Adequate Inner Bound for Geometric Modeling with Compact Field Function

International audienceRecent advances in implicit surface modeling now provide highly controllable blending effects. These effects rely on the field functions of $\mathbb{R}^3 \rightarrow \mathbb{R}$ in which the implicit surfaces are defined. In these fields, there is an outside part in which blending is defined and an inside part. The implicit surface is the interface between these two parts. As recent operators often focus on blending, most efforts have been made on the outer part of field functions and little attention has been paid on the inner part. Yet, the inner fields are important as soon as difference and intersection operators are used. This makes its quality as crucial as the quality of the outside. In this paper, we analyze these shortcomings, and deduce new constraints on field functions such that differences and intersections can be seamlessly applied without introducing discontinuities or field distortions. In particular, we show how to adapt state of the art gradient-based union and blending operators to our new constraints. Our approach enables a precise control of the shape of both the inner or outer field boundaries. We also introduce a new set of asymmetric operators tailored for the modeling of fine details while preserving the integrity of the resulting fields

A Gradient-Based Implicit Blend

International audienceWe introduce a new family of binary composition operators that solves four major problems of constructive implicit modeling: suppressing bulges when two shapes merge, avoiding unwanted blending at a distance, ensuring that the resulting shape keeps the topology of the union, and enabling sharp details to be added without being blown up. The key idea is that field functions should not only be combined based on their values, but also on their gradients.We implement this idea through a family of C1 composition operators evaluated on the GPU for efficiency, and illustrate it by applications to constructive modeling and animation

High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

PHYSICS-BASED SHAPE MORPHING AND PACKING FOR LAYOUT DESIGN

The packing problem, also named layout design, has found wide applications in the mechanical engineering field. In most cases, the shapes of the objects do not change during the packing process. However, in some applications such as vehicle layout design, shape morphing may be required for some specific components (such as water and fuel reservoirs). The challenge is to fit a component of sufficient size in the available space in a crowded environment (such as the vehicle under-hood) while optimizing the overall performance objectives of the vehicle and improving design efficiency. This work is focused on incorporating component shape design into the layout design process, i.e. finding the optimal locations and orientations of all the components within a specified volume, as well as the suitable shapes of selected ones. The first major research issue is to identify how to efficiently and accurately morph the shapes of components respecting the functional constraints. Morphing methods depend on the geometrical representation of the components. The traditional parametric representation may lend itself easily to modification, but it relies on assumption that the final approximate shape of the object is known, and therefore, the morphing freedom is very limited. To morph objects whose shape can be changed arbitrarily in layout design, a mesh based morphing method based on a mass-spring physical model is developed. For this method, there is no need to explicitly specify the deformations and the shape morphing freedom is not confined. The second research issue is how to incorporate component shape design into a layout design process. Handling the complete problem at once may be beyond our reach,therefore decomposition and multilevel approaches are used. At the system level, a genetic algorithm (GA) is applied to find the positions and orientations of the objects, while at the sub-system or component level, morphing is accomplished for select components. Although different packing applications may have different objectives and constraints, they all share some common issues. These include CAD model preprocessing for packing purpose, data format translation during the packing process if performance evaluation and morphing use different representation methods, efficiency of collision detection methods, etc. These common issues are all brought together under the framework of a general methodology for layout design with shape morphing. Finally, practical examples of vehicle under-hood/underbody layout design with the mass-spring physical model based shape morphing are demonstrated to illustrate the proposed approach before concluding and proposing continuing work

Implicit Skinning: Real-Time Skin Deformation with Contact Modeling

SIGGRAPH 2013 Conference ProceedingsInternational audienceGeometric skinning techniques, such as smooth blending or dualquaternions, are very popular in the industry for their high performances, but fail to mimic realistic deformations. Other methods make use of physical simulation or control volume to better capture the skin behavior, yet they cannot deliver real-time feedback. In this paper, we present the first purely geometric method handling skin contact effects and muscular bulges in real-time. The insight is to exploit the advanced composition mechanism of volumetric, implicit representations for correcting the results of geometric skinning techniques. The mesh is first approximated by a set of implicit surfaces. At each animation step, these surfaces are combined in real-time and used to adjust the position of mesh vertices, starting from their smooth skinning position. This deformation step is done without any loss of detail and seamlessly handles contacts between skin parts. As it acts as a post-process, our method fits well into the standard animation pipeline. Moreover, it requires no intensive computation step such as collision detection, and therefore provides real-time performances

Towards additive manufacturing oriented geometric modeling using implicit functions

Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools. However, it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology, the object has to be converted into a solid representation. However, converting a known surface-based geometric representation into a printable representation is essentially a redesign process, and this is especially the case, when its interior material structure needs to be considered. To specify a 3D geometric object that is ready to be digitally manufactured, its representation has to be in a certain volumetric form. In this research, we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects. Like surface-based geometric representation is subtractive manufacturing-friendly, implicitly described geometric objects are additive manufacturing-friendly: implicit shapes are 3D printing ready. The implicit geometric representation allows to combine a geometric shape, material colors, an interior material structure, and other required attributes in one single description as a set of implicit functions, and no conversion is needed. In addition, as implicit objects are typically specified procedurally, very little data is used in their specifications, which makes them particularly useful for design and visualization with modern cloud-based mobile devices, which usually do not have very big storage spaces. Finally, implicit modeling is a design procedure that is parallel computing-friendly, as the design of a complex geometric object can be divided into a set of simple shape-designing tasks, owing to the availability of shape-preserving implicit blending operations

Study of the composition models of field functions in computer graphics

Les fonctions de champ scalaire sont un outil mathématique puissant pour la représentation de surfaces en informatique graphique. Malgré l'information de volume qu'elles offrent, combiné aux modèles de composition qui les accompagnent, les fonctions de champ scalaire ne sont encore utilisées que dans très peu d'applications en raison de leurs limitations, telles qu'une interaction utilisateur lente et un contrôle de la forme de la surface difficile.Dans cette thèse, nous étudions ces modèles de composition dans le but de les développer, de les améliorer et de faire en sorte qu'ils soient efficaces et pertinents pour l'informatique graphique. Pour cela, nous nous intéressons à deux applications.La première est la modélisation géométrique, où les fonctions de champ scalaire représentent des composants d'objets qui sont assemblés par paires dans un processus de création incrémental pour construire des objets complexes. Nous proposons une représentation unifiée des fonctions de champ scalaire et du modèle de composition afin d'obtenir un processus de modélisation plus stable et sans artefacts.La deuxième application à laquelle nous nous intéressons est la simulation et la reconstruction de fluides basées particules. Ici, les fonctions de champ scalaire représentent les contributions des particules qui échantillonnent le volume du fluide. Ces contributions sont alors combinées d'un coup pour reconstruire la surface du fluide. Nous proposons dans ce cadre de prendre en compte la topologie de la surface reconstruite dans la simulation, évitant ainsi un comportement inapproprié des particules, et donc du fluide ainsi simulé.Field functions are a powerful mathematical tool for surface representation in computer graphics. Despite the volume information they provide, combined with the composition models accompanying them, field functions are still used in only a few number of applications due to their limitations such as slow user interactions and a difficult shape control.In this thesis we study these composition models in order to develop and improve them and make them efficient and relevant for computer graphics. We do so through two applications.The first one is geometric modelling, where field functions represent object compounds that are combined pairwisely in an iterative creation process to design complex objects. We propose to unify and make consistent both the field function representation and the composition model to provide a more stable and artefact-free modelling process.The second one is fluid simulation and reconstruction based on particles. Here, field functions represent contributions of the particles sampling the fluid volume. These contributions are then combined in a row to build the fluid surface. In this application, we propose to take the topology of the reconstructed surface into account when running the fluid simulation, thus avoiding an inappropriate behavior of the particles, and then of the simulated fluid

CAD-Based Porous Scaffold Design of Intervertebral Discs in Tissue Engineering

With the development and maturity of three-dimensional (3D) printing technology over the past decade, 3D printing has been widely investigated and applied in the field of tissue engineering to repair damaged tissues or organs, such as muscles, skin, and bones, Although a number of automated fabrication methods have been developed to create superior bio-scaffolds with specific surface properties and porosity, the major challenges still focus on how to fabricate 3D natural biodegradable scaffolds that have tailor properties such as intricate architecture, porosity, and interconnectivity in order to provide the needed structural integrity, strength, transport, and ideal microenvironment for cell- and tissue-growth. In this dissertation, a robust pipeline of fabricating bio-functional porous scaffolds of intervertebral discs based on different innovative porous design methodologies is illustrated. Firstly, a triply periodic minimal surface (TPMS) based parameterization method, which has overcome the integrity problem of traditional TPMS method, is presented in Chapter 3. Then, an implicit surface modeling (ISM) approach using tetrahedral implicit surface (TIS) is demonstrated and compared with the TPMS method in Chapter 4. In Chapter 5, we present an advanced porous design method with higher flexibility using anisotropic radial basis function (ARBF) and volumetric meshes. Based on all these advanced porous design methods, the 3D model of a bio-functional porous intervertebral disc scaffold can be easily designed and its physical model can also be manufactured through 3D printing. However, due to the unique shape of each intervertebral disc and the intricate topological relationship between the intervertebral discs and the spine, the accurate localization and segmentation of dysfunctional discs are regarded as another obstacle to fabricating porous 3D disc models. To that end, we discuss in Chapter 6 a segmentation technique of intervertebral discs from CT-scanned medical images by using deep convolutional neural networks. Additionally, some examples of applying different porous designs on the segmented intervertebral disc models are demonstrated in Chapter 6