Dual Contouring - Cutting Cubes into the Terrain

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I have a very simple Dual Contouring setup right now; I have a grid of chunks, each consisting of 16x16x16 grid points which store the density at that position along with the normal vectors at intersection points along the X Positive, Y Positive, and Z Positive edges, to allow flexibility in modifying normals (i.e. so a player can sculpt the terrain by modifying the normals of grid points).

In essence, my GridPoint data structure is as follows:

struct GridPoint
{
float density;
vector3 xpositiveNormal; // normal at the intersection point formed by this point and the next point in the XPositive direction (if there is an intersection point)
vector3 ypositiveNormal; // same as above, except for the Y direction
vector3 zpositiveNormal; // same as above, except for the Z direction
}


When I build the mesh of each chunk, I loop through all the grid points, find edges that have sign changes, calculate the QEF-minimizing position, and then connect all the QEF-minimizing positions.  This works great, except I'm having issues modifying my terrain.

My current goal is to allow a player to remove cubes from the terrain.  At first, I tried to accomplish this by setting the selected point to have a density of -1 (lowest), setting the densities of the surrounding points to 1 (highest), and setting the normal vectors of the surrounding points to point towards the selected point.  This worked...sort of.  It would only work if the cubes formed by the selected gridpoint and the 26 surrounding grid points (8 cubes) only had the intersection points between the selected gridpoint and the neighboring gridpoint as the only intersection points.  Here's what I mean (in 2D):

Filled circles represent densities of 1.0, the empty circle represents a density of -1.0, the arrows are the normal vectors, and the square is the resulting extracted surface.  Since each neighboring square has only intersection points from the selected gridpoint and neighboring gridpoints, the QEF finds the vertex at the correct position, and a square is formed.  However, this does not work if there are other intersection points...

The gray square represents the cut I want to achieve (ignore the part of the square outside of the terrain), while the red represents the actual generated surface.  Gray circles represent grid points with densities less than the isovalue.  The gridpoint in the middle of the gray square has a density of -1.0, per the method I described above of removing cubes.

The issue is that the other intersections and their normals affect the output of the QEF, and so the QEF generated positions are not where I want them to be.

This leads me to believe that my current method of modifying the terrain is fundamentally flawed; any ideas on how to fix this?

Thanks!

Edited by _untitled_

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I haven't done dual contouring before, but this seems similar to how my voxel engine works. At each voxel I store 3 values representing the x, y, and z potential displacement of the surface from that sample point. The special case of 0, 0, 0 represents an empty voxel.

When building the mesh, I use a variant of marching cubes and consider each cubic cell with 8 voxels at the corners. Any cell which has a mix of 0 and non-0 voxels will contain a surface. Any cell edge connecting a 0 and non-0 voxel will contain a vertex of the mesh, and the position of the vertex along the edge is equal to the x, y, or z displacement from the non-zero voxel. This makes it very easy to calculate the vertex locations and gives me a lot of control over the surface, but still gives a lot of surface variability.

To dig a a "hole", I set a voxel to 0,0,0, and set its neighbors associated x, y, or z displacement to a random value within a controlled range. If you want straight edges, you can also get that effect by choosing consistent displacements for the neighbors.

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I actually discovered that it wasn't working because of a smaller bug.  After fixing it, the method I described above works really well.  Probably wasn't using my brain the night I wrote this post.  Anyway, I appreciate your help!