Perspective Rules | |
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David Percy seems to have a love/hate relationship toward perspective convergence. When he insisted that shadows always appear parallel, he ignored perspective. To preserve his notion that flags look the same from different angles, he rejected it. But when he thought perspective convergence might support his fantasies, he embraced it. Standing on the lunar surface and photographing from chest height, it is only possible to "look up" at the LM as it is virtually 23 feet high. We should therefore see a form of convergence. (Dark Moon, p. 41)Apparently Percy believes that perspective works only vertically but not horizontally, but at least he's half right. The leaning back effect comes from holding the camera at an angle; if you try to avoid leanback by pointing the camera straight at the building then you'll probably cut off the top. So you have to raise the camera higher, which is what Percy thinks was done when Alan Shepard took this picture of the Apollo 14 Lunar Module.
And how does Percy back up this tall tale? He doesn't, that's how. There is no examination of lines for non-convergence, no comparison with other structures, nothing but a caption and a "certainly not" which we are supposed to accept on blind faith. But before we use our eyes and examine this picture a little closer, let's give Big Dave the benefit of the doubt. Let's see if we can find some parallel vertical lines in this picture, and let's see whether they converge upward as David Percy expects. It so happens that the portside fuel tank housing has a square-shaped facet facing the photographer. In a high-resolution version of that picture the facet appears as almost a perfect square with no "railroad track" convergence. So does that mean Al Shepard took this picture while standing on the shoulders of a whistle blower? Not at all. In the first place, the version of AS14-66-9277 that appeared in Dark Moon makes it appear that the photographer was standing much closer to the LM than he really was. But the image has been cropped to eliminate a lot of foreground. If you check the original, uncut version of AS14-66-9277 over here, you can see that there is considerable real estate in front of the LM. By photographing some 3-storey houses with a 35mm lens (and Shepard did use a wide-angle lens, because AS14-66-9277 is part of a panorama which you can download here), I figure the Lunar Module Antares had to be at least 30 feet away to appear that small in the intact image. The following picture is a 1:24 scale demonstration of what kind of distortion we can expect from an LM-sized object taken at approximately the same distance as AS14-66-9277. This 11½" high book was photographed from 5 feet away with a 35mm camera raised 2½ inches above the floor, giving the equivalent of photographing a 23-foot LM from a 30-foot distance with a camera 5 feet above ground. 
Notice also how the walls in this picture give an excellent example of convergence. The courses between the bricks all appear to point toward the camera in the mirror. What's more, the top of the rubber floor moulding slants down, while the bottom slants up toward the camera. Finally, the receding lines of the floor tiles converge toward a point indicating the camera's horizontal position. That is the Law of Perspective Convergence, which states that orthogonal lines appear to converge toward a single vanishing point which corresponds to the viewpoint of the spectator. This was all worked out by Italian painters in the 15th century and is just as valid today, and you can read more about it here. It works on the earth, on the moon, it works for railroad tracks and shadows, houses and lunar modules, and it continues to work no matter what some self-anointed photo experts say. We can also see it working in this picture: This row house is 26 feet high and was photographed from the same distance and orientation as AS14-66-9277. Unlike the chunky LM, this piece of modernist architecture has plenty of long lines and right angles to show convergence. Notice, though, that the second-floor window on the rightmost house has sides that are almost parallel. That's because, like Antares' fuel tank housing, it's near the middle of the picture, where perspective is minimized.Notice also the two horizontal strips on the righthand side wall. These are 8 and 16 feet above the ground (conforming to the floors of the house). They both slant down and converge at a point representing the vertical plane of the camera, which is indicated by the intersection of the green dashes---. This convergence tells us that the camera must have been 5 feet above the ground. Now let's study the house from 12 feet up. (I couldn't raise the camera, so I had to lower the house.) 
If we can locate some parallel lines on Antares, and if we extend them to their point of convergence, then we can find the camera. |
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The camera was aimed at a spot about 9 feet up the LM as indicated by the large central reticle, and by plotting the centre of the uncropped Hasselblad image. The green lines were drawn from the roof of the LM (about 20 feet aboveground) and the shadow of the bottom of the Aft Equipment Bay (approximately 11 feet up), while the light blue lines extend from the roof of the AEB (18 feet) and the aft RCS thrusters which are 15 feet up. These lines converge to a point about 4-5 feet above the ground. So this image must have been taken either at chest height or by a 12-foot astronaut holding the camera at knee level.
The proof is in the detail which David Percy studiously ignored. Note how the top of the descent stage is 10 feet above ground but is completely hidden from view. Meanwhile, the underside of the AEB is quite visible. This part of the LM is 12 feet above the surface and would not be seen if this picture had been taken by David's imagined Goliath.
The dish that flanks Antares' pad in the next trio of pictures is 6 inches across. Since the LM's landing pads are 3 feet in diameter, this gives us a scale of 1:6. I photographed the dish from 5 feet away, first from 10 inches above the floor, then at 2 feet. By the Law of Similar Triangles, this is the same as photographing a 3-foot landing pad from 30 feet away at a height of 5 feet, then 12 feet. Look at the two views of the dish on either side of the LM's pad and decide for yourself how high the astronaut had to be.
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