I'm not sure whether you've interpreted this aspect of Groves' analysis correctly. To my mind, the angle of view has to be linear, otherwise the image would need to 'compress' increasingly from the centre towards the edges, which I think is what your saying is the case.
The image 'expands' increasingly from the centre towards the edges.
That would mean, though, that the image, by definition, is distorted, other than right in the centre, and I don't see how that can be the case.
Do a web search on rectilinear projection.
When you write:
The significant non-linearity of the distance-angle conversion can be clearly seen.
what part of the photo, excatly, are you referring to?
Clearly seen in the example values, not in the photo.
Just out of interest, how did you undertake this measurement to a 1/100mm accuracy?
I did not undertake this measurement to a 1/100mm accuracy. That's why I said "about". I put two digits after the decimal point, because the high resolution scans available online offer resolution of about 0.022 mm per pixel.
Intuitively, looking at the photo, Aldrin seems to be much farther away than your 2.7m.
2.7 m would be the distance between the edges of Aldrin's visor and the camera; the distance that Groves tried to calculate. "Aldrin" is a large object and different parts of his body will have different distances from the camera; his feet will be considerably farther away, for example. Distances from other points, such as the front of Armstrong's left foot, or back of Armstrong's right foot, will be different still. "Intuitive" distance has little to no meaning.
(Also, it's possible that the width of Aldrin's visor is not 280 mm as Groves claims; I've been unable to verify that.)
It is obvious, therefore, that you have studied this part of the analysis and paraphrased Groves in such a way as to mislead the reader and try to discredit him where it seems to be unwarranted.
I mean exactly what I said, I stand by it and I will repeat it here again, in case you did not understand that clearly before:
The values appear out of thin air and no derivation is shown. This is exactly the case, and I encourage the readers to read carefully the section of Groves' analysis that you quoted and confirm that the values suddenly appear in the middle of the text without any derivation - at least not anywhere in the document that you sent to me. Make sure you understand what deriving a value means.
What seems curious to me is how you mistakenly refer to Groves estimating 'the height of Aldrin's eye level' when the dimensions derived purport to determine the height of the centre of the camera imaging plane, as quoted and highlighted above.
I refer to what Groves does, not what he claims to do. Groves claims to determine the height of the camera, but what he does is determine the height of the Aldrin's visor where the horizon intersects it. I believe it's apparent to any intelligent person that what Groves does and claims to do are two generally unrelated things.
In any event, even if Groves had estimated the height of Aldrin's shins above the lunar surface, that would still add credence to his analysis far more than estimating Aldrin's entire height, as the margin for error would be significantly reduced.
Of course it wouldn't, because "Aldrin's shins" is a vague, arbitrary term. You ignore the uncertainty inherent in guessing the actual height at which the optical axis crosses vertically under Aldrin's visor. (Hint: this is not the same height as the height marked on Aldrin's leg by the central crosshair.)
This isn't correct, and you've shown it not be correct above by referring to the calculation! You might disagree with Groves' methodology, assumptions, apparent ignorance and conclusions, but he certainly did a calculation!
Please read what I wrote again, this time paying extra attention to the underlined words:
No calculation whatsoever has been done to determine the height difference, even along the displayed portion of the shadow.
Unfortunatley, I don't agree that it does. It seems potentially to be as flawed, at least in places, as the analysis that it sets out to discredit.
Does anyone else feel this way? If yes, please, speak up.
In any event, I do not consider Groves' claim to be 'baseless and unsupported', and don't really think that you honestly do either. His claim is clearly based on and supported by a thorough and detailed analysis.
Groves' claim (that "the variation in height of the surface between the astronauts is typically a few inches") is baseless and unsupported. This is because there is no basis for that claim (not because it wouldn't be "based on" anything), and nothing in his pseudoscientific analysis supports that claim. I understand that your intention is to fudge these simple truths with semantic obscurity. Good luck with that.
I don't think you can honestly quote any of these as 'fact', remembering that associated with the allegation that the photo could not have been taken with a chest-mounted camera is the allegation that the image appearing in Aldrin's visor is a cut & paste job. All you have as the basis of your 'facts' is that very image. If these were indeed facts I doubt you would have seen the need to critique Groves' analysis, but simply stated the 'facts' instead, which would, by definition, have completely and undisputably countered his analysis.
You obviously have a very distorted perception of what a 'fact' is. The facts, of course, completely and undisputably counter his
claim. You, however, have said that:
... an authoritative study and analysis exists that convincingly demonstrates otherwise ...
and you advertised
... the existence of an authoritative scientific, mathematical study and analysis contradicting your opinion ...
Despite these big claims, you have failed to present an analysis that would overturn the established facts. In fact, you have not presented any authoritative or scientific analysis at all. I would therefore respectfully encourage you to consume your words.
That is all from me. Having fulfilled my commitment here, I have no desire to participate in this thread any further.
