Ross Moore

Three-dimensional reconstruction and modelling of complexly folded surfaces using Mathematica

In this paper we provide the following three examples of how the software system Mathematica can be used to reconstruct or model the three-dimensional shapes of folded surfaces. (1) First, we revisit the reconstruction of the central inclusion surface within a garnet porphyroblast that contains spiral-shaped inclusion trails. (2) Next, we revisit the reconstruction of five foliation surfaces that define oppositely concave folds within and surrounding a plagioclase porphyroblast. (3) For the main part of this paper we model superposed folds, and the many interference patterns that can be found in two-dimensional sections through these folds. Because this special issue is accompanied by a compact disk, we have included a series of reconstructions, models and animations to illustrate these three examples. Our reconstructions and models have, in some instances, provided important constraints on the interpretations of complex or controversial microstructures, and in all instances have provided useful teaching aids.

Geometry in the space of horrocks–mumford surfaces

using explicit constructions and calculations. The major property of FHM which we use is its large group of symmetries; which group indeed determines the bundle itself. Further properties of 9,,, as stated e.g. in Cl], are used in section 3 where a method is described to construct the abelian surfaces. This method is then applied in special cases. The paper contains the following results: 0.1. There is a surface A of degree 10, the trisecant surface to a rational sextic curve C, c

Surface reconstruction from parallel serial sections using the program Mathematica : example and source code

Abstract A “package”—module of commented source code—for the computer program Mathematica has been designed to reconstruct surfaces from curves, collected in parallel serial sections through these surfaces. The package contains routines to interpolate digitized curves using continuous functions, to interpolate transversally between the resulting continuous curves, and to render the results of this later operation as a parametrized surface in three dimensions. This paper provides a listing of the package and an example of surface reconstruction using curves which were collected from serial thin sections through a garnet porphyroblast with spiral-shaped inclusion trails.

PDF/A-3u as an Archival Format for Accessible Mathematics

Including Open image in new window source of mathematical expressions, within the PDF document of a text-book or research paper, has definite benefits regarding ‘Accessibility’ considerations. Here we describe three ways in which this can be done, fully compatibly with international standards ISO 32000, ISO 19005-3, and the forthcoming ISO 32000-2 (PDF 2.0). Two methods use embedded files, also known as ‘attachments’, holding information in either Open image in new window or Open image in new window formats, but use different PDF structures to relate these attachments to regions of the document window. One uses structure, so is applicable to a fully ‘Tagged PDF’ context, while the other uses Open image in new window tagging of the relevant content. The third method requires no tagging at all, instead including the source coding as the Open image in new window relacement of a so-called ‘fake space’. Information provided this way is extracted via simple Open image in new window / Open image in new window / Open image in new window actions, and is available to existing screen-reading software and assistive technologies.

On Rational Plane Sextics with Six Tritangents

Publisher Summary A rational plane sextic curve in general has ten nodes. This chapter describes a family of such sextics Sx, (parametrized by x ∈P3) admitting six tritangents. The double plane X branched over is the Kummer surface of an abelian surface carrying a polarization of type (1, 5). The double plane Y branched over the union of the six tritangents is also the Kummer surface of such an abelian surface. All the properties needed to control the double cover X drop out of some polynomial identities.