Smooth curve drawing (runtime)

I need to draw curves like in game Doodle Astro for iOS (is it for android? - i don’t know).

This is what I need to achieve (smooth lines with rounded endings without corners):
[16376-фото-3.jpg|16376]
[16375-фото-4.jpg|16375]

This is what I have achieved (using Vectrosity):

Original

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Original

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Problem places:

Original

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Original

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Please help =)

Edit:
New Images links

Check this PDF for path smoothing. Kind of tricky to get right but all it really entails is averaging out the last three points of your path.