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

Gauge Invariant Framework for Shape Analysis of Surfaces

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energy that measures only the normal components of velocities along the path. In other words, this paper defines and solves for geodesics directly on the shape space and avoids complications resulting from the quotient operation. This comprehensive framework is invariant to arbitrary parameterizations of surfaces along paths, a phenomenon termed as gauge invariance. Additionally, this paper makes a link between different elastic metrics used in the computer science literature on one hand, and the mathematical literature on the other hand, and provides a geometrical interpretation of the terms involved. Examples using real and simulated 3D objects are provided to help illustrate the main ideas.Comment: 15 pages, 11 Figures, to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence in a better resolutio

XMM-Newton Witness of M86 X-ray Metamorphosis

The environmental influence of cluster media on its member galaxies, known as Butcher--Oemler effect, has recently been subject to revision due to numerous observations of strong morphological transformations occurring outside the cluster virial radii, caused by some unidentified gas removal processes. In this context we present new XMM-Newton observations of M86 group. The unique combination of high spatial and spectral resolution and large field of view of XMM-Newton allows an in-depth investigation of the processes involved in the spectacular disruption of this object. We identify a possible shock with Mach number of ~1.4 in the process of crushing the galaxy in the North-East direction. The latter is ascribed to the presence of a dense X-ray emitting filament, previously revealed in the RASS data. The shock is not associated with other previously identified features of M86 X-ray emission, such as the plume, the north-eastern arm and the southern extension, which are found to have low entropy, similar to the inner 2 kpc of M86. Finally, mere existence of the large scale gas halo around the M86 group, suggests that the disruptions of M86's X-ray halo may be caused by small-scale types of interactions such as galaxy-galaxy collisions.Comment: 11 pages, A&A in pres

Virtual sculpting and 3D printing for young people with disabilities

In this paper, we present the SHIVA project which was designed to provide virtual sculpting tools for young people 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) and a suitable geometric modelling system and used these to produce two prototype modelling exercises. These tools were deployed in a school for students with complex disabilities and are now being used for a variety of educational and developmental purposes. In this paper, we present the project's motivations, approach and implementation details together with initial results, including 3D printed objects designed by young people who have disabilties

Automatically Controlled Morphing of 2D Shapes with Textures

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

Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond

A novel, protean, topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here we present a minimal and local continuum model that can explain many of the features of the phyllotactic soliton, such as locked speed, screw shift, energy transport and, for Wigner crystal on a nanotube, charge transport. The treatment is general and should apply to other spiraling systems. Unlike e.g. Sine-Gornon-like systems, our solitons can exist between non-degenerate structure, imply a power flow through the system, dynamics of the domains it separates; we also predict pulses, both static and dynamic. Applications include charge transport in Wigner Crystals on nanotubes or A- to B-DNA transitions.Comment: 8 Pages, 6 Figures, Phys Rev E in pres

S-brane Actions

We derive effective actions for Spacelike branes (S-branes) and find a solution describing the formation of fundamental strings in the rolling tachyon background. The S-brane action is a Dirac-Born-Infeld action for Euclidean worldvolumes defined in the context of time-dependent tachyon condensation of non-BPS branes. It includes gauge fields and in particular a scalar field associated with translation along the time direction. We show that the BIon spike solutions constructed in this system correspond to the production of a confined electric flux tube (a fundamental string) at late time of the rolling tachyon.Comment: 10 pages, 1 figure. References added, typos correcte

Form, performance and trade-offs in swimming and stability of armed larvae

Diverse larval forms swim and feed with ciliary bands on arms or analogous structures. Armed morphologies are varied: numbers, lengths, and orientations of arms differ among species, change through development, and can be plastic in response to physiological or environmental conditions. A hydromechanical model of idealized equal-armed larvae was used to examine functional consequences of these varied arm arrangements for larval swimming performance. With effects of overall size, ciliary tip speed, and viscosity factored out, the model suggested trade-offs between morphological traits conferring high swimming speed and weight-carrying ability in still water (generally few arms and low arm elevations), and morphologies conferring high stability to external disturbances such as shear flows (generally many arms and high arm elevations). In vertical shear, larvae that were passively stabilized by a center of buoyancy anterior to the center of gravity tilted toward and consequently swam into downwelling flows. Thus, paradoxically, upward swimming by passively stable swimmers in vertical shear resulted in enhanced downward transport. This shear-dependent vertical transport could affect diverse passively stable swimmers, not just armed larvae. Published descriptions of larvae and metamorphosis of 13 ophiuroids suggest that most ophioplutei fall into two groups: those approximating modeled forms with two arms at low elevations, predicted to enhance speed and weight capacity, and those approximating modeled forms with more numerous arms of equal length at high elevations, predicted to enhance stability in shear