Complex skeletal implicit surfaces

Recent research has demonstrated the effectiveness of complex skeletal primitives such as subdivision curves and surfaces in implicit surface modeling. This paper presents a hierarchichal modeling system with an automatic levels of detail management for a simpler modeling with an accelerated rendering. We manage levels of detail with smooth transitions and tree optimizations speeding up visualization by an order of magnitude, which allows an interactive editing of the shapes

Morphological shape generation through user-controlled group metamorphosis

Morphological shape design is interpreted in this paper as a search for new shapes from a particular application domain represented by a set of selected shape instances. This paper proposes a new foundation for morphological shape design and generation. In contrast to existing generative procedures, an approach based on a user-controlled metamorphosis between functionally based shape models is presented. A formulation of the pairwise metamorphosis is proposed with a variety of functions described for the stages of deformation, morphing and offsetting. This formulation is then extended to the metamorphosis between groups of shapes with user-defined, dynamically correlated and weighted feature elements. A practical system was implemented in the form of plugin to Maya and tested by an industrial designer on a group of representative shapes from a particular domain. © 2013 Elsevier Ltd

Controlled metamorphosis between skeleton-driven animated polyhedral meshes of arbitrary topologies

Enabling animators to smoothly transform between animated meshes of differing topologies is a long-standing problem in geometric modelling and computer animation. In this paper, we propose a new hybrid approach built upon the advantages of scalar field-based models (often called implicit surfaces) which can easily change their topology by changing their defining scalar field. Given two meshes, animated by their rigging-skeletons, we associate each mesh with its own approximating implicit surface. This implicit surface moves synchronously with the mesh. The shape-metamorphosis process is performed in several steps: first, we collapse the two meshes to their corresponding approximating implicit surfaces, then we transform between the two implicit surfaces and finally we inverse transition from the resulting metamorphosed implicit surface to the target mesh. The examples presented in this paper demonstrating the results of the proposed technique were implemented using an in-house plug-in for Maya™. © 2013 The Authors Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd

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. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. 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

Space-Time Transfinite Interpolation of Volumetric Material Properties

The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures

Morphological Shape Generation through User-Controlled Group Metamorphosis

Abstract Morphological shape design is interpreted in this paper as a search for new shapes from a particular application domain represented by a set of selected shape instances. This paper proposes a new foundation for morphological shape design and generation. In contrast to existing generative procedures, an approach based on a user-controlled metamorphosis between functionally based shape models is presented. A formulation of the pairwise metamorphosis is proposed with a variety of functions described for the stages of deformation, morphing and offsetting. This formulation is then extended to the metamorphosis between groups of shapes with user-defined, dynamically correlated and weighted feature elements. A practical system was implemented in the form of plugin to Maya and tested by an industrial designer on a group of representative shapes from a particular domain

Morphing arquitectónico: transformaciones entre las casas usonianas de Frank Lloyd Wright

Esta tesis investiga sobre el proceso de transformación de la forma arquitectónica, analizando una técnica específica denominada morphing. La técnica del morphing se utiliza en los gráficos por ordenador para la transformación de la forma entre dos o más objetos dados. Desde un punto de vista técnico, se revisan y actualizan las metodologías y aplicaciones existentes, sus características específicas y sus incidencias sobre la arquitectura. Desde un punto de vista práctico, se utilizan una serie de modelos de las casas Usonianas de Frank Lloyd Wright, con el fin de experimentar la técnica y ver qué utilidades se pueden obtener a partir de su lógica de diseño. Como resultado de este análisis se obtiene una metodología genérica para el procedimiento de un morphing arquitectónico.This thesis investigates the transformation of architectural form, analyzing a specific technique called morphing. Morphing is a technique used in computer graphics to transform a form between two or more given objects. From a technical point of view, the existing techniques are reviewed and updated, as well as their specific characteristics and impact on architecture. From a practical point of view, some models of Usonian houses of Frank Lloyd Wright are used to experience the technique and see which utilities are available from his design logic. As a result of this analysis a generic methodology for the process of architectural morphing is obtained.Postprint (published version

Hybrid modelling of heterogeneous volumetric objects.

