854 research outputs found

    Blending using ODE swept surfaces with shape control and C1 continuity

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    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

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    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.

    Blending Cylinders and Cones using Canal Surfaces

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    There is reviewed the construction of a rational blending surface between cylinders and cones in some interlocation cases. This surface is constructed as a patch of rolling ball envelope, i.e. as a patch of tangent canal surface of rational-variable radius. This construction defines rational parameterization of a blending surface. The constructed surface is Laguerre invariant

    Tangent-ball techniques for shape processing

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    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

    Rational rolling ball blending of natural quadrics

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    We construct a blending surface of two natural quadrics using rational variable rolling ball approach, i.e. as a canal surface with a rational spine curve and a rational radius. All general positions of the given quadric surfaces are considered. The proposed construction is Laguerre invariant. In particular, the blending surface has rational offset of the same degree. Natūralių kvadrikių jungimas racionalaus apriedančio rutuliuko metodu Santrauka Natūralios kvadrikos (sferos, apskritiminiai cilindrai ir kūgiai) dažnai naudojamos geometriniame modeliavime. Šiame darbe siūlomas naujas dvieju natūraliu kvadrikiu glodaus jungimo metodas, naudojant kintamo racionalaus spindulio apriedančio rutuliuko metoda, t.y. jungiamasis paviršius ‐ tai kanalinis paviršius, kuris turi racionalia ašine kreive ir racionalu spinduli. Metodas tinka visiems dvieju kvadrikiu bendru poziciju atvejams. Konstrukcija yra invariantiška Laguerre geometrijos atžvilgiu: pavyzdžiui, jungiamasis paviršius turi to paties laipsnio racionalu ofseta. First Published Online: 14 Oct 201

    Merging enriched Finite Element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance

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    A new approach to the merging of Finite Element (FE) triangle meshes is proposed. Not only it takes into account the geometric aspects, but it also considers the way the semantic information possibly associated to the groups of entities (nodes, faces) can be maintained. Such high level modification capabilities are of major importance in all the engineering activities requiring fast modifications of meshes without going back to the CAD model. This is especially true in the context of industrial maintenance where the engineers often have to solve critical problems in very short time. Indeed, in this case, the product is already designed, the CAD models are not necessarily available and the FE models might be tuned. Thus, the product behaviour has to be studied and improved during its exploitation while prototyping directly several alternate solutions. Such a framework also finds interest in the preliminary design phases where alternative solutions have to be simulated. The algorithm first removes the intersecting faces in an n-ring neighbourhood so that the filling of the created holes produces triangles whose sizes smoothly evolve according to the possibly heterogeneous sizes of the surrounding triagles. The holefilling algorithm is driven by an aspect ratio factor which ensures that the produced triangulation fits well the FE requirements. It is also constrained by the boundaries of the groups of entities gathering together the simulation semantic. The filled areas are then deformed to blend smoothly with the surroundings meshes

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

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    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

    DETC2002/CIE-34494 FEATURE SIMPLIFICATION IN SURFACE MODELS FOR EFFICIENT FINITE ELEMENT MESH GENERATION

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    ABSTRACT Sheet metal components are typically modelled as freeform surface models. Finite element meshes generated automatically for such models have poor quality around small detailed features. These features need to be simplified in order to obtain an acceptable mesh. Simplification involves recognition of the feature and modification of its geometry or complete suppression of the feature. This paper proposes techniques to directly query the CAD data structure to recognise and suppress two basic features, viz. holes and fillets in freeform surface models. Results of a software implementation for the same are discussed with suitable examples
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