scholarly journals Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Tension Control ◽  
Free Form ◽  
Subdivision Surfaces ◽  
Smooth Curves ◽  
Practical Applications ◽  
Tension Parameter ◽  
Exact Reproduction ◽  
Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

Stability Analysis of the MRT-Based Compliant Polishing Tool System

2012 ◽  
Vol 201-202 ◽  
pp. 473-476
Author(s):  
Chong Yang Yuan ◽  
Di Zheng ◽  
Jian Ming Zhan ◽  
Li Yong Hu
Keyword(s):  
Geometric Modeling ◽  
Mixed Model ◽  
Simulation Software ◽  
Free Form ◽  
Cnc Milling ◽  
Element Analysis ◽  
Compliant Polishing ◽  
The Stability ◽  
Free Form Surfaces ◽  
Polishing Tool

In order to meet the needs for the precise polishing of free-form surfaces, a new compliant polishing tool system was designed based on a magnetorheological torque servo (MRT), and integrated into a CNC milling machine. Through analysis, it was pointed out that the key factor affecting the polishing quality of this system is the stability of the system. By means of the 3D geometric modeling software ProE, the finite element analysis software ANSYS, and the dynamic simulation software ADAMS, the rigid-flexible mixed model of the system was established and the stability of the polishing pressure and tool position was numerically analyzed.

Geometric Modeling and Analysis of Single Point Cutting Tools With Generic Profile

2011 ◽  
Author(s):  
Kumar Sambhav ◽  
Puneet Tandon ◽  
Sanjay G. Dhande
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Single Point ◽  
Cutting Tools ◽  
Free Form ◽  
Generic Model ◽  
Modeling And Analysis ◽  
Grinding Parameters ◽  
Two Generations ◽  
Free Form Surfaces

The presented work models the geometry of Single Point Cutting Tools (SPCTs) with generic profile. Presently few standard shapes of SPCTs defined in terms of projective geometry are being employed while there is a need to design free-form tools to efficiently machine free-form surfaces with few passes and chosen range of cutting angles. To be able to produce SPCT face and flanks with generic shapes through grinding, a comprehensive geometric model of the tool in terms of the varying grinding angles and the ground depths is required which helps design the tool with arbitrarily chosen tool angles. The surface modeling begins with the creation of a tool blank model followed by transformation of unbounded planes to get the cutting tool surfaces. The intersection of these surfaces with the blank gives the complete model of the tool. Having created the geometric model in two generations of generalization, the paper presents the methodology to obtain the conventional tool angles from the generic model. An illustration of the model has been provided showing variation of tool angles along the cutting edge with changing grinding parameters. When the geometric model is not to be related to the grinding parameters, the SPCT can be modeled as a composite NURBS surface which has been presented towards the end of the work.

Tool Contact Maps by Rectangular Grid Decomposition

2011 ◽  
Author(s):  
Eyyup Aras
Keyword(s):  
Geometric Modeling ◽  
Free Form ◽  
Tool Geometry ◽  
Depth Of Cut ◽  
Force Model ◽  
Rectangular Grid ◽  
Ongoing Research ◽  
Circle Plane ◽  
Milling Operations ◽  
Free Form Surfaces

This paper is intended to contribute to ongoing research [1–3] in geometric modeling of the virtual machining. In geometric modeling the tool paths are verified by performing the machining simulations and also the cutter workpiece engagements (CWEs) are extracted. CWE geometry is a key input to force calculations and feed rate scheduling in milling operations. Finding these engagements is challenging due to the complicated and changing intersection geometry between the cutter and the in-process workpiece. This paper presents a discrete model based methodology for extracting CWEs generated during a multi axis machining of free form surfaces using a range of different types of milling tools. In this method the in-process workpiece is represented by a set of z-axis aligned rectangular grids. Each grid is made up of four planes, with their normals aligned with respect to the x and y-axis of the Cartesian coordinate system. In developing the methodology the parametric representations of the automatically programmed tool (APT)-type milling cutters are used. The milling tool surfaces are decomposed into circles. During the material removal process only some portions of those circles which are called the engagement arcs may contact the in-process workpiece. To find the geometric limits of those arcs the concept of the feasible contact surface is utilized. The CWE extraction simulation is performed through intersecting those arcs with the planes of each rectangular grid. Thus the intersection calculations reduce to circle/plane intersections which can be performed analytically for the geometry found on milling cutters. To be used in the force model, the CWE boundaries are mapped from Euclidean 3D space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. Then using a sort algorithm the neighboring engagements in the same arc level are combined.