Heterogeneous multi-material volumetric modelling is an emerging and rapidly developing field. A Heterogeneous object is a volumetric object with interior structure where different physically-based attributes are defined. The attributes can be of different nature: material distributions, density, microstructures, optical properties and others. Heterogeneous objects are widely used where the presence of the interior structures is an important part of the model. Computer-aided design (CAD), additive manufacturing, physical simulations, visual effects, medical visualisation and computer art are examples of such applications. In particular, digital fabrication employing multi-material 3D printing techniques is becoming omnipresent. However, the specific methods and tools for representation, modelling, rendering, animation and fabrication of multi-material volumetric objects with attributes are only starting to emerge. The need for adequate unifying theoretical and practical framework has been obvious. Developing adequate representational schemes for heterogeneous objects is in the core of research in this area. The most widely used representations for defining heterogeneous objects are boundary representation, distance-based representations, function representation and voxels. These representations work well for modelling homogeneous (solid) objects but they all have significant drawbacks when dealing with heterogeneous objects. In particular, boundary representation, while maintaining its prevailing role in computer graphics and geometric modelling, is not inherently natural for dealing with heterogeneous objects especially in the con- text of additive manufacturing and 3D printing, where multi-material properties are paramount as well as in physical simulation where the exact representation rather than an approximate one can be important. In this thesis, we introduce and systematically describe a theoretical and practical framework for modelling volumetric heterogeneous objects on the basis of a novel unifying functionally-based hybrid representation called HFRep. It is based on the function representation (FRep) and several distance-based representations, namely signed distance fields (SDFs), adaptively sampled distance fields (ADFs) and interior distance fields (IDFs). It embraces advantages and circumvents disadvantages of the initial representations. A mathematically substantiated theoretical description of the HFRep with an emphasis on defining functions for HFRep objects’ geometry and attributes is provided. This mathematical framework serves as the basis for developing efficient algorithms for the generation of HFRep objects taking into account both their geometry and attributes. To make the proposed approach practical, a detailed description of efficient algorithmic procedures has been developed. This has required employing a number of novel techniques of different nature, separately and in combination. In particular, an extension of a fast iterative method (FIM) for numerical solving of the eikonal equation on hierarchical grids was developed. This allowed for efficient computation of smooth distance-based attributes. To prove the concept, the main elements of the framework have been implemented and used in several applications of different nature. It was experimentally shown that the developed methods and tools can be used for generating objects with complex interior structure, e.g. microstructures, and different attributes. A special consideration has been devoted to applications of dynamic nature. A novel concept of heterogeneous space-time blending (HSTB) method with an automatic control for metamorphosis of heterogeneous objects with textures, both in 2D and 3D, has been introduced, algorithmised and implemented. We have applied the HSTB in the context of ‘4D Cubism’ project. There are plans to use the developed methods and tools for many other applications

Hybrid modelling of time-variant heterogeneous objects.

The physical world consists of a wide range of objects of a diverse constitution. Past research was mainly focussed on the modelling of simple homogeneous objects of a uniform constitution. Such research resulted in the development of a number of advanced theoretical concepts and practical techniques for describing such physical objects. As a result, the process of modelling and animating certain types of homogeneous objects became feasible. In fact most physical objects are not homogeneous but heterogeneous in their constitution and it is thus important that one is able to deal with such heterogeneous objects that are composed of diverse materials and may have complex internal structures. Heterogeneous object modelling is still a very new and evolving research area, which is likely to prove useful in a wide range of application areas. Despite its great promise, heterogeneous object modelling is still at an embryonic state of development and there is a dearth of extant tools that would allow one to work with static and dynamic heterogeneous objects. In addition, the heterogeneous nature of the modelled objects makes it appealing to employ a combination of different representations resulting in the creation of hybrid models. In this thesis we present a new dynamic Implicit Complexes (IC) framework incorporating a number of existing representations and animation techniques. This framework can be used for the modelling of dynamic multidimensional heterogeneous objects. We then introduce an Implicit Complexes Application Programming Interface (IC API). This IC API is designed to provide various applications with a unified set of tools allowing these to model time-variant heterogeneous objects. We also present a new Function Representation (FRep) API, which is used for the integration of FReps into complex time-variant hybrid models. This approach allows us to create a practical multilevel modelling system suited for complex multidimensional hybrid modelling of dynamic heterogeneous objects. We demonstrate the advantages of our approach through the introduction of a novel set of tools tailored to problems encountered in simulation applications, computer animation and computer games. These new tools empower users and amplify their creativity by allowing them to overcome a large number of extant modelling and animation problems, which were previously considered difficult or even impossible to solve