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Constrained airfoil optimization using the area-preserving free-form deformation

AIRCRAFT ENGINEERING AND AEROSPACE TECHNOLOGY 2018年第6期90卷 914-926页

作者： Leloudas, Stavros N. Strofylas, Giorgos A. Nikolos, Ioannis K. Tech Univ Crete Sch Prod Engn & Management Khania Greece

Purpose The purpose of this paper is the presentation of a technique to be integrated in a numerical airfoil optimization scheme, for the exact satisfaction of a strict equality cross-sectional area constraint. Design/methodology/approach An airfoil optimization framework is presented, based on Area-Preserving Free-Form Deformation (AP FFD) technique. A parallel metamodel-assisted differential evolution (DE) algorithm is used as an optimizer. In each generation of the DE algorithm, before the evaluation of the fitness function, AP FFD is applied to each candidate solution, via coupling a classic B-Spline-based FFD with an area correction step. The area correction step is achieved by solving a sub problem, which consists of computing and applying the minimum possible offset to each one of the free-to-move control points of the FFD lattice, subject to the area preservation constraint. Findings The proposed methodology is able to obtain better values of the objective function, compared to both a classic penalty function approach and a generic framework for handling constraints, which suggests the separation of constraints and objectives (separation-sub-swarm), without any loss of the convergence capabilities of the DE algorithm, while it also guarantees an exact area preservation. Due to the linearity of the area constraint in each axis, the extraction of an inexpensive closed-form solution to the sub problem is possible by using the method of Lagrange multipliers. Practical implications AP FFD can be easily incorporated into any 2D shape optimization/design process, as it is a time-saving and easy-to-implement repair algorithm, independent from the nature of the problem at hand. Originality/value The proposed methodology proved to be an efficient tool in facing airfoil design problems, enhancing the rigidity of the optimal airfoil by preserving its cross-sectional area to a predefined value.

关键词： Neural networks Differential evolution Aerodynamic optimization Area preservation Free-form deformation geometric algorithms

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Place the Vertices Anywhere on the Curve and Simplify

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FUNDAMENTA INFORMATICAE 2021年第3期180卷 275-287页

作者： Rudi, Ali Gholami Babol Noshirvani Univ Technol Dept Elect & Comp Engn Babol Mazandaran Iran

A polygonal curve is simplified to reduce its number of vertices, while maintaining similarity to its original shape. Numerous results have been published for vertex-restricted simplification, in which the vertices of the simplified curve are a subset of the vertices of the input curve. In curve-restricted simplification, i.e. when the vertices of the simplified curve are allowed to be placed on the edges of the input curve, the number of vertices may be much more reduced. In this paper, we present algorithms for computing curve-restricted simplifications of polygonal curves under the local Hausdorff distance measure.

关键词： Curve simplification geometric algorithms computational geometry

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Contact and Mobility Simulation for Mechanical Assemblies Based on Skin Model Shapes

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JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING 2015年第2期15卷 021009页

作者： Schleich, Benjamin Anwer, Nabil Mathieu, Luc Wartzack, Sandro FAU Erlangen Nurnberg Dept Mech Engn Chair Engn Design D-91058 Erlangen Germany ENS Cachan Dept Mech Engn Automated Prod Res Lab F-94230 Cachan France

Assembly modeling as one of the most important steps in the product development activity relies more and more on the extensive use of computer-aided design (CAD) systems. The modeling of geometric interfaces between the components of the assembly is of central importance in the simulation of mechanical assemblies. Over the past decades, many researchers have devoted their efforts to establish theories and systems covering assembly modeling. Although the product form or shape has been extensively investigated considering the nominal CAD geometry, inevitable limitations can be reported. Computer aided tolerancing (CAT) systems provide simulation tools for modeling the effects of tolerances on the assembly but still lack of form deviation considerations. The skin model concept which stemmed from the theoretical foundations of geometrical product specification and verification (GPS) has been developed to enrich the nominal geometry considering realistic physical shapes. However, the digital representation of the skin model has been investigated only recently. This paper presents a novel approach for a skin model based simulation of contact and mobility for assemblies. Three important issues are addressed: the geometric modeling of the contact, the contact quality evaluation, and the motion analysis. The main contribution to CAT can be found in the analysis of the effects of geometric form deviations on the assembly and motion behavior of solid mechanics, which comprises models for the assembly simulation, for the contact quality evaluation, and for the motion analysis. A case study is presented to illustrate the proposed approaches.