On the Classification of Fitting Problems for Single Patch Free-Form Surfaces in Reverse Engineering

2001 ◽  
Author(s):  
Mohammed M. Shalaby ◽  
Ashraf O. Nassef ◽  
Sayed M. Metwalli
Keyword(s):  
Reverse Engineering ◽  
Geometric Modeling ◽  
Linear Optimization ◽  
Optimization Methods ◽  
Industrial Applications ◽  
Spare Parts ◽  
Free Form ◽  
Modeling Techniques ◽  
Free Form Surfaces ◽  
Die And Mold

Abstract The design and manufacture of free-form surfaces increased in industrial applications, especially for the re-manufacture of spare parts, or in the die and mold industry. Reverse engineering has become the status quo technique in reproducing parts whose original designs are no longer existing or for parts, which assume slightly different shapes after manufacturing as in the case of die and mold industry. Laser scanners have been used extensively in sampling points from parts surfaces. The sampled points are then fitted with a free-form surface using one of the geometric modeling techniques such as Bezier or B-Spline surfaces. Since Non-Uniform Rational B-Splines (NURBS) is the most general form of geometric modeling techniques, this paper presents the possible formulations of the fitting problem optimization and presents some guidelines of the choice of the independent NURBS parameters, once the control points are evaluated using least squares fitting. The work shows that the use of NURBS weights can provide better improvements for the significant reduction of the fitting error, rather than the widely used knot values. In addition the work shows that parts with semi planar surfaces do not need further refinement using non-linear optimization methods.

A Virtual Cutting Based Method for Aero Engine Turbine Blade Reverse Modeling from Its Cone Beam CT Images

2006 ◽  
Vol 532-533 ◽  
pp. 877-880
Author(s):  
Yun Yong Cheng ◽  
Kun Pu ◽  
Yuan Peng Liu ◽  
Xin Bo Zhao
Keyword(s):  
Turbine Blade ◽  
Geometric Modeling ◽  
Cone Beam Ct ◽  
Cone Beam ◽  
Free Form ◽  
Airfoil Surface ◽  
Mesh Model ◽  
Aero Engine ◽  
Marching Cube Algorithm ◽  
Free Form Surfaces

Turbine blade is one of the critical parts of the aero engine and usually has complex structures. The main purpose of this paper is to present a virtual cutting based method for aero engine turbine blade reverse modeling from its cone beam computed tomography (CBCT) images. Based on the turbine blade CBCT images, an improved Marching Cube algorithm was used to construct a 3D mesh model of the turbine blade. Then, cutting tools of parallel planes, concentric cylinders, concentric cones or revolved free form surfaces were used to cut the turbine blade mesh model to get the profile curves. After the profile curves were constructed by curve fitting and joining, the lofting geometric modeling technique was used to generate the turbine blade airfoil surface working in parallel flow, cylindrical flow, conical flow and revolved free form flow respectively. A set of computer simulating turbine blade CBCT images (512×512×512) was used to test the presented method and the testing results showed that the method was feasible and convenient.

