922 research outputs found

    Boundary-Conforming Finite Element Methods for Twin-Screw Extruders using Spline-Based Parameterization Techniques

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    This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw geometries are generated using Elliptic Grid Generation. They are evaluated in a number of discrete points to yield a coarse classical mesh. The use of a special control mapping allows to fine-tune properties of the coarse mesh like orthogonality at the boundaries. The coarse mesh is used as a 'scaffolding' to generate a boundary-conforming mesh out of a fine background mesh at run-time. Storing only a coarse mesh makes the method cheap in terms of memory storage. Additionally, the adaptation at run-time is extremely cheap compared to computing the flow solution. Furthermore, this method circumvents the need for expensive re-meshing and projections of solutions making it efficient and accurate. It is incorporated into a space-time finite element framework. We present time-dependent test cases of non-Newtonian fluids in 2D and 3D for complex screw designs. They demonstrate the potential of the method also for arbitrarily complex industrial applications

    An isogeometric finite element formulation for phase transitions on deforming surfaces

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    This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn-Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation. Both PDEs can be efficiently discretized using C1C^1-continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise C1C^1-continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-α\alpha scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton-Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to the text, added supplementary movie file

    Non-rigid registration of 2-D/3-D dynamic data with feature alignment

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    In this work, we are computing the matching between 2D manifolds and 3D manifolds with temporal constraints, that is we are computing the matching among a time sequence of 2D/3D manifolds. It is solved by mapping all the manifolds to a common domain, then build their matching by composing the forward mapping and the inverse mapping. At first, we solve the matching problem between 2D manifolds with temporal constraints by using mesh-based registration method. We propose a surface parameterization method to compute the mapping between the 2D manifold and the common 2D planar domain. We can compute the matching among the time sequence of deforming geometry data through this common domain. Compared with previous work, our method is independent of the quality of mesh elements and more efficient for the time sequence data. Then we develop a global intensity-based registration method to solve the matching problem between 3D manifolds with temporal constraints. Our method is based on a 4D(3D+T) free-from B-spline deformation model which has both spatial and temporal smoothness. Compared with previous 4D image registration techniques, our method avoids some local minimum. Thus it can be solved faster and achieve better accuracy of landmark point predication. We demonstrate the efficiency of these works on the real applications. The first one is applied to the dynamic face registering and texture mapping. The second one is applied to lung tumor motion tracking in the medical image analysis. In our future work, we are developing more efficient mesh-based 4D registration method. It can be applied to tumor motion estimation and tracking, which can be used to calculate the read dose delivered to the lung and surrounding tissues. Thus this can support the online treatment of lung cancer radiotherapy

    Density-equalizing maps for simply-connected open surfaces

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    In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in R3\mathbb{R}^3. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored

    Learning quadrangulated patches for 3D shape parameterization and completion

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    We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface features of the shape. Unlike previous methods, we are able to encode surface patches of variable size as determined by the user. We propose novel methods for dictionary learning and patch reconstruction based on the query of a noisy input patch with holes. We evaluate the patch dictionary towards various applications in 3D shape inpainting, denoising and compression. Our method is able to predict missing vertices and inpaint moderately sized holes. We demonstrate a complete pipeline for reconstructing the 3D mesh from the patch encoding. We validate our shape parameterization and reconstruction methods on both synthetic shapes and real world scans. We show that our patch dictionary performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201

    Matrix-based Parameterizations of Skeletal Animated Appearance

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    Alors que le rendu réaliste gagne de l’ampleur dans l’industrie, les techniques à la fois photoréalistes et basées sur la physique, complexes en terme de temps de calcul, requièrent souvent une étape de précalcul hors-ligne. Les applications en temps réel, comme les jeux vidéo et la réalité virtuelle, se basent sur des techniques d’approximation et de précalcul pour atteindre des résultats réalistes. L’objectif de ce mémoire est l’investigation de différentes paramétrisations animées pour concevoir une technique d’approximation de rendu réaliste en temps réel. Notre investigation se concentre sur le rendu d’effets visuels appliqués à des personnages animés par modèle d’armature squelettique. Des paramétrisations combinant des données de mouvement et d’apparence nous permettent l’extraction de paramètres pour le processus en temps réel. Établir une dépendance linéaire entre le mouvement et l’apparence est ainsi au coeur de notre méthode. Nous nous concentrons sur l’occultation ambiante, où la simulation de l’occultation est causée par des objets à proximité bloquant la lumière environnante, jugée uniforme. L’occultation ambiante est une technique indépendante du point de vue, et elle est désormais essentielle pour le réalisme en temps réel. Nous examinons plusieurs paramétrisations qui traitent l’espace du maillage en fonction de l’information d’animation par squelette et/ou du maillage géométrique. Nous sommes capables d’approximer la réalité pour l’occultation ambiante avec une faible erreur. Notre technique pourrait également être étendue à d’autres effets visuels tels le rendu de la peau humaine (diffusion sous-surface), les changements de couleur dépendant du point de vue, les déformations musculaires, la fourrure ou encore les vêtements.While realistic rendering gains more popularity in industry, photorealistic and physically- based techniques often necessitate offline processing due to their computational complexity. Real-time applications, such as video games and virtual reality, rely mostly on approximation and precomputation techniques to achieve realistic results. The objective of this thesis is to investigate different animated parameterizations in order to devise a technique that can approximate realistic rendering results in real time. Our investigation focuses on rendering visual effects applied to skinned skeletonbased characters. Combined parameterizations of motion and appearance data are used to extract parameters that can be used in a real-time approximation. Trying to establish a linear dependency between motion and appearance is the basis of our method. We focus on ambient occlusion, a simulation of shadowing caused by objects that block ambient light. Ambient occlusion is a view-independent technique important for realism. We consider different parameterization techniques that treat the mesh space depending on skeletal animation information and/or mesh geometry. We are able to approximate ground-truth ambient occlusion with low error. Our technique can also be extended to different visual effects, such as rendering human skin (subsurface scattering), changes in color due to the view orientation, deformation of muscles, fur, or clothe
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