#1 Wed 10 July 2013 11:41
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- Date d'inscription: 10 Jul 2013
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Barycentre ou Centroide
Bonjour,
Je veux établir un point central de plusieurs équipements d'égale importance (aucune pondération).
Etant donné que le barycentre et le centroïde de mon ensemble de points ne correspondant pas, je m'interroge sur la donnée la plus pertinente à utiliser.
Pouvez-vous m'éclairer ?
Merci par avance
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#2 Wed 10 July 2013 12:04
Re: Barycentre ou Centroide
Une piste : http://georezo.net/forum/viewtopic.php?id=15636
Un truc qui cloche, cependant dans le lien ci dessus : dans le cas de polygones non convexes, le centroïde peut être situé à l'extérieur du polygone...
The geometric centroid of a convex object always lies in the object. A non-convex object might have a centroid that is outside the figure itself. The centroid of a ring or a bowl, for example, lies in the object's central void.
En anglais, l'article est plus explicite sur les différences brycentre et centroïde, selon le domaine (geométrie ou physique)
In mathematics and physics, the centroid or geometric center of a two-dimensional region is, informally, the point at which a cardboard cut-out of the region could be perfectly balanced on the tip of a pencil (assuming uniform density and a uniform gravitational field). Formally, the centroid of a plane figure or two-dimensional shape is the arithmetic mean ("average") position of all the points in the shape. The definition extends to any object in n-dimensional space: its centroid is the mean position of all the points in all of the coordinate directions.
While in geometry the term barycenter is a synonym for "centroid", in physics "barycenter" may also mean the physical center of mass or the center of gravity, depending on the context. The center of mass (and center of gravity in a uniform gravitational field) is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, then its center of mass is the same as the centroid of its shape.
In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is known as the region's geographical center.
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#3 Wed 24 July 2013 11:04
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Re: Barycentre ou Centroide
Robin,
Tout à mes calculs et à mes comparaison, j'ai oublié un essentiel : merci
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#4 Wed 24 July 2013 15:00
Re: Barycentre ou Centroide
J'espère que ça aidera.
J'oubliais aussi, la source de l'article cité est wikipedia (en anglais) : http://en.wikipedia.org/wiki/Centroid
A prendre avec les pincettes de rigueur, of course, comme tout ce qui vient de wikipedia.
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#5 Wed 24 July 2013 16:25
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Re: Barycentre ou Centroide
Sur ce sujet, j'aime bien le papier http://www.tandfonline.com/doi/abs/10.1 … e_jo6zcB20,
The Centroid? Where would you like it to be be?
DOI:10.1080/00690805.2002.9714213
R. E. Deakina, S. C. Birda & R. I. Grenfellb
pages 153-167
dispo http://user.gs.rmit.edu.au/rod/files/pu … ntroid.pdf
The concept of a centroid is useful for many spatial applications, and the determination of the centroid of a plane polygon is standard functionality in most Geographic Information System (GIS) software. A common reason for determining a centroid is to create a convenient point of reference for a polygon, often for positioning a textual label. For such applications, the rigour with which the centroid is determined is not critical, because in the positioning of a label, for example, the main criteria is that it be within the polygon and reasonably central for easy interpretation.
However, there may be applications where the determination of a centroid has, at the very least, an impact on civic pride and quite possibly financial repercussions. We refer here to an administrative or natural region where a nominated centroid has a certain curiosity value with the potential to become a tourist attraction. Such centroids provide economic benefit to those in a sub-region, usually in close proximity to the centroid.
Various interpretations of a centroid exist and this paper explores these and the methods of calculation. Variation in position resulting from different interpretations is examined in the context of the centroid of the Australian State of Victoria, and GIS software are evaluated to determine the efficacy of their centroid functions.
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