Review of Subdivision Schemes and their Applications

2021 ◽  
Vol 16 ◽  
Author(s):  
Yan Liu ◽  
Huahao Shou ◽  
Kangsong Ji
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Hot Spot ◽  
Geometric Constraints ◽  
Future Application ◽  
Subdivision Surfaces ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Curves And Surfaces ◽  
Subdivision Curves

Background: Subdivision surfaces modeling method and related technology research gradually become a hot spot in the field of computer-aided design(CAD) and computer graphics (CG). In the early stage, research on subdivision curves and surfaces mainly focused on the relationship between the points, thereby failing to satisfy the requirements of all geometric modeling. Considering many geometric constraints is necessary to construct subdivision curves and surfaces for achieving high-quality geometric modeling. Objective: This paper aims to summarize various subdivision schemes of subdivision curves and surfaces, particularly in geometric constraints, such as points and normals. The findings help scholars to grasp the current research status of subdivision curves and surfaces better and to explore their applications in geometric modeling. Methods: This paper reviews the theory and applications of subdivision schemes from four aspects. We first discuss the background and key concept of subdivision schemes. We then summarize the classification of classical subdivision schemes. Next, we show the subdivision surfaces fitting and summarize new subdivision schemes under geometric constraints. Applications of subdivision surfaces are also discussed. Finally, this paper gives a brief summary and future application prospects. Results: Many research papers and patents of subdivision schemes are classified in this review paper. Remarkable developments and improvements have been achieved in analytical computations and practical applications. Conclusion: Our review shows that subdivision curves and surfaces are widely used in geometric modeling. However, some topics need to be further studied. New subdivision schemes need to be presented to meet the requirements of new practical applications.

A Solid Modeler Approach for Extracting Cutter Workpiece Engagements in Milling

2008 ◽  
Author(s):  
Eyyup Aras ◽  
Derek Yip-Hoi
Keyword(s):  
Geometric Modeling ◽  
Cutting Tools ◽  
Free Form ◽  
Tool Geometry ◽  
Depth Of Cut ◽  
Modeling Methodology ◽  
Engagement Angle ◽  
Solid Modeler ◽  
Free Form Surfaces ◽  
Boundary Curves

This paper presents a Solid modeling methodology for finding Cutter Workpiece Engagements (CWEs) generated during 3+2 -axis machining (spindle can tilt) of free – form surfaces using a range of different types of cutting tools and tool paths. Swept volumes of the cutters are generated utilizing the envelope theory. For the CWE extractions the removal volumes of the cutter constituent surfaces are used. For this purpose the cutter surfaces are decomposed with respect to the tool feed direction and then they intersected with their removal volumes for obtaining the boundary curves of the closed CWE area. The CWE boundary curves are mapped from Euclidean space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry. The reported method has been implemented using a commercial geometric modeler (ACIS) which is selected to be the kernel around which the geometric simulator is built. The described geometric methodology is being developed as part of a Virtual Milling methodology that combines the geometric modeling aspects of milling material removal with the modeling of the process.

Some aspects of the pedagogical model of constructive geometric modeling

2020 ◽  
Author(s):  
Denis Voloshinov ◽  
K. Solomonov ◽  
Lyudmila Mokretsova ◽  
Lyudmila Tishchuk
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Educational Process ◽  
Educational Institutions ◽  
Software Systems ◽  
Teaching Methodology ◽  
Models Of Teaching ◽  
Software Product ◽  
The University

The application of constructive geometric modeling to pedagogical models of teaching graphic disciplines today is a promising direction for using computer technology in the educational process of educational institutions. The essence of the method of constructive geometric modeling is to represent any operation performed on geometric objects in the form of a transformation, as a result of which some constructive connection is established, and the transformation itself can be considered as a result of the action of an abstract cybernetic device. Constructive geometric modeling is a popular information tool for information processing in various applied areas, however, this tool cannot be appreciated without the presence of appropriate software systems and developed design techniques. Traditionally, constructive geometric modeling is used in the design of mechanical engineering, energy, aircraft and shipbuilding facilities, in architectural and design engineering. The need to study descriptive geometry at the university in recent years has something in common with the issues of mastering graphic packages of computer programs in the framework of the new discipline "Engineering and Computer Graphics". The well-known KOMPAS software product is considered the simplest and most attractive for training. It should be noted the important role of graphic packages in the teaching of geometric disciplines that require a figurative perception of the material by students. Against the background of a reduction in classroom hours, computer graphics packages are practically the only productive teaching methodology, successfully replacing traditional tools - chalk and blackboard.

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