On the spine of a PDE surface

yesThe spine of an object is an entity that can characterise the object¿s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes

Interactive surface design and manipulation using PDE-method through Autodesk Maya plug-in.

This paper aims to propose a method for geometric design, modelling and shape manipulation using minimum input design parameters. Here, we address the method for the construction of 3D geometry based on the use of Elliptic Partial Differential Equations (PDE). The geometry corresponding to an object is treated as a set of surface patches, whereby each surface patch is represented using four boundary curves in the 3D space that formulate the appropriate boundary conditions for the chosen PDE. We present our methodology using a plugin that was developed utilizing Maya API. The plug-in provides the user with tools that could be used easily and effectively for designing purposes. Maya is a popular 3D modelling tool. Various types of shapes with different complexities are presented here. Our proposed method allow the designer to utilize the Maya functionality for sketching curves in the 3D space that represents the outline of arbitrary shapes, construct the corresponding model using the PDE method, deform and sculpt these models interactively by editing the boundary curves

Parametric surface meshing for design optimisation using a PDE formulation

yesThe problem of parametric surface meshing for the purpose of design optimisation using finite element analysis is considered. Here the surface mesh is generated as a solution of a suitably posed boundary value problem implemented on a 2D parameter space. A robust meshing scheme is presented where an initial mesh is manipulated, with the aid of the 2D parameter space, so as to obtain a suitable surface triangulation. This meshing scheme can then be used to create suitable finite element meshes with which accurate design optimisations can be carried out

Cyclic animation using Partial differential Equations

YesThis work presents an efficient and fast method for achieving cyclic animation using Partial Differential Equations (PDEs). The boundary-value nature associ- ated with elliptic PDEs offers a fast analytic solution technique for setting up a framework for this type of animation. The surface of a given character is thus cre- ated from a set of pre-determined curves, which are used as boundary conditions so that a number of PDEs can be solved. Two different approaches to cyclic ani- mation are presented here. The first consists of using attaching the set of curves to a skeletal system hold- ing the animation for cyclic motions linked to a set mathematical expressions, the second one exploits the spine associated with the analytic solution of the PDE as a driving mechanism to achieve cyclic animation, which is also manipulated mathematically. The first of these approaches is implemented within a framework related to cyclic motions inherent to human-like char- acters, whereas the spine-based approach is focused on modelling the undulatory movement observed in fish when swimming. The proposed method is fast and ac- curate. Additionally, the animation can be either used in the PDE-based surface representation of the model or transferred to the original mesh model by means of a point to point map. Thus, the user is offered with the choice of using either of these two animation repre- sentations of the same object, the selection depends on the computing resources such as storage and memory capacity associated with each particular application

Intelligent Data Storage and Retrieval for Design Optimisation – an Overview

This paper documents the findings of a literature review conducted by the Sir Lawrence Wackett Centre for Aerospace Design Technology at RMIT University. The review investigates aspects of a proposed system for intelligent design optimisation. Such a system would be capable of efficiently storing (and compressing if required) a range of types of design data into an intelligent database. This database would be accessed by the system during subsequent design processes, allowing for search of relevant design data for re-use in later designs, allowing it to become very efficient in reducing the time for later designs as the database grows in size. Extensive research has been performed, in both theoretical aspects of the project, and practical examples of current similar systems. This research covers the areas of database systems, database queries, representation and compression of design data, geometric representation and heuristic methods for design applications.

Modelling and Animation using Partial Differential Equations. Geometric modelling and computer animation of virtual characters using elliptic partial differential equations.

This work addresses various applications pertaining to the design, modelling and animation of parametric surfaces using elliptic Partial Differential Equations (PDE) which are produced via the PDE method. Compared with traditional surface generation techniques, the PDE method is an effective technique that can represent complex three-dimensional (3D) geometries in terms of a relatively small set of parameters. A PDE-based surface can be produced from a set of pre-configured curves that are used as the boundary conditions to solve a number of PDE. An important advantage of using this method is that most of the information required to define a surface is contained at its boundary. Thus, complex surfaces can be computed using only a small set of design parameters. In order to exploit the advantages of this methodology various applications were developed that vary from the interactive design of aircraft configurations to the animation of facial expressions in a computer-human interaction system that utilizes an artificial intelligence (AI) bot for real time conversation. Additional applications of generating cyclic motions for PDE based human character integrated in a Computer-Aided Design (CAD) package as well as developing techniques to describe a given mesh geometry by a set of boundary conditions, required to evaluate the PDE method, are presented. Each methodology presents a novel approach for interacting with parametric surfaces obtained by the PDE method. This is due to the several advantages this surface generation technique has to offer. Additionally, each application developed in this thesis focuses on a specific target that delivers efficiently various operations in the design, modelling and animation of such surfaces.The project files will not be available online

Geometric modelling and shape optimisation of pharmaceutical tablets. Geometric modelling and shape optimisation of pharmaceutical tablets using partial differential equations.

