scholarly journals Parametric Blending of Hole Patches Based on Shape Difference

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1759
Author(s):  
Jung-Ho Park ◽  
Sanghun Park ◽  
Seung-Hyun Yoon
Keyword(s):  
Geometric Modeling ◽  
Positive Definite Matrix ◽  
3D Models ◽  
Triangular Mesh ◽  
Principal Curvatures ◽  
Third Order ◽  
Shape Difference ◽  
Curvature Variation ◽  
Laplacian Smoothing ◽  
The Given

A triangular mesh obtained by scanning 3D models typically contains holes. We present an effective technique for filling a hole in a triangular mesh in geometric modeling. Simple triangulation of a hole is refined and remeshed iteratively to generate an initial patch. The generated patch is then enhanced to become a target patch by minimizing the variation of principal curvatures. In discrete approximation, this produces a third-order Laplacian system of sparse symmetric positive definite matrix, and the symmetry can efficiently be used to find the robust solutions to the given Laplacian system. Laplacian smoothing of the target patch is defined as a source patch. The shape difference between two corresponding vertices of the source and the target patches is measured in terms of Euclidean distance and curvature variation. On the basis of the shape difference and a user-specified control parameter, different blending weights are determined for each vertex, and the final patch is generated by blending two patches. We demonstrate the effectiveness of our technique by discussing several examples. The experimental results show that our technique can effectively restore salient geometric features of the original shape.

scholarly journals Geodesic Hermite Spline Curve on Triangular Meshes

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1936
Author(s):  
Yujin Ha ◽  
Jung-Ho Park ◽  
Seung-Hyun Yoon
Keyword(s):  
Geometric Modeling ◽  
Hermite Interpolation ◽  
Interpolation Method ◽  
Triangular Mesh ◽  
Triangular Meshes ◽  
Polygonal Mesh ◽  
Spline Curve ◽  
Geodesic Vector ◽  
Hermite Spline ◽  
The Given

Curves on a polygonal mesh are quite useful for geometric modeling and processing such as mesh-cutting and segmentation. In this paper, an effective method for constructing C1 piecewise cubic curves on a triangular mesh M while interpolating the given mesh points is presented. The conventional Hermite interpolation method is extended such that the generated curve lies on M. For this, a geodesic vector is defined as a straightest geodesic with symmetric property on edge intersections and mesh vertices, and the related geodesic operations between points and vectors on M are defined. By combining cubic Hermite interpolation and newly devised geodesic operations, a geodesic Hermite spline curve is constructed on a triangular mesh. The method follows the basic steps of the conventional Hermite interpolation process, except that the operations between the points and vectors are replaced with the geodesic. The effectiveness of the method is demonstrated by designing several sophisticated curves on triangular meshes and applying them to various applications, such as mesh-cutting, segmentation, and simulation.

Automatic Parametric Modeling From Non-Feature Based Designs for Additive Manufacturing

2021 ◽  
Author(s):  
Xinyi Xiao ◽  
Byeong-Min Roh
Keyword(s):  
Additive Manufacturing ◽  
3D Models ◽  
Parametric Modeling ◽  
Parametric Models ◽  
Performance Simulation ◽  
Cad Modeling ◽  
3D Cad ◽  
Feature Based ◽  
And Performance ◽  
The Given

Abstract The integration of Topology optimization (TO) and Generative Design (GD) with additive manufacturing (AM) is becoming advent methods to lightweight parts while maintaining performance under the same loading conditions. However, these models from TO or GD are not in a form that they can be easily edited in a 3D CAD modeling system. These geometries are generally in a form with no surface/plane information, thus having non-editable features. Direct fabricate these non-feature-based designs and their inherent characteristics would lead to non-desired part qualities in terms of shape, GD&T, and mechanical properties. Current commercial software always requires a significant amount of manual work by experienced CAD users to generate a feature-based CAD model from non-feature-based designs for AM and performance simulation. This paper presents fully automated shaping algorithms for building parametric feature-based 3D models from non-feature-based designs for AM. Starting from automatically decomposing the given geometry into “formable” volumes, which is defined as a sweeping feature in the CAD modeling system, each decomposed volume will be described with 2D profiles and sweeping directions for modeling. The Boolean of modeled components will be the final parametric shape. The volumetric difference between the final parametric form and the original geometry is also provided to prove the effectiveness and efficiency of this automatic shaping methodology. Besides, the performance of the parametric models is being simulated to testify the functionality.

