Dimension on Discrete Spaces

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious geometrical background. This work presents some discrete models of n-dimensional Euclidean spaces, n-dimensional spheres, a torus and a projective plane. It explains how to construct new discrete spaces and describes in this connection several three-dimensional closed surfaces with some topological singularities It also analyzes the topology of (3+1)-spacetime. We are also discussing the question by R. Sorkin [19] about how to derive the system of simplicial complexes from a system of open covering of a topological space S.Comment: 16 pages, 8 figures, Latex. Figures are not included, available from the author upon request. Preprint SU-GP-93/1-1. To appear in "International Journal of Theoretical Physics

Twisty itsy bitsy topological field theory

We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on those surfaces respecting signs (sutures). It has information-theoretic (``itsy'') and quantum-field-theoretic (``bitsy'') aspects. In the process we extend some results of sutured Floer homology, consider associated ribbon graph structures, and construct explicit admissible Heegaard decompositions.Comment: 52 pages, 26 figure

Issues and techniques for collaborative music making on multi-touch surfaces

A range of systems exist for collaborative music making on multi-touch surfaces. Some of them have been highly successful, but currently there is no systematic way of designing them, to maximise collaboration for a particular user group. We are particularly interested in systems that will engage novices and experts. We designed a simple application in an initial attempt to clearly analyse some of the issues. Our application allows groups of users to express themselves in collaborative music making using pre-composed materials. User studies were video recorded and analysed using two techniques derived from Grounded Theory and Content Analysis. A questionnaire was also conducted and evaluated. Findings suggest that the application affords engaging interaction. Enhancements for collaborative music making on multi-touch surfaces are discussed. Finally, future work on the prototype is proposed to maximise engagement

Working Document on Gloss Ontology

This document describes the Gloss Ontology. The ontology and associated class model are organised into several packages. Section 2 describes each package in detail, while Section 3 contains a summary of the whole ontology

Subdivision Directional Fields

We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the finite-element representation with discrete exterior calculus. By commuting with differential operators, our subdivision is structure-preserving: it reproduces curl-free fields precisely, and reproduces divergence-free fields in the weak sense. Moreover, our subdivision scheme directly extends to directional fields with several vectors per face by working on the branched covering space. Finally, we demonstrate how our scheme can be applied to directional-field design, advection, and robust earth mover's distance computation, for efficient and robust computation

Designing Familiar Open Surfaces

While participatory design makes end-users part of the design process, we might also want the resulting system to be open for interpretation, appropriation and change over time to reflect its usage. But how can we design for appropriation? We need to strike a good balance between making the user an active co-constructor of system functionality versus making a too strong, interpretative design that does it all for the user thereby inhibiting their own creative use of the system. Through revisiting five systems in which appropriation has happened both within and outside the intended use, we are going to show how it can be possible to design with open surfaces. These open surfaces have to be such that users can fill them with their own interpretation and content, they should be familiar to the user, resonating with their real world practice and understanding, thereby shaping its use

A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds

This paper proposes a segmentation-free, automatic and efficient procedure to detect general geometric quadric forms in point clouds, where clutter and occlusions are inevitable. Our everyday world is dominated by man-made objects which are designed using 3D primitives (such as planes, cones, spheres, cylinders, etc.). These objects are also omnipresent in industrial environments. This gives rise to the possibility of abstracting 3D scenes through primitives, thereby positions these geometric forms as an integral part of perception and high level 3D scene understanding. As opposed to state-of-the-art, where a tailored algorithm treats each primitive type separately, we propose to encapsulate all types in a single robust detection procedure. At the center of our approach lies a closed form 3D quadric fit, operating in both primal & dual spaces and requiring as low as 4 oriented-points. Around this fit, we design a novel, local null-space voting strategy to reduce the 4-point case to 3. Voting is coupled with the famous RANSAC and makes our algorithm orders of magnitude faster than its conventional counterparts. This is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes. Results on synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201