offers the possibility of simplifying each subobject independently and at different levels of detail. This way, the user can simplify the whole model and then modify some parts, by simplifying more or by refining the desired subobjects. This can be performed while the total number of triangles in the simplified model is maintained. In this method any error metric based on an edge collapse operation can be used. Boundaries between subobjects are preserved and important attributes in the final aspect of simplified models, like normals and texture coordinates, are also considered.     

Analyzing topological changes for structural shape simplification

The shapes of regions tend to be simplified with the decrease of spatial scale or resolution, which further leads to topological changes. Analyzing topological changes is an important aspect of formalizing semantic relations. An important fact is observed that shape simplification can be considered as a combination of generalizing basic primitives. Based on this fact, a shape is decomposed first into a set of simple primitives including convexities and concavities. And then the topological changes between lines and regions can be derived from the relations between lines and primitives. The approaches presented in this study can help to analyze the exact types and locations of topological changes for generalizing convexities and concavities, respectively. The approaches need not to conduct the real simplification of shapes, and they instead incorporate the idea of simplification for deriving the changes. Thus, they are independent on the algorithms of geometrical simplification. A prototype is developed and tested using the real world examples. The results show that the approaches in this study are helpful to analyze topological changes for shape simplification.     

Robust adaptive polygonal approximation of implicit curves

We present an algorithm for computing a robust adaptive polygonal approximation of an implicit curve in the plane. The approximation is adapted to the geometry of the curve because the length of the edges varies with the curvature of the curve. Robustness is achieved by combining interval arithmetic and automatic differentiation.     

Geometric model simplification for distributed CAD

Visualization of CAD models in distributed design environment is an essential feature to support collaborative design. To efficiently transmit and render CAD models geometric simplification can be applied to CAD models. However, it is difficult to use available general geometric simplification algorithms because these algorithms are not designed to handle mechanical CAD parts. Applying general simplification on a CAD model would result in distortion of design features and make them unrecognizable to viewers. In this paper, a novel approach is proposed to exploit trimming information in CAD models to simplify their geometry. Visibility culling is integrated into this approach to facilitate selective refinements. The work introduced here aims to support visualization of multiple CAD models in a distributed CAD environment. Implementation details are included and case studies are demonstrated.     

A genetic algorithm for combined topology and shape optimisations

A method to find optimal topology and shape of structures is presented. With the first the optimal distribution of an assigned mass is found using an approach based on homogenisation theory, that seeks in which elements of a meshed domain it is present mass; with the second the discontinuous boundaries are smoothed. The problem of the optimal topology search has an ON/OFF nature and has suggested the employment of genetic algorithms. Thus in this paper a genetic algorithm has been developed, which uses as design variables, in the topology optimisation, the relative densities (with respect to effective material density) 0 or 1 of each element of the structure and, in the shape one, the coordinates of the keypoints of changeable boundaries constituted by curves. In both the steps the aim is that to find the variable sets producing the maximum stiffness of the structure, respecting an upper limit on the employed mass. The structural evaluations are carried out with a FEM commercial code, linked to the algorithm. Some applications have been performed and results compared with solutions reported in literature.     

Perception-based model simplification for motion blur rendering

Motion blur effects are important to motion perception in visual arts, interactive games and animation applications. Usually, such motion blur rendering is quite time consuming, thus blocking the online/interactive use of the effects. Motivated by the human perception in relation to moving objects, this paper presents simplified geometric models that enable to speedup motion blur rendering, which has not been tracked in motion blur rendering specifically. We develop a novel algorithm to simplify models with motion-aware, to preserve the features whose characteristics are perceivable in motion. We deduce the formula to outline the level of detail simplification by the object moving velocity. Using our simplified models, methods for motion blur rendering can achieve the rendering quality as using the original models, and obtain the processing acceleration mostly. The experimental results have shown the effectiveness of our approach, more acceleration with the larger models or faster motion (e.g. for the dragon model with over a million facets, the motion-blur rendering via hierarchical stochastic rasterization is sped up by over 27 times).     

Manifold-guaranteed out-of-core simplification of large meshes with controlled topological type

In this paper, a simple and efficient algorithm is proposed for manifold-guaranteed out-of-core simplification of large meshes with controlled topological type. By dual-sampling the input large mesh model, the proposed algorithm utilizes a set of Hermite data (sample points with normals) as an intermediate model representation, which allows the topological structure of the mesh model to be encoded implicitly and thus makes it particularly suitable for out-of-core mesh simplification. Benefiting from the construction of an in-core signed distance field, the proposed algorithm possesses a set of features including manifoldness of the simplified meshes, toleration of nonmanifold mesh data input, topological noise removal, topological type control and, sharp features and boundary preservation. A novel, detailed implementation of the proposed algorithm is presented, and experimental results demonstrate that very large meshes can be simplified quickly on a low-cost off-the-shelf PC with tightly bounded approximation errors and with time and space efficiency.     

