Or maybe instead of using shapes I should use the pen tool?
Yes. That is the ESSENCE of using a vector drawing program.
In addition to what James said, the image shows a rather crude shape; you could use ellipses for the rounded parts seen at an angle.
is there a bend tool?
Check the Warp tool and it's colleagues...
Or will I have to manually do this using points? Or maybe instead of using shapes I should use the pen tool?
That's of course how seasoned illustrators do it mostly. It's all about control - you want to avoid funky deformations and the generation of unnecessary points.
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Let me disagree about the supremacy of the pen tool for shape generation. While I use the pen daily and for many, many things, a number of talented precision artists I've come to admire create beautifully intricate and original vector artwork by combining, compounding, subtracting, dividing and intersecting simple shapes. They would claim that the pith of vector art is not the pen tool but the pathfinder operations applied to cleverly assembled and arranged basic shapes.
Of course it's not an either/or proposition. It rarely is. In truth, one can make the same artwork by resort to different strategies and techniques. But maybe that's the point. One tool is the "preferred" one for this or that specific tak simply because someone prefers it! Not because it's the only right tool for the job. Or even the best for every artist.
Thank you for all the helpful suggestions.
I think I will do a combination of the pen tool and shapes, sounds like the best way to go for what I am doing.
While I would be hard-pressed to argue with the suggestions offered thus far, let me voice another "vote" for learning the pen tool. One cannot be master of a vector illustration program without pen tool basics firmly under one's belt.
One of the "fun" things about Illustrator is, when one has the time, discovering the different ways in which one can "skin the cat." Such flights of discovery often lead to genuine shortcuts -- ingenious timesavers. But none of that is a substitute for learning the pen tool.
You can harness all sorts of diesel-powered tools to speed the process, but you'll never be a master ditch-digger unless you know how to use a shovel.
OK... so I suck at analogies.
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Probably one should also get familiar with the reshape tool which is probably under utilized but makes what the OP wants to do quite a simple task.
Crudely drawn but a combination of the pen tool and reshape tool offers an extra flexibility.
Clicking and dragging the center of the paths to bend them.
I have nt found a way of bending all of these at one time which would be a even better tool.
Basic forms, expand stroke and live paint with a little bit of pen is the best and very easy way to drow this kind pf drowing.
Using other effects you can change the "warm" of the primitive drowing.
So old school and the new one, together, could be the answer.