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Post by Ron Walker on Oct 21, 2022 10:53:08 GMT -7
Posted by: Philostopher1 Jun 5 2021, 03:54 PM QUOTE(Scott T @ Mar 7 2021, 01:23 PM) * Thanks Ron and Sir Gare - on with the story.
3. The tessellation problem.
I struggled with the following conundrum for a while. A projection lens will project an upside down image. Anyone who uses old fashioned 35mm side projectors knows to put the slides in upside down and the problem is solved.
Similarly, inverted projection is not a problem with hexagonal sections – just invert the star plates and the projected image will be fine. However, when the pentagons are inverted surely they would lead to horrible gaps in the sky (as shown in the diagram).
Holy crap! I think I just dodged a bullet. I am getting closer to having the photomasks made... I didn't think about inverting the pentagon problem! 😨
Back to the drawing board.
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Post by Ron Walker on Oct 21, 2022 10:53:29 GMT -7
Posted by: Philostopher1 Jun 5 2021, 04:42 PM QUOTE(Scott T @ Mar 15 2021, 12:31 PM) * Thanks Ron. To be honest I have always been jealous of people to whom maths seems to come naturally- this stuff takes me ages and you don't see all of the stupid things I do on the way. It has taken me years to gradually change my slightly unhealthy outlook on maths. Too many people label themselves as either good or bad at maths and that's it. We really need to think in terms of being 'good enough' at the particular bit of maths we need to achieve the task we want to do.
I will of course send my final spreadsheet to anyone here who wants it when it is done - for use as is, further refinement or whatever.
I am following this now that I can get back on the site. I am terrible at math. That's why I hired Paul Bourke. The inversion of the pentagons pointed out earlier is a problem...
I have got to test my lenses again. As I mentioned earlier, I was about ready to order the photomasks... Dodging bullets at the moment...
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Post by Ron Walker on Oct 21, 2022 10:53:45 GMT -7
Posted by: Ron Walker Jun 5 2021, 05:08 PM QUOTE(Philostopher1 @ Jun 5 2021, 04:42 PM) * I am following this now that I can get back on the site. I am terrible at math. That's why I hired Paul Bourke. The inversion of the pentagons pointed out earlier is a problem...
I have got to test my lenses again. As I mentioned earlier, I was about ready to order the photomasks... Dodging bullets at the moment...
Just remember that everything else is inverted as well so it should all equal out.
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Post by Ron Walker on Oct 21, 2022 10:54:09 GMT -7
Posted by: Philostopher1 Jun 5 2021, 10:49 PM QUOTE(Scott T @ Mar 7 2021, 01:23 PM) * Thanks Ron and Sir Gare - on with the story.
3. The tessellation problem.
I struggled with the following conundrum for a while. A projection lens will project an upside down image. Anyone who uses old fashioned 35mm side projectors knows to put the slides in upside down and the problem is solved.
Similarly, inverted projection is not a problem with hexagonal sections – just invert the star plates and the projected image will be fine. However, when the pentagons are inverted surely they would lead to horrible gaps in the sky (as shown in the diagram).
I am having a hard time wrapping my head around this.
I have been testing one of my canon lenses. They invert in X and Y. (!)
Here is the set up. I pointed a laser pointer at each corner of the white object plane:
Upper right corner illuminated see green dot on screen lower left.
Lower right corner illuminated see green dot on screen upper left.
Upper left corner illuminated see green dot on screen lower right.
Lower left corner illuminated see green dot on screen upper right.
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Post by Ron Walker on Oct 21, 2022 10:54:37 GMT -7
Posted by: Ron Walker Jun 6 2021, 11:19 AM Just remember every projection is reversed top to bottom as well as left to right so it all joins together properly projected on the dome..
It is kind of like looking at a pin hole star ball from the inside (looks like a correct night sky) and then from the outside (where everything is backwards) and yet all still fits even though it is all backwards.
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Post by Ron Walker on Oct 21, 2022 10:55:03 GMT -7
Posted by: Philostopher1 Jun 6 2021, 11:32 AM QUOTE(Ron Walker @ Jun 6 2021, 11:19 AM) * Just remember every projection is reversed top to bottom as well as left to right so it all joins together properly projected on the dome..
It is kind of like looking at a pin hole star ball from the inside (looks like a correct night sky) and then from the outside (where everything is backwards) and yet all still fits even though it is all backwards.