ASM: An adaptive simplification method for 3D point-based models

Due to the popularity of computer games and computer-animated movies, 3D models are fast becoming an important element in multimedia applications. In addition to the conventional polygonal representation for these models, the direct adoption of the original scanned 3D point set for model representation is recently gaining more and more attention due to the possibility of bypassing the time consuming mesh construction stage, and various approaches have been proposed for directly processing point-based models. In particular, the design of a simplification approach which can be directly applied to 3D point-based models to reduce their size is important for applications such as 3D model transmission and archival. Given a point-based 3D model which is defined by a point set P () and a desired reduced number of output samples n^s, the simplification approach finds a point set P_s which (i) satisfies |P_s|=n^s (|P_s| being the cardinality of P_s) and (ii) minimizes the difference of the corresponding surface S_s (defined by P_s) and the original surface S (defined by P). Although a number of previous approaches has been proposed for simplification, most of them (i) do not focus on point-based 3D models, (ii) do not consider efficiency, quality and generality together and (iii) do not consider the distribution of the output samples. In this paper, we propose an Adaptive Simplification Method (ASM) which is an efficient technique for simplifying point-based complex 3D models. Specifically, the ASM consists of three parts: a hierarchical cluster tree structure, the specification of simplification criteria and an optimization process. The ASM achieves a low computation time by clustering the points locally based on the preservation of geometric characteristics. We analyze the performance of the ASM and show that it outperforms most of the current state-of-the-art methods in terms of efficiency, quality and generality.     

Generating high-quality discrete LOD meshes for 3D computer games in linear time

The real-time interactive 3D multimedia applications such as 3D computer games and virtual reality (VR) have become prominent multimedia applications in recent years. In these applications, both visual fidelity and degree of interactivity are usually crucial to the success or failure of employment. Although the visual fidelity can be increased using more polygons for representing an object, it takes a higher rendering cost and adversely affects the rendering efficiency. To balance between the visual quality and the rendering efficiency, a set of level-of-detail (LOD) meshes has to be generated in advance. In this paper, we propose a highly efficient polygonal mesh simplification algorithm that is capable of generating a set of high-quality discrete LOD meshes in linear run time. The new algorithm adopts memoryless vertex quadric computation, and suggests the use of constant size replacement selection min-heap, pipelined simplification, two-stage optimization, and a new hole-filling scheme, which enable it to generate very high-quality LOD meshes using relatively small amount of main memory space in linear runtime.     

Moment-based methods for polygonal approximation of digitized curves

Object shape representation plays an important role in the area of image processing, pattern recognition and computer vision. In the past two decades, many algorithms have been suggested for creating approximated polygons. In this study, two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of Legendre polynomials are proposed. The difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function. Each algorithm provides various polygonal approximation results with different number of line segments for different application situations. For a given error bound, we can determine the optimal polygon with a minimum number of line segments. The procedures are applied to some digital curves and better results are obtained in comparison with some known methods.     

A new construction of smooth surfaces from triangle meshes using parametric pseudo-manifolds

We introduce a new manifold-based construction for fitting a smooth surface to a triangle mesh of arbitrary topology. Our construction combines in novel ways most of the best features of previous constructions and, thus, it fills the gap left by them. We also introduce a theoretical framework that provides a sound justification for the correctness of our construction. Finally, we demonstrate the effectiveness of our manifold-based construction with a few concrete examples.     

Computational topology for isotopic surface reconstruction

New computational topology techniques are presented for surface reconstruction of 2-manifolds with boundary, while rigorous proofs have previously been limited to surfaces without boundary. This is done by an intermediate construction of the envelope   (as defined herein) of the original surface. For any compact C²$C^2$-manifold M$M$ embedded in R³${\mathbf{R}}^3$, it is shown that its envelope is C^1,1$C^{1,1}$. Then it is shown that there exists a piecewise linear (PL) subset of the reconstruction of the envelope that is ambient isotopic to M$M$, whenever M$M$ is orientable. The emphasis of this paper is upon the formal mathematical proofs needed for these extensions. (Practical application examples have already been published in a companion paper.) Possible extensions to non-orientable manifolds are also discussed. The mathematical exposition relies heavily on known techniques from differential geometry and topology, but the specific new proofs are intended to be sufficiently specialized to prompt further algorithmic discoveries.     

