How to extrude a spline curve onto a curved surface in solidworks?

I am trying to model a mug in solidworks and I need help. I want to extrude a shape off a surface. Once that extrusion is complete I want to make a circular pattern so that the entire object is tactile. Please help! I am opened to suggestions of other ways to achieve this goal. Many thanks

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Tatiana,
Read through the steps I suggested Robin follow in this post: https://grabcad.com/questions/doing-a-cut-on-2-faces-at-different-angles-in-solidworks

I think by splitting the model face, and then thickening the new surface, you'll get the result you are after. You may also be able to use the Face - Offset command (instead of thicken), depending on the version you are using.
The Wrap command may also work. Give them all a try and see what works best!

You could continue with your plan to extrude the shape, but it would be better if the inside of the cup were not already hollow. You'll also need to set the end condition as offset from surface.

 
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