How to convert gaps between multiple objects into curves

[arcpan]

As shown in the demo design created by Affinity Designer, I want to convert the gaps among the three shapes as curves and then hide all the objects, but I don't know how to realize it. 
Please help me out of this. 

Thank you all guys.

 

demo.afdesign

[Old Bruce]

Put a shape (I used a rectangle) behind the Curves object and subtract. I temporarily set the opacity of the grey curves object to 30% so we could see the green.

After subtracting there will be some cleanup needed, use the Node tool.

[Hangman]

Hi @arcpan and welcome to the forums,

Similar idea to @Old Bruce but using the Shape Builder tool, slightly less cleanup up but you would perhaps want to tidy up the ends of each prong to suit your needs...

[arcpan]

19 minutes ago, Old Bruce said:

Put a shape (I used a rectangle) behind the Curves object and subtract. I temporarily set the opacity of the grey curves object to 30% so we could see the green.

After subtracting there will be some cleanup needed, use the Node tool.

Great!
Thank you for your response! After following your instructions, my issue is temporarily resolved. Thanks again!

[arcpan]

16 minutes ago, Hangman said:

 

Hi @arcpan and welcome to the forums,

Similar idea to @Old Bruce but using the Shape Builder tool, slightly less cleanup up but you would perhaps want to tidy up the ends of each prong to suit your needs...

 

 

 

I tried the solution you suggested, and it worked perfectly.
btw, I wonder is it possible to create a filled area directly by the given shapes, since the real situation I'm faced with is about thirty shapes like this. 

Thanks once more for your help. Your advice was invaluable!

[Hangman]

Hi @arcpan,

That's great to hear...

14 minutes ago, arcpan said:

I wonder is it possible to create a filled area directly by the given shapes, since the real situation I'm faced with is about thirty shapes like this.

It depends on your design but perhaps applying a stroke to the shapes, expanding and filling the resulting Curves using Fill Holes followed by the Shape Builder tool... I don't know if this would save a great deal of time but just an idea...

[thomaso]

@arcpan's task reminds me of a 'magic' method to create a curve using the nodes of a shape. - True, also here we could simply delete unwanted nodes of the shape to get the desired curve… so just for the record… 😇

The workaround to count nodes was posted by @carl123:
https://forum.affinity.serif.com/index.php?/topic/168691-objects-count/&do=findComment&comment=965627