Honeycomb Wachspress finite elements for structural topology optimization

Traditionally, standard Lagrangian-type finite elements, such as linear quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these conventional elements exhibit the well-known “checkerboard” pathology in the iterative solution of topology optimization problems. A feasible alternative to eliminate such long-standing problem consists of using hexagonal (honeycomb) elements with Wachspress-type shape functions. The features of the hexagonal mesh include two-node connections (i.e. two elements are either not connected or connected by two nodes), and three edge-based symmetry lines per element. In contrast, quads can display one-node connections, which can lead to checkerboard; and only have two edge-based symmetry lines. In addition, Wachspress rational shape functions satisfy the partition of unity condition and lead to conforming finite element approximations. We explore the Wachspress-type hexagonal elements and present their implementation using three approaches for topology optimization: element-based, continuous approximation of material distribution, and minimum length-scale through projection functions. Examples are presented that demonstrate the advantages of the proposed element in achieving checkerboard-free solutions and avoiding spurious fine-scale patterns from the design optimization process.     

Interpolatory,solid subdivision of unstructured hexahedral meshes

This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes. To date, nearly every existing volumetric subdivision scheme is approximating, i.e., with each application of the subdivision algorithm, the geometry shrinks away from its control mesh. Often, an approximating algorithm is undesirable and inappropriate, producing unsatisfactory results for certain applications in solid modeling and engineering design (e.g., finite element meshing). We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials. We show that our algorithm is a natural generalization of the butterfly subdivision surface scheme to a tri-variate, volumetric setting.     

A review of optimization of cast parts using topology optimization

In recent years, there has been considerable progress in the optimization of cast parts with respect to strength, stiffness, and frequency. Here, topology optimization has been the most important tool in finding the optimal features of a cast part, such as optimal cross-section or number and arrangement of ribs. An optimization process with integrated topology optimization has been used very successfully at Adam Opel AG in recent years, and many components have been optimized. This two-paper review gives an overview of the application and experience in this area. This is the first part of a two-paper review of optimization of cast parts.Here, we want to focus on the application of the original topology optimization codes, which do not take manufacturing constraints for cast parts into account. Additionally, the role of shape optimization as a fine-tuning tool will be briefly analyzed and discussed.     

Uniform offsetting of polygonal model based on Layered Depth-Normal Images

Uniform offsetting is an important geometric operation for computer-aided design and manufacturing (CAD/CAM) applications such as rapid prototyping, NC machining, coordinate measuring machines, robot collision avoidance, and Hausdorff error calculation. We present a novel method for offsetting (grown and shrunk) a solid model by an arbitrary distance r. First, offset polygons are directly computed for each face, edge, and vertex of an input solid model. The computed polygonal meshes form a continuous boundary; however, such a boundary is invalid since there exist meshes that are closer to the original model than the given distance r as well as self-intersections. Based on the problematic polygonal meshes, we construct a well-structured point-based model, Layered Depth-Normal Image (LDNI), in three orthogonal directions. The accuracy of the generated point-based model can be controlled by setting the tessellation and sampling rates during the construction process. We then process all the sampling points in the model by using a set of point filters to delete all the invalid points. Based on the remaining points, we construct a two-manifold polygonal contour as the resulting offset boundary. Our method is general, simple and efficient. We report experimental results on a variety of CAD models and discuss various applications of the developed uniform offsetting method.     

A survey of CAD model simplification techniques for physics-based simulation applications

Automated CAD model simplification plays an important role in effectively utilizing physics-based simulation during the product realization process. Currently a rich body of literature exists that describe many successful techniques for fully-automatic or semi-automatic simplification of CAD models for a wide variety of applications. The purpose of this paper is to compile a list of the techniques that are relevant for physics-based simulations problems and to characterize them based on their attributes. We have classified them into the following four categories: techniques based on surface entity based operators, volume entity based operators, explicit feature based operators, and dimension reduction operators. This paper also presents the necessary background information in the CAD model representation to assist the new readers. We conclude the paper by outlining open research directions in this field.     

Automatic small blend recognition from B-rep models for analysis

The recognition and suppression of small features from B-rep models play an important role in effectively generating the qualified mesh for analysis. This paper presents a new algorithm for recognizing small blends automatically for the purpose of mesh generation. The algorithm first transforms the input B-rep model into an aggregation of faces. Then, each face is judged to be a blend or not based on matching conditions. At last, the blends with larger physical sizes than a threshold value are excluded. The innovations lie in the recognition conditions and the unique calculating procedure of the blend physical size. Several examples are given to demonstrate the validity and applicability of the algorithm.     

Gradient algorithms for polygonal approximation of convex contours

The subjects of this paper are descent algorithms to optimally approximate a strictly convex contour with a polygon. This classic geometric problem is relevant in interpolation theory and data compression, and has potential applications in robotic sensor networks. We design gradient descent laws for intuitive performance metrics such as the area of the inner, outer, and “outer minus inner” approximating polygons. The algorithms position the polygon vertices based on simple feedback ideas and on limited nearest-neighbor interaction.