When I first started working with Paul Bourke I was fixated on the backwards aspect since I am building a pinhole projector too. Then a couple nights ago when testing the lens, I realized, Oh @#$! the lenses also flip upside down! I completely forgot that. I thought, oh well I'll just flip the plates around. Then I got back into OC and found this thread addressing the upside down pentagon problem. So clearly the mapping has to be changed to include upside down as well. I am having trouble imagining an upside down and backwards celestial sphere.
Paul said it's relatively easy for him to change the data but he isn't an optics guy so I have to get real clear on the lens behavior.
So when you talk about flipping your talking about the maps on the plates being flipped not the plates per se, yes?
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Post by Ron Walker on Oct 21, 2022 10:55:27 GMT -7
Posted by: Ron Walker Jun 6 2021, 12:25 PM QUOTE(Philostopher1 @ Jun 6 2021, 11:32 AM) * When I first started working with Paul Bourke I was fixated on the backwards aspect since I am building a pinhole projector too. Then a couple nights ago when testing the lens, I realized, Oh @#$! the lenses also flip upside down! I completely forgot that. I thought, oh well I'll just flip the plates around. Then I got back into OC and found this thread addressing the upside down pentagon problem. So clearly the mapping has to be changed to include upside down as well. I am having trouble imagining an upside down and backwards celestial sphere.
Paul said it's relatively easy for him to change the data but he isn't an optics guy so I have to get real clear on the lens behavior.
So when you talk about flipping your talking about the maps on the plates being flipped not the plates per se, yes?
Ii think I am making this whole thing a lot harder then it actually is. Actually you can just rotate it 180 degrees if my thinking is correct. Just take a step back with me and follow my thinking. Think about looking at a 35mm slide. You can hold it up to the light and view it in perfect perspective. When you put it in a slide projector you need to rotate it upside down. This simple 180 degree rotation will flip top to bottom but also left to right satisfying both requirements of the lens. Just like when you look at the outside of a pinhole star ball. So you can do the same with a star plate which can be manufactured to look properly. Then you flip it upside down and put it in the projector. It will then project properly on the dome and all of the various segments will align correctly as the lens flips side to side and top to bottom like looking at the inside of a pinhole star ball. Actually don't even think about a pin hole star ball as it just adds confusion. Think about a series of slide projectors projecting a panorama or perhaps the city scape at the bottom on the dome. We can place the slides with segments of the city on a backlit viewer and see the entire skyline and then with the slides of the original city placed in upside down and backwards into the projectors project them out in perfect perspective at the base of the dome.
We were so worried about the upside down pentagon "problem" that we forgot that the pentagon would be placed in the projector upside down and backwards and the lens would do the correction in both directions for us and present it properly on the dome screen.
So basically there is no magic to this at all. Just divide the sky up into the various segments, place the stars, make the plates, and then just turn them over 180 degrees in the projectors and the lenses will do the rest.
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Post by Ron Walker on Oct 21, 2022 10:55:48 GMT -7
Posted by: Ron Walker Jun 9 2021, 11:40 AM Again we are all making this harder than it is. Make a pentagon star plate with let's say the flat part at the top looking normal as if you're inside the star ball looking out at a properly positioned sky. Take this star plate and flip it 180 degrees so that the flat top is on the bottom and left is right and bottom is on top and right is left. Put it in the projector and the lens will reverse top to bottom and left to right and project it properly with the flat top and left to left inside the star ball. Now just continue the image out to the dome which is like a large star ball and all of the projections fit together perfectly with the flat top of the pentagon once again on top as originally punched on the star plate. There is no reverse positioning of anything. I don't know why I didn't see this before, probably because I always saw that star ball from the outside and thus backwards like the stars on a pinhole projector being backward. The thing is we must look at the star ball from the inside just like we are inside a dome and looking at the inside of the projected sphere. When we make the star plate we must make it look like the inside of the dome or star ball or just like the sky looks in that direction. There is no reversal of any stars when making the plate.
Again, look at the dodecahedron from the inside and not the outside. When you project on the dome you are looking at the inside of that star ball with all the stars in their proper positions just expanded out bigger onto the dome but you are still looking at the inside. This is not like a pinhole star globe where we are drilling from the outside so everything is backwards from our drilling position.
