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Woodwork with sharp curves

Dear expert,
I am trying to build a project that has very sharp curves. like a small jigsaw puzzle.
The surface to cut is 3/4" thick, wood, and is like a topograph curve. 
The whole surface measures 4 ft by 2 ft, so it is not small pieces, just the cuts that in some places will be a lot sharp.
My question is, what would be the best tool to use. I do have a jigsaw and it did not work, as the blades would not do the curves. 

Thanks in advance.
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Posted 2014-04-22T14:24:12+0000  by Marciof Marciof
Do you need to cut from the middle of the piece or just take slices off?

I'm thinking a band saw might be a good choice but finding one that can use small blades to cut the curves might be a challenge.  The old Inca band saws were advertised the take a 1/16" blade but good luck finding the saw or the blades.

Can you post more details about your project or maybe some pictures?
Posted 2014-04-23T03:47:52+0000  by Adam444
Hey Adam,
Thanks for your quick response.
Saw something in the net that might work... The scroll saws. My problem is that I will cut wood 1" thick. Dont know if those machines will work for it.
I do not have pictures of the project as this will be the first one. And the drawings I made is just for my understanding. No one could understamnd such drafts. :)
Posted 2014-04-23T12:04:51+0000  by Marciof
A scroll saw could cut the wood but I think it's going to be really, REALLY slow going.  Maybe one of the premium machines could do it?  Before you go that route try to find a scroll sawing forum and see if anyone has a recommendations.
Posted 2014-04-24T11:25:46+0000  by Adam444
Thanks Adam44, will go that direction you suggested.
Posted 2014-04-24T12:58:18+0000  by Marciof
Once your project is done, please post some pictures.  I'd like to see it and your questions may benefit others.
Posted 2014-04-25T02:18:26+0000  by Adam444
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