Match drawn 3d shapes to a known set of shapes

I am looking to be able to draw a shape using a VR handset and have it matched to an existing shape. I.e. there will be an ordered set of Vector3's. For example if the two shapes are a circle and a square and I draw a circle it should match to the circle. The aim of this is to create a drawing game, with varying levels of difficulty. Going from simple shapes up to more complex drawings (e.g. a line drawing of a dolphin). This will mean that it needs to be extensible. I need to be able to add new shapes later that can be matched. To be clear I'm really only looking for help writing the code to match these two things. I will provide example data to work with.