关键词： Tolerance modeling Simulation Modeling Mechanical admittance Shapes Skin Computational geometry Assembly modeling geometric algorithms Manufacturing GD&

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Layer-based decomposition of solids and its applications

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VISUAL COMPUTER 2005年第6期21卷 406-417页

作者： Rueda, AJ Feito, FR Ortega, LM Univ Jaen Escuela Politecn Super Dept Informat Jaen 23071 Spain

In this work we describe a decomposition scheme for polyhedra called layer-based decomposition. This decomposition can be computed in a straightforward way for any kind of polyhedron: convex or nonconvex, genus 0 or higher, etc. and presents interesting properties and applications like point-in-polyhedron inclusion test, computation of Boolean operations, or 3D location. Two methods for computing this decomposition and several of its applications are described in detail, including experimental results and comparisons with alternative approaches.

关键词： 3D decompositions solid modeling geometric algorithms

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Synthesis of 3D jigsaw puzzles over freeform 2-manifolds

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COMPUTERS & GRAPHICS-UK 2022年 102卷 339-348页

作者： Elber, Gershon Kim, Myung-Soo Technion Comp Sci Dept IL-32000 Haifa Israel Seoul Natl Univ Dept Comp Sci & Engn Seoul 08826 South Korea

We present a simple algorithm for synthesizing 3D jigsaw puzzles from arbitrary 3D freeform 2-manifold geometric models represented with trimmed NURBS surfaces. The construction algorithm is based on a few conventional geometric operations on freeform curves and surfaces. In particular, we need to compute the offset of freeform NURBS surfaces (for thickening the 2-manifold surfaces) and the functional composition of a univariate curve representation to a bivariate rational surface (for breaking up a 3D model into curved jigsaw tiles). It is thus almost straightforward to convert the proposed algorithm to a practical system using standard tools available in B-rep based geometric modeling systems, that employ trimmed NURBS surfaces. We demonstrate the effectiveness of the proposed approach by fabricating several test sets of 3D jigsaw puzzles for freeform solids consisting of trimmed NURBS surface models. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Trimmed NURBS surface Freeform geometric model geometric algorithms Function composition Fabrication 3D printing

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Approximation algorithms for tours of orientation-varying view cones

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2020年第4期39卷 389-401页

作者： Stefas, Nikolaos Plonski, Patrick A. Isler, Volkan Univ Minnesota Minneapolis MN USA

This article considers the problem of finding a shortest tour to visit viewing sets of points on a plane. Each viewing set is represented as an inverted view cone with apex angle alpha and height h. The apex of each cone is restricted to lie on the ground plane. Its orientation angle (tilt) epsilon is the angle difference between the cone bisector and the ground plane normal. This is a novel variant of the 3D Traveling Salesman Problem with Neighborhoods (TSPN) called Cone-TSPN. One application of Cone-TSPN is to compute a trajectory to observe a given set of locations with a camera: for each location, we can generate a set of cones whose apex and orientation angles alpha and epsilon correspond to the camera's field of view and tilt. The height of each cone h corresponds to the desired resolution. Recently, Plonski and Isler presented an approximation algorithm for Cone-TSPN for the case where all cones have a uniform orientation angle of epsilon=0. We study a new variant of Cone-TSPN where we relax this constraint and allow the cones to have non-uniform orientations. We call this problem Tilted Cone-TSPN and present a polynomial-time approximation algorithm with ratio O(1+tan alpha 1-tan epsilon tan alpha(1+logmax(H)min(H))), where H is the set of all cone heights. We demonstrate through simulations that our algorithm can be implemented in a practical way and that by exploiting the structure of the cones we can achieve shorter tours. Finally, we present experimental results from various agriculture applications that show the benefit of considering view angles for path planning.

关键词： Path planning view planning approximation algorithms geometric algorithms euclidean traveling salesman problem traveling salesman problem with neighborhoods

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A framework for uncertainty and validation of 3-D registration methods based on points and frames

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INTERNATIONAL JOURNAL OF COMPUTER VISION 1997年第3期25卷 203-229页

作者： Pennec, X Thirion, JP INRIA BP 93 2004 ROUTE LUCIOLES F-06902 SOPHIA ANTIPOLIS FRANCE

In this paper, we propose and analyze several methods to estimate a rigid transformation from a set of 3-D matched points or matched frames, which are important features in geometric algorithms. We also develop tools to predict and verify the accuracy of these estimations. The theoretical contributions are: an intrinsic model of noise for transformations based on composition rather than addition;a unified formalism for the estimation of both the rigid transformation and its covariance matrix for points or frames correspondences, and a statistical validation method to verify the error estimation, which applies even when no ''ground truth'' is available. We analyze and demonstrate on synthetic data that our scheme is well behaved. The practical contribution of the paper is the validation of our transformation estimation method in the case of 3-D medical images, which shows that an accuracy of the registration far below the size of a voxel can be achieved, and in the case of protein substructure matching, where frame features drastically improve both selectivity and complexity.

