1,169 research outputs found

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

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    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

    Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

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    When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom

    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

    Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

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    This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

    Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

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    International audienceWhen an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom

    Accurate geometry reconstruction of vascular structures using implicit splines

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    3-D visualization of blood vessel from standard medical datasets (e.g. CT or MRI) play an important role in many clinical situations, including the diagnosis of vessel stenosis, virtual angioscopy, vascular surgery planning and computer aided vascular surgery. However, unlike other human organs, the vasculature system is a very complex network of vessel, which makes it a very challenging task to perform its 3-D visualization. Conventional techniques of medical volume data visualization are in general not well-suited for the above-mentioned tasks. This problem can be solved by reconstructing vascular geometry. Although various methods have been proposed for reconstructing vascular structures, most of these approaches are model-based, and are usually too ideal to correctly represent the actual variation presented by the cross-sections of a vascular structure. In addition, the underlying shape is usually expressed as polygonal meshes or in parametric forms, which is very inconvenient for implementing ramification of branching. As a result, the reconstructed geometries are not suitable for computer aided diagnosis and computer guided minimally invasive vascular surgery. In this research, we develop a set of techniques associated with the geometry reconstruction of vasculatures, including segmentation, modelling, reconstruction, exploration and rendering of vascular structures. The reconstructed geometry can not only help to greatly enhance the visual quality of 3-D vascular structures, but also provide an actual geometric representation of vasculatures, which can provide various benefits. The key findings of this research are as follows: 1. A localized hybrid level-set method of segmentation has been developed to extract the vascular structures from 3-D medical datasets. 2. A skeleton-based implicit modelling technique has been proposed and applied to the reconstruction of vasculatures, which can achieve an accurate geometric reconstruction of the vascular structures as implicit surfaces in an analytical form. 3. An accelerating technique using modern GPU (Graphics Processing Unit) is devised and applied to rendering the implicitly represented vasculatures. 4. The implicitly modelled vasculature is investigated for the application of virtual angioscopy

    Ισογεωμετρική Στατική Ανάλυση με T-SPLines

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    Σκοπός αυτής της διπλωματικής είναι η διερεύνηση της ισογεωμετρικής στατικής ανάλυσης χρησιμοποιώντας ΄ενα νέο έιδος συναρτήσεων σχήματος , τις T-SPLines. Τόσο οι T-SPLines όσο και η ανάλυση πεπερασμένων στοιχείων εετάστηκαν ξεχωριστά αφού αποτελούν τις δύο συνιστώσες της ισογεωμετρικής μεθόδου. Τα θέματα που εξετάστηκαν είναι οι T-SPLines και οι ιδιότητές τους, οι τεχνικές πύκνωσης του δικτύου , η μόρφωση του μητρώου στιβαρότητας, η επεξεργασία των αποτελεσμάτων της ανάλυσης (πεδίο μετατοπίσεων, τάσεων και παραμορφώσεων) και εφαρμογές 2Δ για τη διερεύνηση διαφόρων φορέων.The scope of this thesis if the investigation of static isogeometric analysis unsing a new type of shape functions T-SPLines. T-SPLines and finite elements have been examined separately, as the two components of the isogeometric method. The topics considered are T-SPLine formulation and properties, refinement techniques, stiffness matrix formulation , result post-processing (displacement, stress and strain field) and linear 2D applications investigating models of various representations.Δημήτριος Γ. Τσαπέτη
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