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A further question. Is there a way to store such a function in AD that I could call upon when needed?


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22 minutes ago, jackamus said:

As an ellipse goes from a straight line at eye level down to a fatter ellipse at ground level, the major axis will be smaller due to perspective distance.

It isn't that the axis gets smaller; it is the foreshortening effect that causes the 'far' part of the curve to gradually get smaller compared to the 'near' part as the viewing angle changes. You can't simulate that by changing either axis because the change won't be gradual.

2 minutes ago, jackamus said:

A further question. Is there a way to store such a function in AD that I could call upon when needed?

Not that I know of.


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4 minutes ago, R C-R said:

It isn't that the axis gets smaller; it is the foreshortening effect that causes the 'far' part of the curve to gradually get smaller compared to the 'near' part as the viewing angle changes. You can't simulate that by changing either axis because the change won't be gradual.

Not that I know of.

An ellipse is the shape that perfectly describes a 'foreshortened' circle. The major and minor axes of the ellipse is not related to the foreshortened diameter of the circle. The major and minor axes are just construction lines.

The attached file shows how the proportion of the ellipse B is changed due to viewing angle. However the file does not show the vertical perspective convergence. I maintain that, after constructing the correct perspective,  that this vertical convergence angle is proportional to the viewing angle of ellipse B. In other words the 'thinner' ellipse B is the less the convergence angle will be. If A and B were the same proportion then there would be no vertical convergence.

 

Ellipses .afdesign


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42 minutes ago, jackamus said:

An ellipse is the shape that perfectly describes a 'foreshortened' circle.

Not generally true. Consider for the example the cube illustrated in the https://commons.wikimedia.org/wiki/File:Perspective1.jpg#/media/File:Perspective1.jpg file. Imagine what a circle would look like if it was drawn on the top face of the cube in 2 point perspective. It would not be an ellipse because of the foreshortening effect, for the same reason the top face of the cube is not a square or rectangle.


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Not so!. As I said the ellipse is a TRUE reprentation of a circle in perspective. If you were to draw two lines at right-angles (diameters) of a circle on top of a square (shown in my file), the diameters will not coincide with the ellipse axes. The ellipse major and minor axes must be confused with the diameters of a circle viewed at an angle. They are merely construction lines. See my attached file.

In A and B there is no resemblance between the major and minor axes and the perspective diameters of the original circle in perspective.

Ellipses 2 .afdesign


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18 minutes ago, jackamus said:

As I said the ellipse is a TRUE reprentation of a circle in perspective.

No, that is not true. It is not just about the major & minor axis of an ellipse, it is about if every line drawn through lines parallel to them would be parallel to a vanishing point perspective line.

Remember, both an ellipse & a circle are just collections of all points satisfying a mathematical equation. There is no way to do that in a two point perspective drawing except for the special case when the circle or ellipse is equidistant from the two vanishing points.


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I agree that both the ellipse and the circle obey mathematical equations but the extraordinary coincidence is that if you superimpose an ellipse on that of of a circle in perspective they will coincide exactly. This may be no more than a coincidence but it works!.

I think our problem is that I do not see an ellipse as a circle in perspective, which it is, but as a shape that exactly fits a perspective circle and as such it should be possible to do the calculations that I first spoke about. If you simply treat the whole thing as an exercise in geometry i.e. lines and angles then it can be calculated.

In my time I have constructed many perspective grids with correctly drawn perspective measuring axes so I do understand what it is I'm suggesting.

This has now become a major and a minor challenge for me to solve.


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37 minutes ago, jackamus said:

I do not see an ellipse as a circle in perspective, which it is

But it isn’t, and that’s the problem! If you draw two vertical lines side by side and apply perspective projection so that the tops of the lines look as though they’re further away from the viewer, the lines change from being parallel to converging towards the top (like a road going straight ahead into the distance). Exactly the same happens to a circle: it becomes more pointed at the top, unlike a true ellipse where the top half is an exact mirror of the bottom half.


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If you don't believe me then take a photo of a cup or glass, load into AD and check it.


Mac OS X El Capitan Version 10.11.6

AD version 1.6.0

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