Starting point or library for freehand drawing 2D shapes, calculating intersection areas and basic translations?

Hello,

I am working on a PhD research project and trying to find a good software package that will allow me to demo results on a mobile device. I thought Unity might be a good starting point as I have some C# experience and will also be working with 2D shapes.

The first goal is an application that: 1- Allows user to freehand draw a 2D shape 2- Calculate the 2D intersection area of this drawn shape with existing shapes 3- Perform functions such as rotate the shape over pivot point, move shapes, scale etc

Any tips on a starting point on how to achieve this will be extremely welcomed. Been reading on lots of libraries in the asset store or trying to find info in the base documentation but its not clear if Unity has built in functions to achieve this. Thank you!