关键词： Computer vision Pose estimation Recognition Parameters Surfaces Protein Motion Registration Three Dimensions ground truth computer vision images geometric algorithms pose estimation Uncertainty Protein

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Interactive Mesh Cutting Using Constrained Random Walks

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2011年第3期17卷 357-367页

作者： Zhang, Juyong Zheng, Jianmin Cai, Jianfei Nanyang Technol Univ Sch Comp Engn Singapore 639798 Singapore

This paper considers the problem of interactively finding the cutting contour to extract components from an existing mesh. First, we propose a constrained random walks algorithm that can add constraints to the random walks procedure and thus allows for a variety of intuitive user inputs. Second, we design an optimization process that uses the shortest graph path to derive a nice cut contour. Then a new mesh cutting algorithm is developed based on the constrained random walks plus the optimization process. Within the same computational framework, the new algorithm provides a novel user interface for interactive mesh cutting that supports three typical user inputs and also their combinations: 1) foreground/background seed inputs: the user draws strokes specifying seeds for "foreground" (i.e., the part to be cut out) and "background" (i.e., the rest);2) soft constraint inputs: the user draws strokes on the mesh indicating the region which the cuts should be made nearby;and 3) hard constraint inputs: the marks which the cutting contour must pass. The algorithm uses feature sensitive metrics that are based on surface geometric properties and cognitive theory. The integration of the constrained random walks algorithm, the optimization process, the feature sensitive metrics, and the varieties of user inputs makes the algorithm intuitive, flexible, and effective as well. The experimental examples show that the proposed cutting method is fast, reliable, and capable of producing good results reflecting user intention and geometric attributes.

关键词： Computational geometry and object modeling interaction techniques geometric algorithms

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FixtureNet: Interactive computer-aided design via the World Wide Web

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INTERNATIONAL JOURNAL OF HUMAN-COMPUTER STUDIES 1997年第6期46卷 773-788页

作者： Wagner, R Castanotto, G Goldberg, K UNIV CALIF BERKELEY IEOR DEPTBERKELEYCA 94720

The Internet offers tremendous potential for rapid development of mechanical products to meet global competition. In the past several years, a variety of geometric algorithms have been developed to evaluate computer-aided design (CAD) models with respect to manufacturing properties such as feedability, fixturability, assemblability, etc. Unfortunately, most of these algorithms are tailored to a particular CAD system and format and so have not been widely tested by industry. The World Wide Web may offer a solution: its simple interface language offers a de facto standard for the exchange of geometric data with industry and research groups. In this paper, we describe a feasibility study for such an interactive system, which can be tested directly at http://***/fixture/ (C) 1997 Academic Press Limited.

关键词： computer aided design system geometric algorithms interactive systems Fabricability World Wide Web Computer-Aided Design Internets mechanical products industries

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Sets of Globally Optimal Stream Surfaces for Flow Visualization

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COMPUTER GRAPHICS FORUM 2014年第3期33卷 1-10页

作者： Schulze, M. Esturo, J. Martinez Guenther, T. Roessl, C. Seidel, H. -P. Weinkauf, T. Theisel, H. Univ Magdeburg D-39106 Magdeburg Germany

Stream surfaces are a well-studied and widely used tool for the visualization of 3D flow fields. Usually, stream surface seeding is carried out manually in time-consuming trial and error procedures. Only recently automatic selection methods were proposed. Local methods support the selection of a set of stream surfaces, but, contrary to global selection methods, they evaluate only the quality of the seeding lines but not the quality of the whole stream surfaces. Global methods, on the other hand, only support the selection of a single optimal stream surface until now. However, for certain flow fields a single stream surface is not sufficient to represent all flow features. In our work, we overcome this limitation by introducing a global selection technique for a set of stream surfaces. All selected surfaces optimize global stream surface quality measures and are guaranteed to be mutually distant, such that they can convey different flow features. Our approach is an efficient extension of the most recent global selection method for single stream surfaces. We illustrate its effectiveness on a number of analytical and simulated flow fields and analyze the quality of the results in a user study.

关键词： Categories and Subject Descriptors (according to ACM CCS) I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling&mdash geometric algorithms languages and systems

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