Eyes like a hawk

[dalgoma]

This is a perspective projection of a cube at various positions from the line of sight.

 

It will be seen that the footprint of each image gets progressively larger the further to the right it becomes and in this instance the further away it is.

 

This is against all common sense. Objects are supposed to get smaller as they get further away!

 

Just suppose though, that this is true and the construction is valid, we could not possibly discern it. Just try reading a line of text when you are concentrating on the one above.

 

Hawks however have a reputed 270 degree angle of vision.

 

Is it possible that they use this phenomenon to magnify their prey when they stoop?

 

If I look through a pair of binoculars I would not be safe moving around, I would bump into things. And raptores do it travelling at 100mph in 3 dimensional space!

 

However, if they looked straight ahead but "took in the view" of their prey at, to them a constant optimum angle, they would need to fly in a curve to maintain it.

 

I am informed by falconers that hawks do indeed stoop in a curve and it has been established that this curve is a logarithmic spiral.

 

Could this be a reason?

[michel123456]

Here (in Greece) we call that effect "paramorphosi" (παραμόρφωση) and it is real.

 

I use almost the same method than yours for perspective, which I have learned from a Greek Architect who learned it from his Greek teacher in Alexandria of Egypt. We don't use the section. We put the heights in full scale on the perspective at the intersection of the object with the projection screen.

 

I don't know about the hawk, I guess with 270 degrees, his world is quite different from ours.

[Sisyphus]

Could you explain that picture some more? I can't tell what I'm looking at.

[michel123456]

Could you explain that picture some more? I can't tell what I'm looking at.

 

It is a geometric construction on how to draw a perspective drawing of a serie of objects (here, cubes positionned side by side with corner down).

 

There are 3 parts:

the down triangle is a horizontal plane projection.

the left triangle is a vertical section

the center part with the green ABCDEF schemes are the final result of the drawing, the perspective view.

 

_At the bottom you have your eye. The horizontal red line is a representation of a vertical screen (say a sheet of paper) on which you will draw the perspective.

_on this line are positionned several objects you will have to represent in perpective view.

_the lines going from you eye to the objects indicate the projection of the corners of the objects upon the screen.

 

_at left, you have your eye again. the vertical red line is the vertical screen again (distance from eye to screen is the same in both plane & section view)

_the square (like losange) represent the serie of objects in vertical section (all objects superpose one another in this case)

_the lines from the eye to the corners of the object intersect the vertical screen.

 

_the central part is the combination of the plane & vertical projections, the perspective view.

_the bunch of lines going from the green representations, up & down, are the constructions lines of the angled sides of the objects. They all join to the vanishing points up & down. The vanishing points are found drawing parallel lines to the sides of the objects, from the eye to the screen.

 

I hope that helped, it is not the simplest example of perpective drawing.

 

The original question was:

 

(...)I am informed by falconers that hawks do indeed stoop in a curve and it has been established that this curve is a logarithmic spiral.

 

Could this be a reason?

 

from HERE

 

 

"Behavioural studies show that many avian species focus on distant objects preferentially with their lateral and monocular field of vision, and birds will orient themselves sideways to maximise visual resolution. For a pigeon, resolution is twice as good with sideways monocular vision than forward binocular vision, whereas for humans the converse is true.[1]" source wiki http://en.wikipedia.org/wiki/Bird_vision

 

If you move towards an object looking at him sideways, your path will be a logarithmic spiral. I guess that's what the "behavioural studies" tend to show. But if a bird looks sideways, it is probably to avoid the phenomena described by dalgoma, not to use it as a magnifying trick.

 

In short, binocular vision is great to get a steroscopic image which helps on estimating the distance, but monocular vision is much better to focus. If a bird need to focus, he will obligatory look sideways. After approaching, a bird of prey will return to binocular vision to attack, since only by this way he can evaluate distance correctly.

Edited November 20, 2010 by michel123456

[dalgoma]

For Michel - Thanks for reply.

