A unified approach to blending of constant and varying parametric surfaces with curvature continuity

In this paper, we develop a new approach to blending of constant and varying parametric surfaces with curvature continuity. We propose a new mathematical model consisting of a vector-valued sixth-order partial differential equation (PDE) and time-dependent blending boundary constraints, and develop an approximate analytical solution of the mathematical model. The good accuracy and high computational efficiency are demonstrated by comparing the new approximate analytical solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on the continuity at trimlines, and apply the new approximate analytical solution in blending of constant and varying parametric surfaces with curvature continuit

Blending using ODE swept surfaces with shape control and C1 continuity

Surface blending with tangential continuity is most widely applied in computer aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: 1). exact satisfaction of 1C continuous blending boundary constraints, 2). effective shape control of blending surfaces, 3). high computing efficiency due to explicit mathematical representation of blending surfaces, and 4). ability to blend multiple (more than two) primary surfaces

A feature-based approach to the Computer-Aided Design of sculptured products

Computer-Aided Design systems offer considerable potential for improving design process efficiency. To reduce the 'ease of use' barrier hindering full realisation of this potential amongst general mechanical engineering industries, many commercial systems are adopting a Feature-Based Design (FBD) metaphor. Typically the user is allowed to define and manipulate the design model using interface elements that introduce and control parametric geometry clusters, with engineering meaning, representing specific product features (such as threaded holes, slots, pockets and bosses). Sculptured products, such as golf club heads, shoe lasts, crockery and sanitary ware, are poorly supported by current FBD systems and previous research, because their complex shapes cannot be accurately defined using the geometrically primitive feature sets implemented. Where sculptured surface regions are allowed for, the system interface, data model and functionality are little different from that already provided in many commercial surface modelling systems, and so offer very little improvement in ease of use, quality or efficiency. This thesis presents research to propose and develop an FBD methodology and system suitable for sculptured products. [Continues.

Tangent-ball techniques for shape processing

Shape processing defines a set of theoretical and algorithmic tools for creating, measuring and modifying digital representations of shapes.  Such tools are of paramount importance to many disciplines of computer graphics, including modeling, animation, visualization, and image processing.  Many applications of shape processing can be found in the entertainment and medical industries. In an attempt to improve upon many previous shape processing techniques, the present thesis explores the theoretical and algorithmic aspects of a difference measure, which involves fitting a ball (disk in 2D and sphere in 3D) so that it has at least one tangential contact with each shape and the ball interior is disjoint from both shapes. We propose a set of ball-based operators and discuss their properties, implementations, and applications.  We divide the group of ball-based operations into unary and binary as follows: Unary operators include: * Identifying details (sharp, salient features, constrictions) * Smoothing shapes by removing such details, replacing them by fillets and roundings * Segmentation (recognition, abstract modelization via centerline and radius variation) of tubular structures Binary operators include: * Measuring the local discrepancy between two shapes * Computing the average of two shapes * Computing point-to-point correspondence between two shapes * Computing circular trajectories between corresponding points that meet both shapes at right angles * Using these trajectories to support smooth morphing (inbetweening) * Using a curve morph to construct surfaces that interpolate between contours on consecutive slices The technical contributions of this thesis focus on the implementation of these tangent-ball operators and their usefulness in applications of shape processing. We show specific applications in the areas of animation and computer-aided medical diagnosis.  These algorithms are simple to implement, mathematically elegant, and fast to execute.Ph.D.Committee Chair: Jarek Rossignac; Committee Member: Greg Slabaugh; Committee Member: Greg Turk; Committee Member: Karen Liu; Committee Member: Maryann Simmon

Intuitive freeform modeling using subdivision surfaces.