scholarly journals CULTURAL HERITAGE MONUMENT DOCUMENTATION THROUGH ADAPTIVE PARAMETRIC DESIGN PROCESS

2021 ◽  
Vol XLVI-M-1-2021 ◽  
pp. 769-776
Author(s):  
G. Tryfonos ◽  
M. Ioannides ◽  
A. G. Anastasi ◽  
V. A. Apostolou ◽  
P. P. Pieri ◽  
...  
Keyword(s):  
Cultural Heritage ◽  
Parametric Design ◽  
3D Models ◽  
Building Information Modelling ◽  
3D Data ◽  
Time Period ◽  
Building Information ◽  
Game Developers ◽  
The Given ◽  
The City

Abstract. The paper presents a novel adaptive parametric documentation, modelling and sharing methodology, which aims to achieve a continuous holistic documentation, data processing and sharing process for cultural heritage community, such as architects, engineers, archaeologists, conservators, programmers, fabricators, contest creators, game developers, scholars and common citizens. Thus, the use of advance parametric and building information modelling software allows the processing and specification of all data by creating the 3D models needed for the multidisciplinary experts. Two Cypriot case studies from the medieval time period have been chosen for the development, and evaluation of our proposed methodology in order to investigate the process of modelling and sharing all the given metadata and 3D data. The first one is the Asinou Church, a UNESCO Heritage stone monument in the Troodos Mountains with a unique interior and the Kolossi Castle, a former Crusader stronghold on the west of the city of Limassol on the island of Cyprus.

Automatic Creation of Virtual Artefacts from Video Sequences

2005 ◽  
Author(s):  
Andrew W. Fitzgibbon ◽  
Geoff Cross ◽  
Andrew Zisserman
Keyword(s):  
Focal Length ◽  
3D Models ◽  
Video Sequences ◽  
Digital Representation ◽  
The Third ◽  
3D Presentation ◽  
Object Features ◽  
The Given ◽  
System Geometry ◽  
2D Images

Digital representation of an artefact is necessary in order to measure, admire and analyse such ancient pieces. For the purpose of storing, recoding and transmitting information, digital photographs may be enough. However, in the examination purposes of an artefact, a 3D presentation is invaluable as it allows the object viewpoint to be modified freely and 3D measurements to be taken on object features. This chapter describes the system by which 3D models from photographs can be acquired, without the need for the calibration of system geometry such as the camera focal length, relative motion of the camera and object, and the relative positions of the camera and object. This system instead computes the representation of all possible objects and camera configurations which are consistent with the given image. The first section discusses how tracking points observed in 2D images allows for the computation of the relative camera and object geometry. The second section discusses the construction of a triangulated 3D model from the object projections. The third section discusses the refinement of the model based on surface texture.

An Algorithm for Geometric Modeling and Intersection in NC Milling Simulation Based on Triangular Mesh Model

2011 ◽  
Vol 48-49 ◽  
pp. 541-546 ◽  
Author(s):  
Dian Zhu Sun ◽  
Xin Cai Kang ◽  
Yan Rui Li ◽  
Yong Wei Sun
Keyword(s):  
Geometric Modeling ◽  
Tool Path ◽  
Triangular Mesh ◽  
Simulation Process ◽  
Mesh Model ◽  
Milling Simulation ◽  
Nc Simulation ◽  
Simulation Based ◽  
Triangular Mesh Model ◽  
Nc Milling

To achieve the accurate and efficient NC milling simulation based on the discrete triangular mesh model, we proposed an algorithm for geometric modeling and intersection. We construct the R*-tree index for upper-surface nodes of mesh model, based on which the nodes within cutting region can be obtained. We compute tool path segments within cutting projection region of node, and calculate the minimum adjustment height of node according to tool path segments within cutting projection region and then change the z-value of node. Thus, we complete the intersection calculation in simulation process. It has been proved by examples that the algorithm for geometric modeling and intersection in NC milling simulation has strong adaptation to tool path segment type and that it can accurately and efficiently reflect the effect of NC simulation process based on the discrete triangular mesh model of rough.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

scholarly journals A Geometric Modeling Method Based on TH-Type Uniform B-Splines

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jin Xie
Keyword(s):  
Geometric Modeling ◽  
Modeling Method ◽  
Control Points ◽  
Hyperbolic Functions ◽  
Hyperbolic Polynomial ◽  
B Splines ◽  
Control Polygon ◽  
The Given

A geometric modeling method based on TH-type uniform B-splines which are composed of trigonometric and hyperbolic polynomial with parameters is introduced in this paper. The new splines possess many important properties of quadratic and cubic B-splines. Taking different values of the parameters, one can not only locally adjust the shape of the curves, but also change the type of some segments of a curve between trigonometric and hyperbolic functions as well. The given curves can also interpolate directly control polygon locally by selecting special parameters. Moreover, the introduced splines can represent some quadratic curves and transcendental curves with selecting proper control points and parameters.

