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- Brun, Anders, et al.
(författare)
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Computing Riemannian Normal Coordinates on Triangle Meshes
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Imagine an ant walking around on the curved surface of a plant, a radio amateur planning to broadcast to a distant location across the globe or a pilot taking o from an airport - all of them are helped by egocentric maps of the world around them that shows directions and distances to various remote places. It is not surprising that this idea has already been used in cartography, where it is known as Azimuthal Equidistant Projection (AEP). If Earth is approximated by a sphere, distances and directions between two places are computed from arcs along great circles. In physics and mathematics, the same idea is known as Riemannian Normal Coordinates (RNC). It has been given a precise and general denition for surfaces (2-D), curved spaces (3-D) and generalized to smooth manifolds (N-D). RNC are the Cartesian coordinates of vectors that index points on the surface (or manifold) through the so called exponential map, which is a well known concept in dierential geometry. They are easily computed for a particular point if the inverse of the exponential map, the logarithm map, is known. Recently, RNC and similar coordinate systems have been used in computer graphics, visualization and related areas of research. In Fig. 1 for instance, RNC are used to produce a texture on the Stanford bunny through decal compositing. Given the growing use of RNC, which is further elaborated on in the next section, it is meaningful to develop accurate and reproducible techniques to compute this parameterization. In this paper, we describe a technique to compute RNC for surfaces represented by triangular meshes, which is the predominant representation of surfaces in computer graphics. The method that we propose has similarities to the Logmap framework, which has previously been developed for dimension reduction of unorganized point clouds in high-dimensional spaces, a.k.a. manifold learning. For this reason we sometimes refer to it as "Logmap for triangular meshes" or simply Logmap.
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- Philip, Johan, 1932-
(författare)
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The area and perimeter of a random spherical triangle
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We determine the distribution functions for the area and the perimeter of a random spherical triangle. We consider two natural ‘polar’ ways of generating the random triangle. It turnsout that the distribution for the area in the first way is closely related to the distribution of the perimeter in the second way, and vice versa.
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- Bengtsson, M, et al.
(författare)
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The accounting education triangle and its implications for future research
- 2023
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Annan publikation (populärvet., debatt m.m.)abstract
- The rise of the professional status of accountants and auditors has brought expansive growth and embedded privilege into the modern accounting profession. However, the employers’ demand for accounting graduates has not increased at the same pace, indicating decreasing career relevance of accounting education in universities and colleges. In this paper, we propose a conceptual model - the accounting education triangle - which highlights the different expectations among the three essential stakeholders in accounting education, namely, educators, employers, and graduates. By examining the previous literature and relevant frameworks, we document specific expectation gaps within the model and provide value propositions and their implications for future research.
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- Stevens, Jan, 1955
(författare)
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The versal deformation of cyclic quotient singularities
- 2009
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We describe the versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle. The equations of the versal deformation itself are governed by a different combinatorial structure, involving rooted trees.
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