Peter Comninos

The case for research in game engine architecture

This paper is a call for research in the field of game engine architecture and design, a more comprehensive and thorough understanding of which we consider to be essential for its development. We present a number of key aspects that may help to define the problem space and provide a catalogue of questions that we believe identify areas of interest for future investigation.

Technical Section: PDE blending surfaces with C2 continuity

In this paper, we propose to use a general sixth-order partial differential equation (PDE) to solve the problem of C^2 continuous surface blending. Good accuracy and high efficiency are obtained by constructing a compound solution function, which is able to both satisfy the boundary conditions exactly and minimise the error of the PDE. This method can cope with much more complex surface-blending problems than other published analytical PDE methods. Comparison with the existing methods indicates that our method is capable of generating blending surfaces almost as fast and accurately as the closed-form method and it is more efficient and accurate than other extant PDE-based methods.

Blending surface generation using a fast and accurate analytical solution of a fourth-order PDE with three shape control parameters

In this paper, we propose to use a fourth-order partial differential equation (PDE) to solve a class of surface-blending problems. This equation has three vector-valued shape control parameters. It incorporates all the previously published forms of fourth-order PDEs for surface blending and can generate a larger class of blending surfaces than existing equations. To apply the proposed PDE to the solution of various blending problems, we have developed a fast and accurate resolution method. Our method modifies Navier’s solution for the elastic bending deformation of thin plates by making it satisfy the boundary conditions exactly. A comparison between our method, the closed-form solution method, and other existing analytical methods indicates that the developed method is able to generate blending surfaces almost as quickly and accurately as the closed-form solution method, far more efficiently and accurately than the numerical methods and other existing analytical methods. Having investigated the effects that the vector-valued shape parameters and the force function of the proposed equation have on the blending surface, we have found that they have a significant influence on its shape. They provide flexible user handles that surface designers can use to adjust the blending surface to acquire the desired shape. The developed method was employed in the investigation of surface-blending problems where the primary surfaces were expressed in parametric, implicit, and explicit forms.

A solid volumetric deformable muscle model for computer animation using weighted residual method

One of the most important yet expensive tasks in realistic character animation is to represent the body deformation, i.e. the deformation of the muscles. Because of the complexity of the geometry and deformable behaviours of such muscle tissues, three-dimensional (3D) finite element analysis (FEA) is usually employed. FEA however, requires enormous computing power, and often is impractical for computer animation where computational cost needs to be balanced with modelling accuracy. In this sense, it differs from engineering analysis where accuracy is often paramount for many applications, such as in aviation industry. Proposed in this paper is a 3D solid volumetric deformable muscle model which is almost as accurate as the FEA, but requires only a fraction of the computing cost. In this model, the muscle tissues are assumed to be elastic bodies with isotropic behaviour. The governing equations are derived and a weighted residual method is introduced to solve these equations. Suitable trial functions are proposed which satisfy the deformation compatibility and equilibrium equations. Using the least squares technique, the residual values on the boundaries are formulated and minimised to determine the unknown constants in the trial functions. In order to validate our model, the numerical results produced by our model are compared with the finite element computation and it is found that the two results closely agree with each other.

An interpolating piecewise bicubic surface with shape parameters

Abstract This paper presents a new method for the generation of a surface interpolating a mesh of control points. The surface is generated by piecewise bicubic interpolation and is derived from a classical Coons patch. The introduction of three shape parameters (namely the tension, continuity and bias parameters) provides the surface designer with a set of flexible user handles for shaping the surface locally. Modifying the values of the shape parameters allows the designer to introduce soft or hard cross patch boundaries thus introducing creases and corners to the curved surface. This approach is based on a generalisation of Kochanek–Bartels splines.

Technical Section: Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic

Techniques based on interval and affine arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of affine arithmetic called revised affine arithmetic. We extend the range of functions presented in revised affine arithmetic by introducing affine operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained affine forms of arbitrary functions provide faster and tighter function range evaluation. Several case studies for operations using affine forms are presented. The proposed techniques for surface interrogation are tested using ray-surface intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide fast and reliable rendering of a wide range of arbitrary procedurally defined implicit surfaces (including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others). We compare the function range evaluation technique based on extended revised affine arithmetic with other reliable techniques based on interval and affine arithmetic to show that our technique provides the fastest and tightest function range evaluation for fast and reliable interrogation of procedurally defined implicit surfaces.

Generating blending surfaces with a Pseudo-Lévy series solution to fourth order partial differential equations

AbstractIn our previous work, a more general fourth order partial differential equation (PDE) with three vector-valued parameters was introduced. This equation is able to generate a superset of the blending surfaces of those produced by other existing fourth order PDEs found in the literature. Since it is usually more difficult to solve PDEs analytically than numerically, many references are only concerned with numerical solutions, which unfortunately are often inefficient. In this paper, we have developed a fast and accurate resolution method, the pseudo-Lévy series method. Due to its analytical nature, the comparison with other existing methods indicates that the developed method can generate blending surfaces almost as quickly and accurately as the closed form resolution method, and has higher computational accuracy and efficiency than existing Fourier series and pseudo-spectral methods as well as other numerical methods. In addition, it can be used to solve complex surface blending problems which cannot be tackled by the closed form resolution method. To demonstrate the potential of this new method we have applied it to various surface blending problems, including the generation of the blending surface between parametric primary surfaces, general second and higher degree surfaces, and surfaces defined by explicit equations.

Embedded Implicit Stand‐Ins for Animated Meshes: A Case of Hybrid Modelling

In this paper, we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid‐modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand‐in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real‐time preview times are presented.

Augmented Sculpture: Computer Ghosts of Physical Artifacts

This paper describes an approach to computer-based sculpting concerned with the creation and modification of digital models based on physical abstract sculptures. The authors begin by presenting a survey of current methods for the creation of computer-based sculpted artifacts. They proceed to present some original methods and tools based on the Function Representation of geometric models. They introduce a specialized computer language, called Hyper Fun, that facilitates the modeling of complex objects. In addition to presenting computer-generated textured and animated models of pre-existing sculptures, they also show how novel shapes can be generated using the Hyper-Fun system. Finally they outline two advanced projects concerned with creating a sculpture-based augmented reality that allows for the interactive participation of the observer.

Functionally based augmented sculpting

In this paper we describe an approach to computer‐aided sculpting concerned with the creation and modification of digital models based on physical abstract sculptures. We begin by presenting a survey of current methods for the creation of computer‐aided sculptured artefacts. Then we proceed to present some original methods and tools based on the function representation of geometric models. We introduce a specialized computer language, named HyperFun, which facilitates the modelling of complex objects. As well as presenting computer‐generated animated models of pre‐existing sculptures by Russian artist Igor Seleznev, we also show how some interesting novel shapes can be generated using the HyperFun system. Finally we outline two advanced projects concerned with creating a sculpture‐based augmented reality which allows for the interactive participation of the observer. In this paper, we present experimental results, which hopefully have some artistic appeal. These results were produced by an international team of researchers and students collaborating through the Internet. Copyright