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

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

Fast character modeling with sketch-based PDE surfaces

© 2020, The Author(s). Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly

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

Modelling facial action units using partial differential equations.

This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. In particular, a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to suitable boundary conditions is utilized, where the chosen boundary curves are based on muscles movement defined by Facial Action Coding System (FACS). This study involved three stages: modelling faces, manipulating faces and application to simple facial animation. In the first stage, PDE method is used in modelling and generating a smooth 3D face. The PDE formulation using small sets of parameters contributes to the efficiency of human face representation. In the manipulation stage, a generic PDE face of neutral expression is manipulated to a face with expression using PDE descriptors that uniquely represents an action unit. A combination of the PDE descriptor results in a generic PDE face having an expression, which successfully modelled four basic expressions: happy, sad, fear and disgust. An example of application is given using simple animation technique called blendshapes. This technique uses generic PDE face in animating basic expressions.Ministry of Higher Education, Malaysia and Universiti Malaysia Terenggan

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

Generation of 3D characters from existing cartoons and a unified pipeline for animation and video games.

Despite the remarkable growth of 3D animation in the last twenty years, 2D is still popular today and often employed for both films and video games. In fact, 2D offers important economic and artistic advantages to production. In this thesis has been introduced an innovative system to generate 3D character from 2D cartoons, while maintaining important 2D features in 3D as well. However, handling 2D characters and animation in a 3D environment is not a trivial task, as they do not possess any depth information. Three different solutions have been proposed in this thesis. A 2.5D modelling method, which exploits billboarding, parallax scrolling and 2D shape interpolation to simulate the depth between the different body parts of the characters. Two additional full 3D solution have been presented. One based on inflation and supported by a surface registration method, and one that produces more accurate approximations by using information from the side views to solve an optimization problem. These methods have been introduced into a new unified pipeline that involves a game engine, and that could be used for animation and video games production. A unified pipeline introduces several benefits to animation production for either 2D and 3D content. On one hand, assets can be shared for different productions and media. On the other hand, real-time rendering for animated films allows immediate previews of the scenes and offers artists a way to experiment more during the making of a scene

Research Reports: 1997 NASA/ASEE Summer Faculty Fellowship Program

For the 33rd consecutive year, a NASA/ASEE Summer Faculty Fellowship Program was conducted at the Marshall Space Flight Center (MSFC). The program was conducted by the University of Alabama in Huntsville and MSFC during the period June 2, 1997 through August 8, 1997. Operated under the auspices of the American Society for Engineering Education, the MSFC program was sponsored by the Higher Education Branch, Education Division, NASA Headquarters, Washington, D.C. The basic objectives of the program, which are in the 34th year of operation nationally, are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA centers. The Faculty Fellows spent 10 weeks at MSFC engaged in a research project compatible with their interests and background and worked in collaboration with a NASA/MSFC colleague. This document is a compilation of Fellows' reports on their research during the summer of 1997. The University of Alabama in Huntsville presents the Co-Directors' report on the administrative operations of the program. Further information can be obtained by contacting any of the editors

Physics-based modelling, simulation, placement and learning for musculo-skeletal animations.

In character production for Visual Effects, the realism of deformations and flesh dynamics is a vital ingredient of the final rendered moving images shown on screen. This work is a collection of projects completed at the hosting company MPC London focused on the main components needed for the animation of musculo-skeletal systems: primitives modeling, physically accurate simulation, interactive placement. Complementary projects are also presented, including the procedural modeling of wrinkles and a machine learning approach for deformable objects based on Deep Neural Networks. Primitives modeling aims at proposing an approach to generating muscle geometry complete with tendons and fibers from superficial patches sketched on the character skin mesh. The method utilizes the physics of inflatable surfaces and produces meshes ready to be tetrahedralized, that is without compenetrations. A framework for the simulation of muscles, fascia and fat tissues based on the Finite Elements Method (FEM) is presented, together with the theoretical foundations of fiber-based materials with activations and their fitting in the Implicit Euler integration. The FEM solver is then simplified in or- der to achieve interactive rates to show the potential of interactive muscle placement on the skeleton to facilitate the creation of intersection-free primitives using collision detection and resolution. Alongside physics simulation for biological tissues, the thesis explores an approach that extends the Implicit Skinning technique with wrinkles based on convolution surfaces by exploiting the gradients of the combination of bones fields. Finally, this work discusses a possible approach to the learning of physics-based deformable objects based on deep neural networks which makes use of geodesic disks convolutional layers

Generative Mesh Modeling

Generative Modeling is an alternative approach for the description of three-dimensional shape. The basic idea is to represent a model not as usual by an agglomeration of geometric primitives (triangles, point clouds, NURBS patches), but by functions. The paradigm change from objects to operations allows for a procedural representation of procedural shapes, such as most man-made objects. Instead of storing only the result of a 3D construction, the construction process itself is stored in a model file. The generative approach opens truly new perspectives in many ways, among others also for 3D knowledge management. It permits for instance to resort to a repository of already solved modeling problems, in order to re-use this knowledge also in different, slightly varied situations. The construction knowledge can be collected in digital libraries containing domain-specific parametric modeling tools. A concrete realization of this approach is a new general description language for 3D models, the "Generative Modeling Language" GML. As a Turing-complete "shape programming language" it is a basis of existing, primitv based 3D model formats. Together with its Runtime engine the GML permits - to store highly complex 3D models in a compact form, - to evaluate the description within fractions of a second, - to adaptively tesselate and to interactively display the model, - and even to change the models high-level parameters at runtime.Die generative Modellierung ist ein alternativer Ansatz zur Beschreibung von dreidimensionaler Form. Zugrunde liegt die Idee, ein Modell nicht wie üblich durch eine Ansammlung geometrischer Primitive (Dreiecke, Punkte, NURBS-Patches) zu beschreiben, sondern durch Funktionen. Der Paradigmenwechsel von Objekten zu Geometrie-erzeugenden Operationen ermöglicht es, prozedurale Modelle auch prozedural zu repräsentieren. Statt das Resultat eines 3D-Konstruktionsprozesses zu speichern, kann so der Konstruktionsprozess selber repräsentiert werden. Der generative Ansatz eröffnet unter anderem gänzlich neue Perspektiven für das Wissensmanagement im 3D-Bereich. Er ermöglicht etwa, auf einen Fundus bereits gelöster Konstruktions-Aufgaben zurückzugreifen, um sie in ähnlichen, aber leicht variierten Situationen wiederverwenden zu können. Das Konstruktions-Wissen kann dazu in Form von Bibliotheken parametrisierter, Domänen-spezifischer Modellier-Werkzeuge gesammelt werden. Konkret wird dazu eine neue allgemeine Modell-Beschreibungs-Sprache vorgeschlagen, die "Generative Modeling Language" GML. Als Turing-mächtige "Programmiersprache für Form" stellt sie eine echte Verallgemeinerung existierender Primitiv-basierter 3D-Modellformate dar. Zusammen mit ihrer Runtime-Engine erlaubt die GML, - hochkomplexe 3D-Objekte extrem kompakt zu beschreiben, - die Beschreibung innerhalb von Sekundenbruchteilen auszuwerten, - das Modell adaptiv darzustellen und interaktiv zu betrachten, - und die Modell-Parameter interaktiv zu verändern