Original - Perspective triangles. When produced, corresponding sides of the triangles meet at collinear points along the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of perspectivity. Desargues' theorem guarantees that the truth of the first condition is necessary and sufficient for the truth of the second.ALT
Reason
Its easier to make sense of than "In a projective space, two triangles are in perspective axially if and only if they are in perspective centrally".
Support. Not much to say here, but I didn't understand before I looked at the image, and did understand afterwards. The image quality is good. J Milburn (talk) 18:15, 3 March 2010 (UTC)[reply]
Opposeoriginal. The lines Aa and Bb are shown as meeting somewhat to the right of the point labeled the center of perspectivity, and below the line Cc. This flaw is visible even at the nominal size, and is more obvious in the larger renditions linked on the file description page. I agree the diagram has high EV, and the flaw is small enough that it shouldn't hinder understanding, but I think a diagram should be free of visible defects to become an FP. -- Avenue (talk) 10:09, 5 March 2010 (UTC)[reply]
I'm really not seeing that. To me the lines all go through the exact same point. Perhaps it's confusing because the lines are dashed? JujutacularT · C17:14, 5 March 2010 (UTC)[reply]
No, he's right, and I'm surprised I didn't spot it. Look at the dashed lines- they cross (on dashes) around 4mm to the right and 2mm below the center of the dot representing the center of perspectivity (at least, it does on my screen, sorry for the not-so-technical explanation). This should really be fixed. As such, oppose until this is fixed or an explanation is forthcoming. J Milburn (talk) 18:07, 5 March 2010 (UTC)[reply]
I see it now. I've made an alternate to account for this. Let me know if I need to make any alterations to it. I Support ALTJujutacularT · C23:05, 5 March 2010 (UTC)[reply]
Thanks for fixing this. Is there any chance of making the lines a bit thicker (like the original)? It lets you see the diagram at article size clearly. Noodle snacks (talk) 05:52, 6 March 2010 (UTC)[reply]
On reflection, I have another concern. It seems like the axis of perspectivity is parallel to the line Cc, but I don't believe this is a requirement for perspective triangles, and showing them as parallel could mislead readers into believing this is a necessary condition. I don't believe showing them as parallel makes the diagram significantly easier to follow, either, so I would prefer for those lines not to be parallel. -- Avenue (talk) 06:38, 6 March 2010 (UTC)[reply]
This occurred to me too, but I personally do feel that it makes the diagram easier to follow. I certainly see where you are coming from, but I remember when I did this kind of thing at school, making one of the lines completely horizontal, if possible, did make the issue a little simpler. J Milburn (talk) 09:11, 6 March 2010 (UTC)[reply]
One of the lines being horizontal is okay. What he's saying is making two of the lines horizontal implies a relationship where there needn't be one. I've made an adjustment for this, thank you again Avenue. JujutacularT · C15:17, 6 March 2010 (UTC)[reply]
