What is the difference between an isometric deformation and a conformal deformation? In fact, even the definition of both deformations is still unclear clear for me.
Is it possible to define an isometric deformation from $\mathrm{R}^2$ to $\mathrm{R}^3$ ?
So I would like to ask if anyone has a reference in mind that can help me understand each concept. Any help will be appreciated, but please note that I am not a geometry student, but a mathematics student working in applied mathematics. Honestly, I am working in computer vision, and precisely in the 3D reconstruction domain. There is an idea saying that one can reconstruct a 3D object after being isometricaly defomed, just using its initial 3D form and a 2D image of the deformed object. So, in order to comprehensively understand the problem it is important for me to understand what "deformation" (isometric) refers to.
I already searched for some references, but isometry is usually considered from an algebraic point of view, as isometric transfomation.