ChatterBank1 min ago
affines
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what does 'affines' mean
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Is the word 'aphine'? I think PP has it correctly. Distortion of an image when projected onto a two-dimensional surface?
Like when you get an image of a bicycle symbol, for instance, painted on a road - it's distorted when applied to the road surface but is readable when viewed from the point of view of the motorist.
Like when you get an image of a bicycle symbol, for instance, painted on a road - it's distorted when applied to the road surface but is readable when viewed from the point of view of the motorist.
Hi me again
You k n ow if you cut a cone directly across, the base is a circle and if you do it at an angle the base will be an ellipse
I think the circle and the ellipse are related to each other through an affine transformation
The point (ha!) being that the corresponding points on the circle and the ellipse sort of go to the apex of the cone.
and in projective geometry, which sort of goes around as RP2, then the apex of the cone sort of becomes the point of perspective on the horizon.
Having said that, Descartes spent about ten years proving that an ellipse can always be drawn around an irregular hexagon, and now you can see, with an affine transformation, its a regular hexagon and a circle and REALLY easy to prove.
yeah honestly, someone asked what an affine was........
You k n ow if you cut a cone directly across, the base is a circle and if you do it at an angle the base will be an ellipse
I think the circle and the ellipse are related to each other through an affine transformation
The point (ha!) being that the corresponding points on the circle and the ellipse sort of go to the apex of the cone.
and in projective geometry, which sort of goes around as RP2, then the apex of the cone sort of becomes the point of perspective on the horizon.
Having said that, Descartes spent about ten years proving that an ellipse can always be drawn around an irregular hexagon, and now you can see, with an affine transformation, its a regular hexagon and a circle and REALLY easy to prove.
yeah honestly, someone asked what an affine was........
1 to 9 of 9
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