Science! Or, a new page on the wiki for technical works

[rob]

Hey all,

I've started a new page on the wiki, Science!, which is an index to technical works relating to book scanning, page dewarping, image processing, vision, OCR, and mathematics relating to same. I've added a bunch of papers that I found in the forums, but I probably missed a bunch.

Anyone can add to the list, and it doesn't necessarily have to be papers, but also patents and websites that have technical information, as well as pointers to the wiki where you might have your own technical investigations.

Enjoy!

[the.traveller]

Good morning Rob,

Since you started the new Wiki page Science! and showing to be a crack in mathematics, could you make a worksheet which calculates sides a and b if one part (the lenght of c) of the cradle is given ?
Preferatly when the angle of bc is 45 degrees.
See picture below for the naming of the sides:
http://upload.wikimedia.org/wikipedia/c ... an.svg.png

I have been looking to the following sites for research:

In Dutch:
http://nl.wikipedia.org/wiki/Pythagoras
http://nl.wikipedia.org/wiki/Stelling_van_Pythagoras

In English:
http://en.wikipedia.org/wiki/Pythagoras
http://en.wikipedia.org/wiki/Pythagorean_theorem
http://www.cut-the-knot.org/pythagoras/index.shtml

Especially the last one gave me headache, there are to many examples on how to calculate. All the ones I have been investigating need to have at least 2 sides known.
But there should be a way to calculate sides a and b if c is known together with the angle (45 degrees) of b and c.

Now on the last website there is a remark (#2) which looks like it is explaining how to calculate the sides with the degrees each corner has.
http://www.cut-the-knot.org/wiki-math/i ... eanTheorem

And now I am in the dark, I have never had any trigonometry so I don't know if this is the explanation to dig in.
And if so how to put that in a worksheet.

My idea is to have all the calculations in a worksheet for everybody to use (me first ) when calculating how large your cradle needs to be to hold even the largest book/document which has to be scanned. Because at the start of building your scanner one need to know what maximum size is needed, and from there all other calculations follow.
The calculation of the base where the cradle rest on.
The calculation of the height of the camera.
See also the explanation at Fix Keystoning via hardware adjustments
Postby jay » 18 Apr 2011, 22:54

Well I hope you and other members (Jay) can help to put those calculations into a worksheet in which one can simply put measurement(s) and all unknown numbers will follow.

A very simple attempt is here:
[*]Different Calculations[/*]

The suggestion of Spamsickle is incorporated into the sheet.
Jay's explanation is now added, so does DPC's explanation for cradles larger then 90 degrees.

[spamsickle]

When you're dealing with a right-angle equilateral triangle (which seems to be the base you're describing, and the base almost everyone builds), you should just need to square your "C" (multiply C by itself), divide the result by 2, and take the square root of that. The answer you get will be the length of "A" and "B" (which are identical).

I have to say, though, that this seems to be going about it backwards. I've always begun with the size of the books I wanted to scan, and matched the sides of the cradle to that.

[the.traveller]

I have to say, though, that this seems to be going about it backwards. I've always begun with the size of the books I wanted to scan, and matched the sides of the cradle to that.

Spamsickle, thank you for explaining.
Exactly what I am trying to do. Lets have a look to one of the pictures from dpc


I am looking to the 3 sides of the green triangle. I have to figure out the sides a and b if only c (the hypothenusa) is known. In my case I calculated that I need a board of 35 cm2 to hold my largest books. When I know what sides a and b are, I can measure how large the total base should be.

So using your calculation

you should just need to square your "C" (multiply C by itself), divide the result by 2, and take the square root of that. The answer you get will be the length of "A" and "B" (which are identical).

C = 35

35*35 = 1225

1225/2 = 612,5

square root(612,5) = 24,74873734

Yeahh, I finally can proceed with adding the thickness of the thickest book and 2 times the size of the found horizontal plane of the base (24,74873734) and add the 2 sides of the base. Then I will know how large my final build will be.

(Ron: Bloody Hell)