Field functions for implicit surfaces

The use of 3D computer generated models is a rapidly growing part of the animation industry. But the established modelling techniques, using polygons or parametric patches, are not the best to define characters which can change their shape as they move. A newer method, using iso-surfaces in a scalar field, enables us to create models that can make the dynamic shape changes seen in hand animation. We call such modelsSoft Objects.From the user's point of view, a soft object is built from primitive key objects that blend to form a compound shape. In this paper, we examine some of the problems of choosing suitable keys and introduce some new field functions that increase the range of shapes available as keys.     

Transparent and Specular Object Reconstruction

This state of the art report covers reconstruction methods for transparent and specular objects or phenomena. While the 3D acquisition of opaque surfaces with Lambertian reflectance is a well‐studied problem, transparent, refractive, specular and potentially dynamic scenes pose challenging problems for acquisition systems. This report reviews and categorizes the literature in this field. Despite tremendous interest in object digitization, the acquisition of digital models of transparent or specular objects is far from being a solved problem. On the other hand, real‐world data is in high demand for applications such as object modelling, preservation of historic artefacts and as input to data‐driven modelling techniques. With this report we aim at providing a reference for and an introduction to the field of transparent and specular object reconstruction. We describe acquisition approaches for different classes of objects. Transparent objects/phenomena that do not change the straight ray geometry can be found foremost in natural phenomena. Refraction effects are usually small and can be considered negligible for these objects. Phenomena as diverse as fire, smoke, and interstellar nebulae can be modelled using a straight ray model of image formation. Refractive and specular surfaces on the other hand change the straight rays into usually piecewise linear ray paths, adding additional complexity to the reconstruction problem. Translucent objects exhibit significant sub‐surface scattering effects rendering traditional acquisition approaches unstable. Different classes of techniques have been developed to deal with these problems and good reconstruction results can be achieved with current state‐of‐the‐art techniques. However, the approaches are still specialized and targeted at very specific object classes. We classify the existing literature and hope to provide an entry point to this exiting field.     

Modelling polyhedral solids bounded by multi-curved parametric surfaces

Since the beginning of geometric modelling as a field of CAD a decade ago, the methods for interactive design of solid objects and interactive design of free-formed surfaces (of degree three and higher) were developed along parallel yet disjoint lines. One led to the development of techniques for representing and manipulating the shape of polyhedral solids bounded mostly by planes, while the other led to the development of techniques for the mathematical representation of curved surfaces, without paying attention to their combination into volumetric solids. Though the need for integrating solid object modelling with surface modelling for the design of such artefacts as machine parts, aircraft, cars and ships has been widely recognized, there is so far no single modelling system which provides such capabilities in a general way.An integrated solids modelling system for representing and manipulating polyhedral objects bounded by bicubic parametric surfaces is presented. Its basic capabilities include the representation of solids through a surface-based model, such that the surface underlying any face can be replaced by another surface that has been modelled independently. Other functionalities include scaling, rotation and translation of shapes and their pairwise combination into more complex shapes by means of spatial set operators.     

OCL for formal modelling of topological constraints involving regions with broad boundaries

Integrity constraints can control topological relations of objects in spatial databases. These constraints can be modelled using formal languages such as the spatial extension of the Object Constraint Language (Spatial OCL). This language allows the expression of topological integrity constraints involving crisp spatial objects but it does not support constraints involving spatial objects with vague shapes (e.g. forest stand, pollution zone, valley or lake). In this paper, we propose an extension of Spatial OCL based on (1) a geometric model for objects with vague shapes, and (2) an adverbial approach for modelling topological constraints involving regions with broad boundaries. This new language provides an easiness in the formal modelling of these complex constraints. Our approach has been implemented in a code generator. A case study is also presented in the paper in the field of agriculture spreading activities. AOCL _OVS takes account of the shape vagueness of spread parcel and improve spatial reasoning about them.     

FORMS: A flexible object recognition and modelling system

We describe a flexible object recognition and modelling system (FORMS) which represents and recognizes animate objects from their silhouettes. This consists of a model for generating the shapes of animate objects which gives a formalism for solving the inverse problem of object recognition. We model all objects at three levels of complexity: (i) the primitives, (ii) the mid-grained shapes, which are deformations of the primitives, and (iii) objects constructed by using a grammar to join mid-grained shapes together. The deformations of the primitives can be characterized by principal component analysis or modal analysis. When doing recognition the representations of these objects are obtained in a bottom-up manner from their silhouettes by a novel method for skeleton extraction and part segmentation based on deformable circles. These representations are then matched to a database of prototypical objects to obtain a set of candidate interpretations. These interpretations are verified in a top-down process. The system is demonstrated to be stable in the presence of noise, the absence of parts, the presence of additional parts, and considerable variations in articulation and viewpoint. Finally, we describe how such a representation scheme can be automatically learnt from examples.     

Modeling bounded and unbounded space with polyhedra: Topology and operators for manifold cell complexes

This paper proposes polyhedral space partitioning as an alternative to component assembly of digital models of objects with complex linear shapes. A partition is specified with a path-connected user model, where each object is bounded by n-manifolds. Faces and cells can be non-convex, multiply-connected and unbounded. The user interacts with the user model and specifies work steps. Each work step splits one edge, face or cell of the partition, or merges two neighboring objects of equal dimension. As a consequence, only a small subset of the model objects, consisting of the user specified objects and their neighbors, are affected by a work step. The user model is automatically mapped to a core model containing methods for topological relations and navigation. The topological structure is described by bundles of twin arrows of opposite direction arranged in polygons, twin facets with normal vectors of opposite direction and dihedral facet cycles at the edges. Imaginary topological objects are introduced to define unbounded cells, faces and edges. The approach guarantees that there is no overlap or gap between any pair of neighboring objects. It supports modelling of non-convex and multiply connected bounded and unbounded objects. For verification, several example models are presented and visualized. The paper ends with conclusions and an outlook to ongoing and planned further research in this field.     

Numerical modelling of wind flow over a complex topography

Numerical modelling of wind flow over complex dune topography is an ambitious prospect. There is an increasing need to understand wind flow over complex topography for land planning purposes to enable prediction of sediment transport at a particular site. New surveying techniques permit the rapid development of digital terrain models, however a stumbling block is the ability of Computational Fluid Dynamics (CFD) to emulate the wind flow over such a landscape. To overcome these difficulties, it is important to establish the parameters within which such simulations can operate. This paper details an initial two-dimensional numerical model developed in order to test various modelling assumptions against experimental field wind data. Mason Bay, Stewart Island, New Zealand was chosen as an undisturbed but accessible experimental site with a prevalent on-shore wind perpendicular to a simple foredune and a complex down-wind parabolic dune system. A complex topographical two-dimensional model with vegetation represented as a roughness was compared against field data along a transect dissecting a dune system.This paper establishes that:

* Replicating the roughness patterns at the surface is important

* The inlet profile should be duplicated with care

* Modelling only a portion of the domain can have an effect on the flow patterns due to outflow effects

* There is a modelling decision to be made between the complexity of the topography and the sophistication of the turbulence model and degree to which vegetation and sand transportation are modelled.

The long-term aim is to instil confidence in numerical techniques so that such technology can be used for predictive purposes.