Brian Wyvill

Data Structure for Soft Objects

We introduce the concept ofsoft objects whose shape changes in response to their surroundings. Established geometric modelling techniques exist to handle most engineering components, including ‘free form’ shapes such as car bodies and telephones. More recently, there has been a lot of interest in modelling natural pheomena such as smoke, clouds, mountains and coastlines where the shapes are described stochastically, or as fractals. None of these techniques lends itself to the description ofsoft objects. This class of objects includes fabrics, cushions, living forms, mud and water. In this paper, we describe a method of modelling such objects and discuss its uses in animation. Our method is to represent asoft object, or collection of objects, as a surface of constant value in a scalar field over three dimensions. The main technical problem is to avoid calculating the field value at too many points. We do this with a combination of data structures at some cost in internal memory usage.

Interactive techniques for implicit modeling

Recent research has demonstrated the usefulness of implicit surfaces for modeling geometric objects. The interactive design of such surfaces has not, however, received the same attention as has the design of parametric surfaces. Principally this is due to the difficulty of controlling the shape of implicit surfaces while displaying the changes quickly enough for use within an interactive design environment. This paper describes progress towards interactive control of implicit surfaces and introduces new techniques useful to the designer.

Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System

Automatic blending has characterized the major advantage of implicit surface modeling systems. Recently, the introduction of deformations based on space warping and Boolean operations between primitives has increased the usefulness of such systems. We propose a further enhancement which will extend the range of models that can be easily and intuitively defined with a skeletal implicit surface system. We describe a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and Boolean operations. We call this structure the BlobTree. Blending and space warping are treated in the same way as union, difference and intersection, i.e. as nodes in the BlobTree. The traversal of the BlobTree is described along with two rendering algorithms; a polygonizer and a ray tracer. We present some examples of interesting models which can be made easily using our approach that would be very difficult to represent with conventional systems.

ShapeShop: sketch-based solid modeling with BlobTrees

Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketch-based modeling system utilizes Hierarchical Implicit Volume Models (BlobTrees) as an underlying shape representation. The BlobTree framework supports interactive creation of complex, detailed solid models with arbitrary topology. A new technique is described for inflating 2D contours into rounded three-dimensional implicit volumes. Sketch-based modeling operations are defined that combine these basic shapes using standard blending and CSG operators. Since the underlying volume hierarchy is by definition a construction history, individual sketched components can be non-linearly edited and removed. For example, holes can be interactively dragged through a shape. ShapeShop also provides 2D drawing assistance using a new curve-sketching system based on variational contours. A wide range of models can be sketched with ShapeShop, from cartoon-like characters to detailed mechanical parts. Examples are shown which demonstrate significantly higher model complexity than existing systems.

Robust iso-surface tracking for interactive character skinning

We present a novel approach to interactive character skinning, which is robust to extreme character movements, handles skin contacts and produces the effect of skin elasticity (sliding). Our approach builds on the idea of implicit skinning in which the character is approximated by a 3D scalar field and mesh-vertices are appropriately re-projected. Instead of being bound by an initial skinning solution used to initialize the shape at each time step, we use the skin mesh to directly track iso-surfaces of the field over time. Technical problems are two-fold: firstly, all contact surfaces generated between skin parts should be captured as iso-surfaces of the implicit field; secondly, the tracking method should capture elastic skin effects when the joints bend, and as the character returns to its rest shape, so the skin must follow. Our solutions include: new composition operators enabling blending effects and local self-contact between implicit surfaces, as well as a tangential relaxation scheme derived from the as-rigid-as possible energy to solve the tracking problem.

Interactive decal compositing with discrete exponential maps

A method is described for texturing surfaces using decals, images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O(N log N) discrete approximation to the exponential map which requires only a single additional step in Dijkstras graph-distance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/feature-matching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.

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 users 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.

Implicit skinning: real-time skin deformation with contact modeling

Geometric skinning techniques, such as smooth blending or dual-quaternions, are very popular in the industry for their high performances, but fail to mimic realistic deformations. Other methods make use of physical simulation or control volume to better capture the skin behavior, yet they cannot deliver real-time feedback. In this paper, we present the first purely geometric method handling skin contact effects and muscular bulges in real-time. The insight is to exploit the advanced composition mechanism of volumetric, implicit representations for correcting the results of geometric skinning techniques. The mesh is first approximated by a set of implicit surfaces. At each animation step, these surfaces are combined in real-time and used to adjust the position of mesh vertices, starting from their smooth skinning position. This deformation step is done without any loss of detail and seamlessly handles contacts between skin parts. As it acts as a post-process, our method fits well into the standard animation pipeline. Moreover, it requires no intensive computation step such as collision detection, and therefore provides real-time performances.

Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.

Fast line scan-conversion

A major bottleneck in many graphics displays is the time required to scan-convert straight line segments. Most manufacturers use hardware based on Bresenhams [5] line algorithm. In this paper an algorithm is developed based on the original Bresenham scan-conversion together with the symmetry first noted by Gardner [18] and a recent double-step technique [31]. This results in a speed-up of scan-conversion by a factor of approximately 4 as compared to the original Bresenham algorithm. Hardware implementations are simple and efficient since the property of using only shift and increment operations is preserved.