Another way to think about it is imagine looking at the night sky and we have divided it up and there is a pentagon in front of us with the flat on top. We take a picture of it with our camera and the lens inverts top to bottom and left for right. We get the slide back and flip it over 180 degrees and we compare it with the night sky and they are identical with the flat top pentagon. We flip it again and put it behind a lens which does the flip for us and project it on the inside of a dome and see an exact reproduction of the outside view because we are inside the globe. We can use this slide to make a star plate and it will align perfectly with the other 31 sections projected the same way.
With a pinhole star globe everything looks proper if we look inside the globe, we cannot think of the stars as they look like from the outside, that will indeed put things backward and drive us all nuts.
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Post by Ron Walker on Oct 21, 2022 10:56:08 GMT -7
Posted by: Philostopher1 Jun 9 2021, 12:02 PM QUOTE(Ron Walker @ Jun 9 2021, 11:40 AM) * Again we are all making this harder than it is. Make a pentagon star plate with let's say the flat part at the top looking normal as if you're inside the star ball looking out at a properly positioned sky. Take this star plate and flip it 180 degrees so that the flat top is on the bottom and left is right and bottom is on top and right is left. Put it in the projector and the lens will reverse top to bottom and left to right and project it properly with the flat top and left to left inside the star ball. Now just continue the image out to the dome which is like a large star ball and all of the projections fit together perfectly with the flat top of the pentagon once again on top as originally punched on the star plate. There is no reverse positioning of anything. I don't know why I didn't see this before, probably because I always saw that star ball from the outside and thus backwards like the stars on a pinhole projector being backward. The thing is we must look at the star ball from the inside just like we are inside a dome and looking at the inside of the projected sphere. When we make the star plate we must make it look like the inside of the dome or star ball or just like the sky looks in that direction. There is no reversal of any stars when making the plate.
Again, look at the dodecahedron from the inside and not the outside. When you project on the dome you are looking at the inside of that star ball with all the stars in their proper positions just expanded out bigger onto the dome but you are still looking at the inside. This is not like a pinhole star globe where we are drilling from the outside so everything is backwards from our drilling position.
Another way to think about it is imagine looking at the night sky and we have divided it up and there is a pentagon in front of us with the flat on top. We take a picture of it with our camera and the lens inverts top to bottom and left for right. We get the slide back and flip it over 180 degrees and we compare it with the night sky and they are identical with the flat top pentagon. We flip it again and put it behind a lens which does the flip for us and project it on the inside of a dome and see an exact reproduction of the outside view because we are inside the globe. We can use this slide to make a star plate and it will align perfectly with the other 31 sections projected the same way.
With a pinhole star globe everything looks proper if we look inside the globe, we cannot think of the stars as they look like from the outside, that will indeed put things backward and drive us all nuts.
DOH! Of course. Wow! Thinking about a Pentagon as a feature on a slide like a piece of art of course it will be correct if placed upside down and backwards. Definitely made this too complicated.
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Post by scotttucker on Oct 21, 2022 22:16:32 GMT -7
Thank you Ron for putting all this back up!
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Post by mrgare5050 on Oct 22, 2022 7:36:08 GMT -7
Like I said last year Duke,
write that book!
I'd buy it, I need more math-ish books since I love numbers you know.
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Post by Ron Walker on Oct 22, 2022 8:56:49 GMT -7
Thank you Ron for putting all this back up! You are more then welcome. It makes it a lot easier to put things that anyone wants if I have a complete title like you gave me. Anything else you would like to see?
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Post by Ron Walker on Oct 22, 2022 9:07:34 GMT -7
Like I said last year Duke, write that book! I'd buy it, I need more math-ish books since I love numbers you know. As you now know, writing a book is no easy task and one wonders if it is worth it or not. This is especially true when the audience is extremely small.
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Post by mrgare5050 on Oct 22, 2022 11:28:10 GMT -7
As you now know, writing a book is no easy task and one wonders if it is worth it or not. This is especially true when the audience is extremely small.
as I told Linda last night, I actually had more fun doing the covers, and there IS a thrill at first at seeing your name in print. But yes, the actual formatting and writing are challenging. Like the podcast, the book and recently sitting my sons first real office were on my bucket list! I've now been able to tick all three boxes. Retirement is looking good at this point.
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Post by scotttucker on Oct 22, 2022 22:35:14 GMT -7
I get a bit behind from time to time. Planetscarium book is on order!
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