Spectral-based mesh segmentation

In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (BRep), which in turn is central for featurebased design, machining, parametric CAD and reverse engineering, among others -- Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited -- We preprocess the mesh to obtain a edgelength homogeneous triangle set and its Graph Laplacian is calculated -- We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature submeshes -- Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh -- We present tests of our method on large complex meshes, which show results which mostly adjust to BRep FACE partition -- The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation -- Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous submesh removals

A dedicated greedy pursuit algorithm for sparse spectral representation of music sound

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal as a linear superposition of as few spectral components as possible, without affecting the quality of the reproduction. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the fast Fourier transform. The achieved sparsity is theoretically equivalent to that rendered by the orthogonal matching pursuit (OMP) method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard OMP algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral representation is illustrated by comparison with the traditional method, in the line of the short time Fourier transform, involving only the corresponding orthonormal trigonometric basis.

Lady Nugent and Tom Cringle on the veranda : early nineteenth century observations on a Caribbean architectural feature

This study of the veranda as seen through the eyes of Lady Maria Nugent and Michael Scott, alias Tom Cringle, clearly demonstrates the important role that the piazza, as it was then more commonly known, played in the life of early nineteenth century Caribbean colonial society. The popularity of the veranda throughout the region, in places influenced by different European as well as African cultures, and among all classes of people, suggests that the appeal of this typical feature was based on something more than architectural fashion. A place of relative comfort in hot weather, the veranda is also a space at the interface of indoors and outdoors which allows for a wide variety of uses, for solitary or small or large group activities, many of which were noted by Nugent and Scott. Quintessentially, the veranda is a place in which to relax and take pleasure, not least of which is the enjoyment of the prospect, be it a panoramic view, a peaceful garden or a lively street scene. Despite the great changes in the nature of society, in the Caribbean and in many other parts of the world, the veranda and related structures such as the balcony continue to play at least as important a role in daily life as they did two centuries ago. The veranda of today’s Californian or Australian bungalow, and the balcony of the apartment block in the residential area of the modern city are among the contemporary equivalents of the lower and upper piazzas of Lady Nugent’s and Tom Cringle’s day.