title: What is "Hermite Data" described in the Dual Contouring algorithm?
body: <p>I have been reading <a href="http://www.frankpetterson.com/publications/dualcontour/dualcontour.pdf" rel="nofollow noreferrer">various sources</a> the past hours and couldn't understand how Dual Contouring works. My problem is that I don't know the meaning of "Hermite Data" and even Google and Wikipedia couldn't help me on that. Could someone explain me what "Hermite Data" is? Also I found <a href="https://stackoverflow.com/questions/6485908/basic-dual-contouring-theory">this</a> which says the important steps are described in 2.2. Sadly I don't quite understand the meaning of it. Because nowhere I could find a description what the (minimizer of the) quadratic function of this equation means:</p>
  
  <p>E[x] = ∑
  i
  (ni
  ·(x− pi
  ))2</p>
  
  <p>I don't know what to "input" in this function nor what it "outputs". Also they are talking about "cubes" but as far as I know a set of Voxels is just a quantity of data(0 or 1) and far as I have understand Dual Contouring takes those Voxels and turns them into a mesh.</p>