Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

Modeling and Visualization of Multi-material Volumes

The terminology of multi-material volumes is discussed. The classification of the multi-material volumes is given from the spatial partitions, spatial domain for material distribution, types of involved scalar fields and types of models for material distribution and composition of several materials points of view. In addition to the technical challenges of multi-material volume representations, a range of key challenges are considered before such representations can be adopted as mainstream practice

Doctor of Philosophy

dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research

Unifying Geometry and Mesh Adaptive Refinement Using Loop Subdivision

RÉSUMÉ Cette thèse présente une nouvelle approche pour le raffinement de trois types de maillages : courbes, surfaces triangulaires et maillages tétraédriques tridimensionnels. Cette approche utilise des représentations par subdivisions afin de définir, modifier, analyser et visualiser des modèles géométriques de topologie arbitraire pour les applications de simulation numérique. Les représentations par subdivisions sont générées à l’aide des subdivisions de Loop. Après avoir étudié les inconvénients du manque de flexibilité dans le contrôle des niveaux de détails et du manque de précision dans les représentations de modèles géométriques utilisant les subdivisions itératives, approximatives et non-uniformes pour se rapprocher des modèles simulés, nous introduisons une nouvelle méthode de subdivision adaptative pour le raffinement de maillages. Cette méthode de raffinement à un seul niveau a été développée afin de supporter les subdivisions adaptatives pour les trois types de maillages. Cette méthode évite le stockage par hiérarchie et les problèmes d’assemblage rencontrés durant la génération des maillages multi-résolutions par subdivisions, surtout pour les maillages tétraédriques. La mise en œuvre de subdivisions pour les maillages adaptatifs tétraédriques amène deux innovations : la configuration de forme de fractionnement des tétraèdres et l’amélioration de la paramétrisation des surfaces de subdivision. La combinaison naturelle de ces deux innovations permet la génération par subdivision de maillages multi-résolutions tétraédriques dont les surfaces frontières sont exactement sur les limites de subdivision. Notre recherche contient cinq parties. Premièrement, nous développons un schéma de Loop pour la subdivision des solides, lequel permet d’intégrer le fractionnement topologique des arêtes avec le lissage géométrique des surfaces frontières. Deuxièmement, nous fusionnons les raffinements adaptatifs avec les techniques de subdivision, ce qui permet la subdivision adaptive complète du maillage tout en ayant les surfaces frontières projetées sur les limites de subdivision. Troisièmement, nous étudions et comparons des techniques existantes de paramétrisation des surfaces de subdivision, ce qui permet d’obtenir directement la limite de subdivision de toutes positions arbitraires sur les surfaces de subdivision de Loop. Quatrièmement, nous construisons les règles de création des sommets fixes et des arêtes vives du schéma de subdivision de Loop pour les modèles solides, ce qui permet de préserver les caractéristiques anguleuses des surfaces frontières des maillages tétraédriques. Finalement, nous utilisons un critère de qualité des maillages pour valider nos résultats et nous présentons la performance des calculs en ce qui a trait à la modélisation des solides.----------ABSTRACT In this thesis, we present a new refinement approach on three types of meshes: curves, triangular surfaces and 3D tetrahedral meshes. This approach utilizes subdivision-based representations to create, modify, analyze and visualize geometric models with arbitrary topology for numerical simulation applications. The subdivision-based representations are generated by utilizing Loop subdivisions. After studying the disadvantage of lack of flexibility in controlling LODs (Level Of Details) and accuracy in representing geometric models by using the non-uniform approximating subdivision iterations to approach simulated models, we introduce adaptive subdivisions in our refinement work. We develop a single-level refinement method to support adaptive subdivisions on the three types of meshes. This single-level method eliminates the hierarchy storage and the stitching issues encountered during the generation of multi-resolution subdivision meshes, especially 3D tetrahedral meshes. The implementation of adaptive tetrahedral mesh subdivisions brings up two innovations: the configuration of tetrahedron split patterns and the improvement in subdivision surface parameterizations. The natural combination of these two innovations fulfills generating multi-resolution subdivision tetrahedral meshes, whose boundary surfaces lie exactly on their subdivision limits. Our research work includes five parts. Firstly, we develop the Loop-based solid subdivision scheme, which permits integrating edge-based topological splits with geometrical smoothing on boundary surfaces. Secondly, we merge subdivision techniques with adaptive refinements with, which permits whole meshes to be adaptively subdivided and boundary meshes to be projected to their subdivision limits. Thirdly, we study and compare the existing subdivision surface parameterization techniques, which eventually permits obtaining the limit subdivision of any arbitrary position on Loop subdivision surfaces. Fourthly, we complete vertex and edge crease creation rules of the Loop-based solid subdivision scheme, which permits preserving sharp features on boundary surfaces of 3D tetrahedral meshes. Finally, we use a mesh quality evaluator to validate our results and we evaluate system performance in the context of solid modeling

