I'm having trouble understanding Dual Contouring yet and I need some explanations from someone who has first hand experience.

I searched all I could before writing this question. I've already read:

• https://upvoid.com/devblog/2013/05/terrain-engine-part-1-dual-contouring/

• http://ngildea.blogspot.com.br/2014/11/implementing-dual-contouring.html

And I'm currently working through:

• http://www.frankpetterson.com/publications/dualcontour/dualcontour.pdf

• http://ngildea.blogspot.com.br/2015/03/engine-overview.html

• http://www.oocities.org/tzukkers/isosurf/isosurfaces.html

I'm not used to all the calculus and math and the information doesn't get into my brain. I really need some clarification, or a tutorial, please.

I'm creating a 3D game with destructible map in Unity 5. I implemented a Minecraft-like voxel system. But how does Dual Contouring work (and how do I implement it in C#)? I don't want to reinvent the wheel, I want to USE it, but if I can't find a ready-made solution in Unity then I need a grounding in how this algorithm works so I can implement it myself.

Not solutions:

Can someone explain dual contouring? is not a duplicate... It's not for me! That question is too straight to the result as the person already mostly understands the proccess. I need help understanding the roles of each function and math components, like the QEF and density.

Also, I looked into Marching Cubes but that won't work for me as I read that it doesn't allow having cubic parts of the mesh in the middle of the smooth ones, and I will use "blocks" in some parts.