Mathematics of Perspective

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momentia

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Mathematics of Perspective
« on: September 22, 2011, 04:58:32 PM »
In the opinion of RE'ers:
FE'ers do not seem to understand the notion of angular resolution, which is exactly what rowbotham's perspective is. They will just say his principle is that lower lines converge before higher lines do, but never give an explanation why this is so. They completely ignore the principle that supposedly gives rise to this perspective.

So, I would like an equation relating any or all of following variables for a distant ship according to Rowbotham's perspective:
H = height of the observer
h = height of the hull that is hidden
d = distance to the ship
m = magnification compared to the naked eye.

Ignore any secondary effects like atmosphere.

Also, don't tell me to read ENaG's explanation myself. I have. I gave my best shot at relating the variables:
Quote from: Rowbotham
The above may be called the law of perspective. It may be given in more formal language, as the following:. when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible.
    The angular diameter of a distant object (distance = d) with height h is h/d radians.
    a magnification of m will multiply the angular diameter by m.
    and this angular diameter has to be less than one arc minute, or 0.000291 radians for the object to be invisible.

    Thus my FE relation between the above variables is:
    (h/d)*m ≤ 0.000291

Now its your turn FE'ers, what do you think the relationship is? Explain why you think so.

Re: Mathematics of Perspective
« Reply #1 on: September 23, 2011, 03:57:20 PM »
"Ignore any secondary effects like atmosphere"

You can't just pick and choose what effects you want to take into account and what you don't! You need to take EVERYTHING into account.

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Nolhekh

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Re: Mathematics of Perspective
« Reply #2 on: September 23, 2011, 09:43:01 PM »
"Ignore any secondary effects like atmosphere"

You can't just pick and choose what effects you want to take into account and what you don't! You need to take EVERYTHING into account.

Shouldn't matter since Rowbotham never invoked any such secondary effects.  Although, I personally agree that they can choose as many effects to factor in as they want.  However, only if their formula uses operators that make logical sense and factors in effects that are independently demonstrable, as well as have the ability to consistently make predictions that fit observations, will the formula be taken seriously.