File:ProjStereoCercles.png
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ProjStereoCercles.png (800 × 500 pixels, file size: 121 KB, MIME type: image/png)
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Summary[edit]
DescriptionProjStereoCercles.png |
Français : Tout cercle de la sphère unité est transformé par la projection stéréographique en un cercle du plan de projection (ou une droite de ce plan si le cercle passe par le pôle N de la projection).
Considérons le cône tangent à la sphère le long du cercle (C) à projeter. Soit P son sommet et P' son image par la projection stéréographique. Alors (C) se projettera en un cercle (C') de centre P'. En effet, l'image d'une génératrice quelconque du cône est l'intersection du plan qui la contient et qui passe par N, avec le plan de projection. Il s'agit donc d'une droite passant par P'. Par ailleurs, la génératrice coupe (C) à angle droit et, la projection stéréographique étant conforme, son image coupe (C') également à angle droit. (C') est donc une courbe coupant toute droite issue de P' à angle droit. Il s'agit d'un cercle de centre P'. |
Date | |
Source | Own work |
Author | Theon |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 09:30, 27 December 2016 | 800 × 500 (121 KB) | Theon (talk | contribs) | User created page with UploadWizard |
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PNG file comment |
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Horizontal resolution | 28.35 dpc |
Vertical resolution | 28.35 dpc |
File change date and time | 09:21, 27 December 2016 |
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