This is all about having some data model of vector graphics. A rendering of this model in a Forms control is a separate layer.
My past answers on related topics can give you pretty good idea how to proceed:
What kind of playful method is Paint? (DataGridViewImageCell.Paint(...))[
^],
Drawing Lines between mdi child forms[
^],
capture the drawing on a panel[
^].
However, why would you do this with Forms? This task is born to be done in WPF. You know so little about how to approach the problem in Forms while in WPF almost all if it is already done in higher level and very professionally. You should use WPF unless you have a really good reason (such as compatibility with Mono of .NET v.2.0) to do in with Forms.
—SA