Hello

I am currently researching how to generate procedural terrain. I have found Dual Contouring, which is as algorithm for generation smooth geometry from voxel information. http://www.frankpetterson.com/publications/dualcontour/dualcontour.pdf

however, I am having a hard time understanding the paper due to my currently understanding of mathematics

a have a variety of questions regarding the paper, which, after searching the internet, decided that I should just ask them here.

First of all
when they mention hermit data, do they mean.
the point the surface intercepts the cell along its edge

and the normal of the surface

When they say scalar field or density field

are the referring to the voxel field, which is the points in space that are occupied or not.

or is scalar field and density field, two different things

if implemented using an octree (I don't think you can't)

does the leaf contain just the voxel vertex,

or the voxel cell state,

or both

and/or the intersection points and normals along the edges

What the hell is the quadratic error function (QEF)

and how would I implement it

Lastly
What fields of math do I have to be familiar with to understand the paper on face value

Some questions might indicate I got the right picture

but I just need to confirm the details

if any admin feels this post is not appropriate for this section.

feel free to move it.