2D and 3D surface image processing algorithms and their applications

This doctoral dissertation work aims to develop algorithms for 2D image segmentation application of solar filament disappearance detection, 3D mesh simplification, and 3D image warping in pre-surgery simulation. Filament area detection in solar images is an image segmentation problem. A thresholding and region growing combined method is proposed and applied in this application. Based on the filament area detection results, filament disappearances are reported in real time. The solar images in 1999 are processed with this proposed system and three statistical results of filaments are presented. 3D images can be obtained by passive and active range sensing. An image registration process finds the transformation between each pair of range views. To model an object, a common reference frame in which all views can be transformed must be defined. After the registration, the range views should be integrated into a non-redundant model. Optimization is necessary to obtain a complete 3D model. One single surface representation can better fit to the data. It may be further simplified for rendering, storing and transmitting efficiently, or the representation can be converted to some other formats. This work proposes an efficient algorithm for solving the mesh simplification problem, approximating an arbitrary mesh by a simplified mesh. The algorithm uses Root Mean Square distance error metric to decide the facet curvature. Two vertices of one edge and the surrounding vertices decide the average plane. The simplification results are excellent and the computation speed is fast. The algorithm is compared with six other major simplification algorithms. Image morphing is used for all methods that gradually and continuously deform a source image into a target image, while producing the in-between models. Image warping is a continuous deformation of a: graphical object. A morphing process is usually composed of warping and interpolation. This work develops a direct-manipulation-of-free-form-deformation-based method and application for pre-surgical planning. The developed user interface provides a friendly interactive tool in the plastic surgery. Nose augmentation surgery is presented as an example. Displacement vector and lattices resulting in different resolution are used to obtain various deformation results. During the deformation, the volume change of the model is also considered based on a simplified skin-muscle model

Distance based heterogeneous volume modelling.

Natural objects, such as bones and watermelons, often have a heterogeneous composition and complex internal structures. Material properties inside the object can change abruptly or gradually, and representing such changes digitally can be problematic. Attribute functions represent physical properties distribution in the volumetric object. Modelling complex attributes within a volume is a complex task. There are several approaches to modelling attributes, but distance functions have gained popularity for heterogeneous object modelling because, in addition to their usefulness, they lead to predictability and intuitiveness. In this thesis, we consider a unified framework for heterogeneous volume modelling, specifically using distance fields. In particular, we tackle various issues associated with them such as the interpolation of volumetric attributes through time for shape transformation and intuitive and predictable interpolation of attributes inside a shape. To achieve these results, we rely on smooth approximate distance fields and interior distances. This thesis deals with outstanding issues in heterogeneous object modelling, and more specifically in modelling functionally graded materials and structures using different types of distances and approximation thereof. We demonstrate the benefits of heterogeneous volume modelling using smooth approximate distance fields with various applications, such as adaptive microstructures, morphological shape generation, shape driven interpolation of material properties through time and shape conforming interpolation of properties. Distance based modelling of attributes allows us to have a better parametrization of the object volume and design gradient properties across an object. This becomes more important nowadays with the growing interest in rapid prototyping and digital fabrication of heterogeneous objects and can find practical applications in different industries