 

If you move towards an object looking at him sideways, your path will be a logarithmic spiral. I guess that's what the "behavioural studies" tend to show. But if a bird looks sideways, it is probably to avoid the phenomena described by dalgoma, not to use it as a magnifying trick.

 

Log. spiral only if the line of sight is maintained with respect to the axis of the bird in flight. Which is a pretty good definition of a log spiral. - the tangent to the curve making the same angle with respect to the origin.

[michel123456]

Correct. You know quite a bit in geometry. You must have been teaching.

Edited November 20, 2010 by michel123456

[Sisyphus]

I still don't understand. Isn't this just an example of a cube having a larger silhouette at a diagonal than straight on? i.e., a sphere wouldn't change, right?

[michel123456]

I still don't understand. Isn't this just an example of a cube having a larger silhouette at a diagonal than straight on? i.e., a sphere wouldn't change, right?

 

No. It is a kind of distortion. The sphere becomes an ellipse.

 

In paintings & architectural drawings, there are 2 methods to avoid this effect:

1. avoiding to represent objects too far on the left or right (further than 45 degrees from the eye).

2. cheating.

 

In photography, the same occurs. I found this showing what happen when the camera is too close (the angle is too wide), with rectification as the camera moves away.

 

In real life, it is very difficult to observe. You have to close one eye, to focus on a point in front of you, and analyze in your head what you are viewing left & right. You need a lot of concentration to do that, usually you change your focus point, and you never take attention of the phenomena. It is a bit like looking in front of you and analyzing where does the picture ends, what is in the back of your head.

Edited November 20, 2010 by michel123456

[dalgoma]

Michel, Thank you very much for your input, I very much appreciate it.

 

Is that what we call anamorphism? - Like the skull in Holbein's "The Ambassadors".

 

If magnification does occur why does a raptor not use it?

 

Merely focusing does not make things bigger, having more rods or whatever in its retina dosen't either -

it just makes magnificatiion possible without loss of definition.

 

As you know log. spirals are closely allied to the fibronacci series used so much in nature from the breeding cycle of rabbits to the arrangments of tree branches and dare I say, architecture, apporoaching the proportion 1:1.6180933...

 

I posted to a falconry forum a received this reply -

 

Great post ! I do not believe they see things at a distance as larger due to the fact of calibrating the distance to acquire the quarry. I have to agree that maybe in fact the eye Zooms in and out like the Lens theory. This has often fascinated myself. But also as I have hawked over many years and I have often wondered when you kick up a Rabbit and it does a wing over and crashes the brush after a snake ? I have certainly have seen some odd things while hunting with a BOP.

 

Surley, the bird would not have seen the snake if it was solely focused on the rabbit.

 

We may have exhusted this subject. I only raised it when looking at the views of Circles in Perspective.

 

It is fun though!

 

 

 

 

 

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[michel123456]

Michel, Thank you very much for your input, I very much appreciate it.

 

Is that what we call anamorphism? - Like the skull in Holbein's "The Ambassadors".

 

 

Anamorphosis is something different.

 

The precedent term, paramorphosis, is a common term in the Greek language meaning "deformation". It may not be the specific term designing the "deformation" you were discussing.

 

If magnification does occur why does a raptor not use it?

 

Merely focusing does not make things bigger, having more rods or whatever in its retina dosen't either -

it just makes magnificatiion possible without loss of definition.

 

I have some doubts about "without loss of definition". It goes out of my qualification. But you have to take into account

_that this effect is due to the projection of the image on a plane surface.(if the projection was on a circular screen, no such effect would appear)

_that the effect applies on object far away from the focus point.

Edited November 21, 2010 by michel123456

[dalgoma]

Yes, I should have said "without so much loss of definition" Like the old days you chose a slow speed film for a fine grain if you wanted to enlarge.

 

Ah, there is the rub! In all my constructions I have assumed a flat picture plane normal to the line of sight in both planes. Just like a camera that does not move.