Lai Yuen-hoo.Thesis submitted in: November 2004.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 100-102).Abstracts in English and Chinese.Abstract --- p.i摘要 --- p.iiAcknowledgment --- p.iiiList of Figures --- p.ivTable of Content --- p.viiChapter 1. --- Introduction --- p.1Chapter 1.1. --- Problem Definition --- p.1Chapter 1.2. --- Proposed Solution --- p.2Chapter 1.3. --- Thesis Contributions --- p.2Chapter 2. --- Modeling Approaches --- p.4Chapter 2.1. --- Polygon Modeling --- p.4Chapter 2.2. --- Patch Modeling --- p.6Chapter 2.3. --- Freehand Sketch-based Modeling --- p.7Chapter 2.4. --- Template Based Modeling --- p.8Chapter 2.5. --- Curve Interpolation Method --- p.9Chapter 3. --- Surface Operations --- p.11Chapter 3.1. --- Surface Blending --- p.11Chapter 3.2. --- Surface Trimming --- p.13Chapter 3.3. --- Boolean Operations --- p.14Chapter 4. --- Subdivision Surface --- p.16Chapter 4.1. --- Basic Principle --- p.16Chapter 4.2. --- Catmull-Clark Surface --- p.17Chapter 5. --- Modeling Algorithm Overview --- p.21Chapter 6. --- Subdivision Surface Generation --- p.23Chapter 6.1. --- Input Curves --- p.23Chapter 6.2. --- Surface Sweeping --- p.24Chapter 6.3. --- Subdivision Surface Fitting --- p.29Chapter 7. --- Surface Blending --- p.32Chapter 7.1. --- Introduction --- p.32Chapter 7.2. --- Problem Definition --- p.32Chapter 7.3. --- Algorithm Overview --- p.36Chapter 7.4. --- Blend Region Detection --- p.39Chapter 7.4.1. --- Collision Detection --- p.40Chapter 7.4.2. --- Result and Analysis --- p.42Chapter 7.5. --- "Mesh Refinement, Surface Fitting and Region Removal" --- p.46Chapter 7.5.1. --- Mesh Refinement --- p.46Chapter 7.5.1.1. --- Adaptive Subdivision --- p.46Chapter 7.5.1.2. --- Additional Subdivision Constraint --- p.47Chapter 7.5.2. --- Surface Fitting --- p.49Chapter 7.5.2.1. --- General Approach --- p.49Chapter 7.5.2.2. --- Surface Point Correspondence --- p.50Chapter 7.5.2.3. --- Numerical Fitting Method --- p.51Chapter 7.5.3. --- Unwanted Region Removal --- p.55Chapter 7.5.4. --- Result and Analysis --- p.56Chapter 7.6. --- Boundary Smoothing --- p.58Chapter 7.6.1. --- General Approach --- p.59Chapter 7.6.2. --- Constraint on Deformation Direction of Vertex --- p.61Chapter 7.6.3. --- Result and Analysis --- p.63Chapter 7.7. --- Blend Curves --- p.65Chapter 7.7.1. --- Problem Definition --- p.65Chapter 7.7.2. --- Proposed Solution Overview --- p.66Chapter 7.7.3. --- Maintenance of Regular Vertex Valence along Blend Curve --- p.67Chapter 7.7.3.1. --- Pairing Up Blend Boundary Vertices --- p.70Chapter 7.7.4. --- Minimization of Distortion Caused by Extraordinary Vertices --- p.72Chapter 7.7.5. --- Blend Vertex Position Optimization Function --- p.74Chapter 7.7.5.1. --- Face Normal Expression --- p.74Chapter 7.7.5.2. --- Face Normal Difference Energy Function --- p.77Chapter 7.7.5.3. --- Midpoint Distance Energy Function --- p.78Chapter 7.7.5.4. --- Weighted Least Square Energy Minimization --- p.78Chapter 8. --- Implementation --- p.81Chapter 8.1. --- Data Structure --- p.81Chapter 8.2. --- User Interface --- p.82Chapter 9. --- Results --- p.83Chapter 9.1. --- Surface Generation --- p.83Chapter 9.2. --- Surface Blending --- p.86Chapter 9.2.1. --- Ideal Case --- p.86Chapter 9.2.2. --- Angle of Insertion --- p.87Chapter 9.2.3. --- Surface Feature Near Intersection --- p.88Chapter 9.2.4. --- Comparison --- p.89Chapter 9.2.5. --- Other Examples --- p.92Chapter 9.3. --- Overall Performance --- p.94Chapter 9.4. --- Limitations --- p.97Chapter 9.4.1. --- Limitation on Generated Shape --- p.97Chapter 9.4.2. --- Limitation on Input Surfaces --- p.98Chapter 10. --- Conclusion and Future Work --- p.99References --- p.10

Manufacturing Processes of Integral Blade Rotors for Turbomachinery, Processes and New Approaches

Manufacturing techniques applied to turbomachinery components represent a challenge in the aeronautical sector. These components are commonly composed of high resistant super-alloys; in order to satisfy the extreme working conditions, they have to support during their useful life. Besides, in the particular case of Integrally Bladed Rotors (IBR), they usually present complex geometries that need to be roughed and finished by milling and grinding processes, respectively. Thermoresistant superalloys present many challenges in terms of machinability what leads to find new alternatives to conventional manufacturing processes. In order to face this issue, this work presents a review of the last advances for IBR manufacturing and repairing processes.We are grateful to Basque Excellence university Groups IT IT1337-19, and Ministry of economy project IBRELIABLE (DPI2016-74845-R), and Elkartek PROCODA KK 2019-004

Differential equation-based shape interpolation for surface blending and facial blendshapes.

Differential equation-based shape interpolation has been widely applied in geometric modelling and computer animation. It has the advantages of physics-based, good realism, easy obtaining of high- order continuity, strong ability in describing complicated shapes, and small data of geometric models. Among various applications of differential equation-based shape interpolation, surface blending and facial blendshapes are two active and important topics. Differential equation-based surface blending can be time-independent and time-dependent. Existing differential equation-based surface blending only tackles time-dependen

In-cylinder fuel and lubricant effects on gasoline engine friction

The purpose of the research reported in this thesis was to investigate the viability and quantify the potential gains of improving fuel economy of the gasoline engine through strategic application of additives. An increased awareness of the link between greenhouse gas emissions and global warming means that there is a desire to reduce carbon dioxide emissions from transportation. There is therefore a growing emphasis on improving the fuel economy performance of vehicles. The addition of friction modifier additives to the fuel is one way to achieve this. Using bespoke in-cylinder sampling techniques, an understanding of the operation of the piston assembly, a system responsible for much of the power loss in the internal combustion engine, is developed. Validation is given to the hypothesis that fuel economy gains can be achieved through the application of friction modifier administered to the engine via the gasoline. Results show gasoline administered friction modifier additive can accumulate in the piston assembly lubricant at levels 77 times greater than the initial fuel treatment level. The performance of a large number of friction modifier additives were uniquely screened in a novel bench-top test which simulated the arduous in-cylinder conditions found in a firing gasoline engine. The test generated vast amounts of information which led to high performance formulations capable of reducing the friction coefficient in both the boundary and mixed lubrication regimes by around 50% when compared with the result for the base oil alone. Surface analysis techniques were also employed 0!l engineering surfaces coated with friction modifier additives and add to the knowledge of their mechanism of action. Finally a series of engine tests were conducted which prove the effectiveness of friction modifier administered to the engine via the gasoline. A fuel economy improvement of approximately 2% was seen where friction modifier gasoline was employed. Application of successful technology such as this is shown to correspond to the projected saving of around 502 million litres of gasoline and 388,000 tonnes of carbon (C02) per year in the UK alone