Linear and Nonlinear Model of Cutting Forces in Peripheral Milling: A Comparison Between 2D and 3D Models

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Mohammad R. Movahhedy ◽  
Gholamreza Vossoughi
Keyword(s):  
Cutting Forces ◽  
Nonlinear Models ◽  
Three Dimensional ◽  
Chip Thickness ◽  
Maximum Error ◽  
3D Models ◽  
Peripheral Milling ◽  
Third Order ◽  
Order Polynomial ◽  
2D And 3D

Peripheral milling is extensively used in manufacturing processes, especially in aerospace industry where end mills are used for milling of wing parts and engine components. Knowledge of the cutting forces is the first necessary stage in analysis of the milling process. In this paper, cutting forces are presented for both two and three dimensional models. Instead of the common linear dependency of cutting forces to the cut chip thickness, two nonlinear models are presented. In the first model, cutting forces are considered as a function of chip thickness with a complete third order polynomial. In the second one, the quadratic and constant terms of the third order polynomial are set to zero. Results show about 2–3% and 2–7% maximum error between the linear, first and second nonlinear models, for 2D and 3D models, respectively. According to the simulation results, both the 2D and 3D models with second type of nonlinearity can be effectively used in practice. The advantage of such modelling is its simplicity in nonlinear analysis of the problem based on perturbation techniques.

DYNAMICS AND CHAOS CONTROL OF NONLINEAR SYSTEMS WITH ATTRACTION/REPULSION FUNCTION

2008 ◽  
Vol 18 (08) ◽  
pp. 2345-2371 ◽  
Author(s):  
XIAN LIU ◽  
JINZHI WANG ◽  
ZHISHENG DUAN ◽  
LIN HUANG
Keyword(s):  
Absolute Stability ◽  
Chaos Control ◽  
Linear Matrix ◽  
Chaotic Attractors ◽  
Matrix Inequality ◽  
Third Order ◽  
Simple Method ◽  
Stabilizing Controller ◽  
The Given ◽  
Absolute Stability Theory

In this paper, a more general third-order chaotic system with attraction/repulsion function is introduced on the basis of [Duan et al., 2005]. A gallery of chaotic attractors, bifurcation diagrams and Lyapunov exponent spectra are presented to show the interesting phenomena of the given system. Based on the absolute stability theory and linear matrix inequality (LMI), a simple method of chaos control for the system is proposed and a stabilizing controller is derived such that chaos oscillations of the system disappear and all chaotic trajectories of it are led to certain equilibrium. Numerical simulations are provided to illustrate the efficiency of the proposed method.

scholarly journals Geometric modeling and development of custom libraries in the design of engineering facilities

2020 ◽  
pp. 1-7
Author(s):  
Elena Sergeevna Reshetnikova ◽  
Irina Aleksandrovna Savelyeva ◽  
Ekaterina Anatolyevna Svistunova
Keyword(s):  
Design Process ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
3D Models ◽  
Conveyor Belt ◽  
General Idea ◽  
Design Stage ◽  
Preliminary Design ◽  
Design Documentation

The subject of research is the process of designing a conveyor belt. The authors consider parameterization in geometric modeling of parts and components of equipment and the creation of custom libraries in Compass 3D as a means of reducing the complexity and improving the quality of the design process. The preliminary design is the design stage of the development of design documentation and aims to determine the fundamental design solutions for a general idea of the device, operating principles and dimensions of the product. It is advisable to develop a preliminary design before the stage of developing a technical project and creating design documentation. Today, at all stages of work on the project, modern computer-aided design (CAD) systems are used, which not only accelerate the design process, but also make it possible to demonstrate to the customer the finished project at the stage of making technical decisions. This allows making timely changes in accordance with the requirements of the customer and to carry out high-quality preparation of the project for its implementation. The volume and time for further stages of work depend on the timing of the presentation of the preliminary design, therefore, the use of three-dimensional modeling parametrization in CAD is an effective way for designing engineering objects. Parameterization when working with 3D models allows you to get a set of typical product designs based on a once-created model by changing the set values of the variables, which significantly reduces the time spent on the project.

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