Author Topic: Warped Chessboard Challenge  (Read 901 times)

samdavo

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Warped Chessboard Challenge
« on: April 14, 2016, 06:23:58 PM »
ok, Here's an interesting effect (I call it a warped chessboard), with a brief video of how it is made.  (see timeline on this facebook page, April 7). 
https://www.facebook.com/ScientifichorizonsEn/
(edit) oops - they seem to have taken that post down. 

 Personally I find it pretty challenging to understand exactly how it is done :)   So I'll post the challenge here - Can anyone do this with DCAD  from first principles,  - i.e. INCLUDING slicing solids, and then re-slicing them and rotating etc as required - and finally assembling them to get the same or a similar pattern?    Cheers  Sam :)

« Last Edit: April 15, 2016, 03:09:55 PM by samdavo »

Dr PR

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Re: Warped Chessboard Challenge
« Reply #1 on: April 14, 2016, 11:24:01 PM »
This is pretty simple. Notice that the chessboard is divided by lines parallel the X and Y axes, just as an ordinary chess board is. The only difference is that on an ordinary board the line spacing is uniform - all spacings equal.

In this case the distance between the parallel lines varies according to some formula - such as a sine wave.

To reproduce this you only need to create 1/4 of the board and then replicate that three more times.

1. To do this produce a line and replicate it a number of times - looks like 10. Then arrange these lines parallel but with increasing spacing according to whatever formula you want to use).

I used sine(10), sine(20), sine(30), ... sine(80) and sine(90).

2. Select 9 of the lines on the left and mirror them around the 10th line. This produces an odd number of lines (19) and an even number of spaces (18).

3. Select all lines, duplicate them and rotate 90 degrees.

4. Overlay the two sets of lines.

5. Now change to a new layer, lock the original layer, and use Hatch Fill to fill in the spaces.

6. Select all of the hatch fills and duplicate them four times, aligning the corners.

****

To get exactly the same pattern as the original example you need to figure out the way he created the spacing. I suspect it wasn't mathematical, but was done geometrically, but I could be wrong.

You can use any spacing formula and get different results with each.

Phil
« Last Edit: April 14, 2016, 11:30:46 PM by Dr PR »
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samdavo

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Re: Warped Chessboard Challenge
« Reply #2 on: April 15, 2016, 04:46:58 AM »
Thanks Phil.  I was actually trying to work out how the carpentry worked.  And indeed it is pretty easy (as you say).  You simply make two  square blocks by gluing slices of widths varying (as you say) according to sine-wave-widths  (They use 4 5 6 8 10, 12, 14, 17, 20, 24 I believe) - and one of them has the sequence white-black-white-etc , and the other black-white-black-etc.
 
(edit) then cut those blocks in the opposite direction using the same slice widths as shown ...

Then you lay them out alternately. (2 cents) 
« Last Edit: April 16, 2016, 02:45:43 PM by samdavo »

Dr PR

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Re: Warped Chessboard Challenge
« Reply #3 on: April 15, 2016, 09:47:53 AM »
Sam,

I was thinking about how to actually make one last night after my post.

1. First you would have to cut a bunch of strips for each width of each color.

You need to make multiple copies of the strips so you have enough to create the entire large pattern.

2. Then glue them together as you suggested, using alternate colors. Make two sets, one with a dark thin strip at the edge and another with a light strip at the edge. You will need to make multiple copies of these laminated pieces.

3. Now you would cut strips off the edge of both laminated pieces, making one strip of each width that you initially used to make the light and dark set of strips in step 1.

The hard part would be setting the gate on a table saw at the exact widths necessary to repeat the same strip widths used in step 1. The widths have to be the same of the parts won't fit together correctly. After the width is set, cut a piece of scrap and measure it to be sure it is the correct width. After the width is correct cut a piece off the edges of all the laminated parts you made in step 2. This ensures that all of the duplicated sections have the same dimensions.

Then set the gate for the next strip width and repeat until you have all the necessary width strips for all the pattern.

Now you have alternate color strips of multiple widths.

4. Glue the alternate color strips together, aligning alternate colors in the warped checkerboard pattern, and being careful to align the edges carefully. This will give you the smaller repeated pattern.

5. Glue the repeating pattern parts together to make the whole.

I would glue one of the smaller pattern to a solid backing board to provide strength for the laminated pieces. Then I would glue each successive smaller pattern to the backing board, aligning it with the previously placed patterns.

****

When you get your real warped checkerboard finished be sure to post a photo.

Phil
« Last Edit: April 15, 2016, 07:56:26 PM by Dr PR »
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samdavo

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Re: Warped Chessboard Challenge
« Reply #4 on: April 15, 2016, 02:07:30 PM »
Lol - I agree and ... yep I'll post a photo, after it's finished :)  Actually I have a "Work Centre" around here somewhere, which permits a sawblade (and/or router) through the bench as they use here - but it was home to a stack of spiders last time I saw it :)  cheers , sam.     

PS I'm thinking that it would be a lot easier to make if it was thinner and you used a router rather than a thicknesser. (2 cents)
« Last Edit: April 15, 2016, 02:14:10 PM by samdavo »