/// <summary>
/// Generate vertices and normals for cube
/// </summary>
/// <param name="vertex"></param>
/// <param name="corners"></param>
private void GenerateVertex(Vertex vertex, Voxel[] corners)
{
var data = new HermiteData
{
intersectionPoints = new List <Vector3>(),
gradientVectors = new List <Vector3>()
};
// Find the point of intersection of the surface in each of the 12 edges
for (int i = 0; i < 12; i++)
{
int n1 = Tables.EdgeConnection[i, 0];
int n2 = Tables.EdgeConnection[i, 1];
if ((vertex.edgeFlags & (1 << i)) == 0)
{
continue;
}
if (Mathf.Abs(corners[n1].density) < ToleranceDensity)
{
data.intersectionPoints.Add(corners[n1].pos);
}
else if (Mathf.Abs(corners[n2].density) < ToleranceDensity)
{
data.intersectionPoints.Add(corners[n2].pos);
}
else
{
Vector3 vDiff = corners[n1].pos - corners[n2].pos;
if (Mathf.Abs(vDiff.x) > ToleranceDensity)
{
Vector3 pos = IntersectXAxis(corners[n1], corners[n2]);
data.intersectionPoints.Add(pos);
}
if (Mathf.Abs(vDiff.y) > ToleranceDensity)
{
Vector3 pos = IntersectYAxis(corners[n1], corners[n2]);
data.intersectionPoints.Add(pos);
}
if (Mathf.Abs(vDiff.z) > ToleranceDensity)
{
Vector3 pos = IntersectZAxis(corners[n1], corners[n2]);
data.intersectionPoints.Add(pos);
}
}
Vector3 normal = GetNormal(data.intersectionPoints[data.intersectionPoints.Count - 1]);
data.gradientVectors.Add(normal);
}
vertex.pos = SchmitzVertexFromHermiteData(data, 0.001f);
vertex.normal = GetNormal(vertex.pos);
vertex.pos -= offset;
}
/// <summary>
/// Calculates an approximated vertex for a row.
/// Based on the algorithm described in the paper "Analysis and Acceleration of High Quality Isosurface Contouring".
/// </summary>
/// <param name="data">The hermite data for a row</param>
/// <param name="threshold">When has a force has a value below it will return the approximated position</param>
/// <returns>Approximated vertex for the row</returns>
private static Vector3 SchmitzVertexFromHermiteData(HermiteData data, float threshold)
{
threshold *= threshold;
List <Vector3> xPoints = data.intersectionPoints;
List <Vector3> grads = data.gradientVectors;
int pointsCount = xPoints.Count;
if (pointsCount == 0)
{
return(new Vector3());
}
// start mass point
// calculated by mean of intersection points
Vector3 c = new Vector3();
for (int i = 0; i < pointsCount; i++)
{
c += xPoints[i];
}
c /= pointsCount;
for (int i = 0; i < MaxParticleIterations; i++)
{
// force that acts on mass
Vector3 force = new Vector3();
for (int j = 0; j < pointsCount; j++)
{
Vector3 xPoint = xPoints[j];
Vector3 xNormal = grads[j];
force += xNormal * -1 * Vector3.Dot(xNormal, c - xPoint);
}
// dampen force
float damping = 1 - (float)i / MaxParticleIterations;
c += force * damping / pointsCount;
if (force.sqrMagnitude < threshold)
{
break;
}
}
return(c);
}
