This paper deals with 2D image transformations from a perspective of a 3D heterogeneous shape modeling and computer animation. Shape and image morphing techniques have attracted a lot of attention in artistic design, computer animation, and interactive and streaming applications. We present a novel method for morphing between two topologically arbitrary 2D shapes with sophisticated textures (raster color attributes) using a metamorphosis technique called space-time blending (STB) coupled with space-time transfinite interpolation. The method allows for a smooth transition between source and target objects by generating in-between shapes and associated textures without setting any correspondences between boundary points or features. The method requires no preprocessing and can be applied in 2D animation when position and topology of source and target objects are significantly different. With the conversion of given 2D shapes to signed distance fields, we have detected a number of problems with directly applying STB to them. We propose a set of novel and mathematically substantiated techniques, providing automatic control of the morphing process with STB and an algorithm of applying those techniques in combination. We illustrate our method with applications in 2D animation and interactive applications.

Abstract This paper presents the latest advances and research in Computer Graphics education in a nutshell. It is concerned with topics that were presented at the Education Track of the Eurographics Conference held in Lisbon in 2016. We describe works corresponding to approaches to Computer Graphics education that are unconventional in some way and attempt to tackle unsolved problems and challenges regarding the role of arts in computer graphics education, the role of research‐oriented activities in undergraduate education and the interaction among different areas of Computer Graphics, as well as their application to courses or extra‐curricular activities. We present related works addressing these topics and report experiences, successes and issues in implementing the approaches.

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.

In this paper we present the SHIVA project which was designed to provide virtual sculpting tools for children with complex disabilities, to allow them to engage with artistic and creative activities that they might otherwise never be able to access. Modern 3D printing then allows us to physically build their creations. To achieve this, we combined our expertise in education, accessible technology, user interfaces and geometric modelling. We built a generic accessible graphical user interface (GUI), a suitable geometric modelling system and used these to produce two prototype modelling systems. These tools were deployed in a school for students with disabilities and are being used for a variety of educational purposes. In this paper, we present the project's motivations, approach and implementation details together with initial results, including 3D printed objects designed by children with disabilities.

Abstract 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™.

Polygonal models are widely used in computer animation. Static polygonal models are commonly animated using an underlying skeleton controlling the deformation of the mesh. This technique, known as skeletal animation, allows the artist to produce complex animation sequences in a relatively easy way. However, performing complex transitions between arbitrary animated meshes remains a challenging problem. There is a set of established techniques to perform metamorphosis (3D morphing) between static 3D meshes [Lazarus and Verroust 1998], but most of these can not be easily applied to animated meshes. The approach presented in this poster allows us to produce with great ease metamorphosing transitions between animated meshes of arbitrary topology using polygonal-functional hybrids [Kravtsov et al. 2010a]. Our technique uses the meshes of the objects as well as their skeleton animations. As a result we are able to generate metamorphosis animations of time-varying meshes of arbitrary topologies in near real-time.

We propose a new approach to modelling heterogeneous objects containing internal spatial geometric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parametrized models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. Examples of rendering and digital fabrication of microstructure models are presented.

Abstract 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.

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions of the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modelling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples.

This paper describes a technology for modelling and rendering heterogeneous objects containing entities of various dimensionalities within a cellular-functional framework based on the implicit complex notion. Implicit complexes make it possible to combine a cellular representation and a constructive function representation. We describe a formal framework for such a hybrid representation and propose a general structure for implicit complexes. Then, we consider how an implicit complex can be described geometrically and topologically along with its associated attributes. Rendering algorithms for implicit complexes using ray-tracing are also discussed. Finally, we present a case study illustrating the proposed methods and algorithms.

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 © 2005 John Wiley & Sons, Ltd.

Function representation (FRep) allows for the construction of quite complex shapes, such as isosurfaces of real-valued functions composed using functionally defined primitives and operations. Calculating such functions in complex cases can be very time-consuming. Interactive extraction and visualization of isosurfaces for them can hardly be imagined. In this paper, we present a method for interactive navigation through a "sculpture garden" containing non-intersecting FRep objects defined in terms of the specialized high-level language HyperFun. Before the actual isosurface extraction and visualization occurs, the objects are voxelized on a regular 3D grid with the possibility of further adaptive voxelization. The polygonization employs a hierarchical representation of the voxelized data and a view-dependent isosurface reconstruction at different levels of detail. To speed up the extraction process, an isosurface is constructed only in the visible part of the data set, with its updates performed incrementally as the observer moves. Due to the low pre-processing costs required for isosurface mesh construction, it is possible to visualize time-dependent objects, if the hardware is capable of calculating the updates in real time.

Abstract The concept of solid texturing is extended in two directions: constructive modeling of space partitions for texturing and modeling of multidimensional textured objects called hypervolumes. A hypervolume is considered as a point set with attributes of both physical (density, temperature, etc.) and photometric (color, transparency, diffuse and specular reflections, etc.) nature. The point set geometry and attributes are modeled independently using real‐valued scalar functions of several variables. Each real‐valued function defining geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This approach provides a framework for modeling, texturing and visualization of 3D solids, time‐dependent and multidimensional objects in a completely uniform manner. We introduced a special modeling language and implemented software tools supporting the proposed approach. The concept of constructive hypervolume textures is independent of the geometry representation. We provide examples of textured Frep and BRep objects as illustrations. Copyright © 2002 John Wiley & Sons, Ltd.

There are limitations to the current BRep based "model then animate" paradigm when animating time-dependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in space-time or even higher dimensional space. The use of the function representation (FRep) is proposed due to the ease with which it handles higher dimensions. After creating a multidimensional FRep object, it then needs to be mapped to "multimedia" space. In the case of animation this means at least one geometric coordinate must be mapped to a dynamic coordinate (time). A case study is presented to explain the technique and demonstrate its use in the animated metamorphosis between several shapes of differing topology.