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Old 08-28-2015, 08:00 PM   #1
darksaurian
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tilted circle, ellipse


Say you're looking straight at a circle around the origin on a cartesian plane. Now you tilt the circle 45 degrees around the x-axis. Pretend objects don't diminish in size with distance, like there is no z-axis. I don't know the mathematical terminology. Now the circle looks the same width as it did before along the x-axis but it's shorter top to bottom along the y-axis. Is the shape the same as an ellipse? I mean there's only one ellipse for every length and width. Would the tilted circle with those same dimensions be the exact same shape?

Last edited by darksaurian; 08-28-2015 at 08:06 PM. Reason: misspelled "tilt"
 
Old 08-28-2015, 09:55 PM   #2
smallpond
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Yes. The equation of an ellipse aligned with the X-axis is
Code:
(x/a)^2 + (y/b)^2 == 1
That means you are scaling (tilting) the x-axis by 1/a and the y-axis by 1/b. If you undo the tilting you get:

Code:
x' = x/a
y' = y/b
x'^2 + y'^2 == 1
That is the equation of a unit circle.
 
Old 08-28-2015, 10:15 PM   #3
darksaurian
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thx

I can't mark threads in general as solved? I guess that says a lot about general. I'm using this saw software. When I cut 45 degree mitres it went too far. Occurred to me later I'm cutting with an ellipse now, not a circle. So to speak. Same width, half the height. So it reaches further. Maybe the software is stopping the center of the blade at the same place as if the blade were vertical.

Last edited by darksaurian; 08-28-2015 at 10:23 PM.
 
  


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