Pharmaceutical tablets have been the most dominant form for drug delivery and they need to be strong enough to withstand external stresses due to packaging and loading conditions before use. The strength of the produced tablets, which is characterised by their compressibility and compactibility, is usually deter-mined through a physical prototype. This process is sometimes quite expensive and time consuming. Therefore, simulating this process before hand can over-come this problem. A technique for shape modelling of pharmaceutical tablets based on the use of Partial Differential Equations is presented in this thesis. The volume and the sur-face area of the generated parametric tablet in various shapes have been es-timated numerically. This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of pa-rameters responsible for describing the surface in order to generate a solid tab-let. The shape and size of the generated solid tablets can be changed by ex-ploiting the analytic expressions relating the coefficients associated with the PDE method. The solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model a displace-ment component of a compressed PDE-based representation of a flat-faced round tablet. The simulation results, which are analysed using the Heckel model, show that the developed model is capable of predicting the compressibility of pharmaceutical powders since it fits the experimental data accurately. The opti-mal design of pharmaceutical tablets with particular volume and maximum strength has been obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation

Skin deformation and animation of character models based on static and dynamic ordinary differential equations.

Animated characters play an important role in the field of computer animation, simulation and games. The basic criterion of good character animation is that the animated characters should appear realistic. This can be achieve through proper skin deformations for characters. Although various skin deformation approaches (Joint-based, Example-based, Physics-based, Curve-based and PDE-based) have been developed, the problem of generating realistic skin deformations efficiently with a small data set is a big challenge. In order to address the limitations of skin deformation, this thesis presents a workflow consisting of three main steps. First, the research has developed a new statistical method to determine the positions of joints based on available X-ray images. Second, an effective method for transferring the deformations of the curves to the polygonal model with high accuracy has been developed. Lastly, the research has produced a simple and efficient method to animate skin deformations by introducing a curved-based surface manipulation method combined with physics and data-driven approaches. The novelty of this method depends on a new model of dynamic deformations and an efficient finite difference solution of the model. The application examples indicate that the curve-based dynamic method developed in this thesis can achieve good realism and high computational efficiency with small data sets in the creation of skin deformations

DEFORM'06 - Proceedings of the Workshop on Image Registration in Deformable Environments

Preface These are the proceedings of DEFORM'06, the Workshop on Image Registration in Deformable Environments, associated to BMVC'06, the 17th British Machine Vision Conference, held in Edinburgh, UK, in September 2006. The goal of DEFORM'06 was to bring together people from different domains having interests in deformable image registration. In response to our Call for Papers, we received 17 submissions and selected 8 for oral presentation at the workshop. In addition to the regular papers, Andrew Fitzgibbon from Microsoft Research Cambridge gave an invited talk at the workshop. The conference website including online proceedings remains open, see http://comsee.univ-bpclermont.fr/events/DEFORM06. We would like to thank the BMVC'06 co-chairs, Mike Chantler, Manuel Trucco and especially Bob Fisher for is great help in the local arrangements, Andrew Fitzgibbon, and the Programme Committee members who provided insightful reviews of the submitted papers. Special thanks go to Marc Richetin, head of the CNRS Research Federation TIMS, which sponsored the workshop. August 2006 Adrien Bartoli Nassir Navab Vincent Lepeti

An efficient active B-spline/nurbs model for virtual sculpting

This thesis presents an Efficient Active B-Spline/Nurbs Model for Virtual Sculpting. In spite of the on-going rapid development of computer graphics and computer-aided design tools, 3D graphics designers still rely on non-intuitive modelling procedures for the creation and manipulation of freeform virtual content. The ’Virtual Sculpting' paradigm is a well-established mechanism for shielding designers from the complex mathematics that underpin freeform shape design. The premise is to emulate familiar elements of traditional clay sculpting within the virtual design environment. Purely geometric techniques can mimic some physical properties. More exact energy-based approaches struggle to do so at interactive rates. This thesis establishes a unified approach for the representation of physically aware, energy-based, deformable models, across the domains of Computer Graphics, Computer-Aided Design and Computer Vision, and formalises the theoretical relationships between them. A novel reformulation of the computer vision approach of Active Contour Models (ACMs) is proposed for the domain of Virtual Sculpting. The proposed ACM-based model offers novel interaction behaviours and captures a compromise between purely geometric and more exact energy-based approaches, facilitating physically plausible results at interactive rates. Predefined shape primitives provide features of interest, acting like sculpting tools such that the overall deformation of an Active Surface Model is analogous to traditional clay modelling. The thesis develops a custom-approach to provide full support for B-Splines, the de facto standard industry representation of freeform surfaces, which have not previously benefited from the seamless embodiment of a true Virtual Sculpting metaphor. A novel generalised computationally efficient mathematical framework for the energy minimisation of an Active B-Spline Surface is established. The resulting algorithm is shown to significantly reduce computation times and has broader applications across the domains of Computer-Aided Design, Computer Graphics, and Computer Vision. A prototype ’Virtual Sculpting’ environment encapsulating each of the outlined approaches is presented that demonstrates their effectiveness towards addressing the long-standing need for a computationally efficient and intuitive solution to the problem of interactive computer-based freeform shape design