/// <summary>
/// Attempts to move the positions of vertices such that they have roughly uniform density, with a bias towards also making sure that the surface areas of the faces also become more uniform.
/// </summary>
/// <param name="topology">The topology to relax.</param>
/// <param name="vertexPositions">The original positions of the vertices to relax.</param>
/// <param name="totalArea">The total surface area of the internal faces of the topology.</param>
/// <param name="lockBoundaryPositions">Indicates that vertices with an external neighboring face should not have their positions altered.</param>
/// <param name="relaxedVertexPositions">A pre-allocated collection in which the relaxed vertex positions will be stored. Should not be the same collection as <paramref name="vertexPositions"/>.</param>
/// <param name="faceCentroids">A pre-allocated collection in which the intermediate face centroid positions will be stored.</param>
/// <param name="vertexAreas">A pre-allocated collection in which the intermediate nearby surface areas of vertices will be stored.</param>
/// <returns>The relaxed vertex positions.</returns>
public static IVertexAttribute <Vector3> RelaxVertexPositionsForEqualArea(Topology topology, IVertexAttribute <Vector3> vertexPositions, float totalArea, bool lockBoundaryPositions, IVertexAttribute <Vector3> relaxedVertexPositions, IFaceAttribute <Vector3> faceCentroids, IVertexAttribute <float> vertexAreas)
{
var idealArea = totalArea / topology.vertices.Count;
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(topology.internalFaces, vertexPositions, faceCentroids);
VertexAttributeUtility.CalculateVertexAreasFromVertexPositionsAndFaceCentroids(topology.vertices, vertexPositions, faceCentroids, vertexAreas);
for (int i = 0; i < topology.vertices.Count; ++i)
{
relaxedVertexPositions[i] = new Vector3(0f, 0f, 0f);
}
foreach (var vertex in topology.vertices)
{
var multiplier = Mathf.Sqrt(idealArea / vertexAreas[vertex]);
foreach (var edge in vertex.edges)
{
var neighborVertex = edge.vertex;
var neighborRelativeCenter = vertexPositions[edge.twin];
relaxedVertexPositions[neighborVertex] += (vertexPositions[neighborVertex] - neighborRelativeCenter) * multiplier + neighborRelativeCenter;
}
}
foreach (var vertex in topology.vertices)
{
if (!lockBoundaryPositions || !vertex.hasExternalFaceNeighbor)
{
relaxedVertexPositions[vertex] /= vertex.neighborCount;
}
else
{
relaxedVertexPositions[vertex] = vertexPositions[vertex];
}
}
return(relaxedVertexPositions);
}
public override IEnumerator BeginGeneration()
{
var surface = surfaceInputSlot.GetAsset <Surface>();
var topology = topologyInputSlot.GetAsset <Topology>();
var vertexPositions = vertexPositionsInputSlot.source != null?vertexPositionsInputSlot.GetAsset <IVertexAttribute <Vector3> >() : null;
var random = randomness.GetRandom();
System.Func <float> relaxIterationFunction = null;
System.Func <bool> repairFunction = null;
System.Action relaxationLoopFunction = null;
if (vertexPositions != null)
{
if (surface is QuadrilateralSurface)
{
if (relaxForRegularityWeight >= 1.0f)
{
var relaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
relaxIterationFunction = () =>
{
PlanarManifoldUtility.RelaxVertexPositionsForRegularity(topology, vertexPositions, lockBoundaryPositions, relaxedVertexPositions);
var relaxationAmount = PlanarManifoldUtility.CalculateRelaxationAmount(vertexPositions, relaxedVertexPositions);
for (int i = 0; i < vertexPositions.Count; ++i)
{
vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
}
else if (relaxForRegularityWeight <= 0.0f)
{
var relaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
var faceCentroids = PositionalFaceAttribute.Create(surface, topology.internalFaces.Count);
var vertexAreas = new float[topology.vertices.Count].AsVertexAttribute();
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(topology.internalFaces, vertexPositions, faceCentroids);
VertexAttributeUtility.CalculateVertexAreasFromVertexPositionsAndFaceCentroids(topology.vertices, vertexPositions, faceCentroids, vertexAreas);
var totalArea = 0f;
foreach (var vertexArea in vertexAreas)
{
totalArea += vertexArea;
}
relaxIterationFunction = () =>
{
PlanarManifoldUtility.RelaxVertexPositionsForEqualArea(topology, vertexPositions, totalArea, lockBoundaryPositions, relaxedVertexPositions, faceCentroids, vertexAreas);
var relaxationAmount = PlanarManifoldUtility.CalculateRelaxationAmount(vertexPositions, relaxedVertexPositions);
for (int i = 0; i < vertexPositions.Count; ++i)
{
vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
}
else
{
var regularityWeight = Mathf.Clamp01(relaxForRegularityWeight);
var equalAreaWeight = 1f - regularityWeight;
var regularityRelaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
var equalAreaRelaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
var relaxedVertexPositions = regularityRelaxedVertexPositions;
var faceCentroids = PositionalFaceAttribute.Create(surface, topology.internalFaces.Count);
var vertexAreas = new float[topology.vertices.Count].AsVertexAttribute();
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(topology.internalFaces, vertexPositions, faceCentroids);
VertexAttributeUtility.CalculateVertexAreasFromVertexPositionsAndFaceCentroids(topology.vertices, vertexPositions, faceCentroids, vertexAreas);
var totalArea = 0f;
foreach (var vertexArea in vertexAreas)
{
totalArea += vertexArea;
}
relaxIterationFunction = () =>
{
PlanarManifoldUtility.RelaxVertexPositionsForRegularity(topology, vertexPositions, lockBoundaryPositions, regularityRelaxedVertexPositions);
PlanarManifoldUtility.RelaxVertexPositionsForEqualArea(topology, vertexPositions, totalArea, lockBoundaryPositions, equalAreaRelaxedVertexPositions, faceCentroids, vertexAreas);
for (int i = 0; i < relaxedVertexPositions.Count; ++i)
{
relaxedVertexPositions[i] = regularityRelaxedVertexPositions[i] * regularityWeight + equalAreaRelaxedVertexPositions[i] * equalAreaWeight;
}
var relaxationAmount = PlanarManifoldUtility.CalculateRelaxationAmount(vertexPositions, relaxedVertexPositions);
for (int i = 0; i < vertexPositions.Count; ++i)
{
vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
}
repairFunction = () =>
{
return(PlanarManifoldUtility.ValidateAndRepair(topology, ((QuadrilateralSurface)surface).normal, vertexPositions, repairRate, lockBoundaryPositions));
};
relaxationLoopFunction = TopologyRandomizer.CreateRelaxationLoopFunction(maxRelaxIterations, maxRepairIterations, relaxRelativePrecision, relaxIterationFunction, repairFunction);
}
else if (surface is SphericalSurface)
{
var sphericalSurface = (SphericalSurface)surface;
if (relaxForRegularityWeight >= 1.0f)
{
var relaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
relaxIterationFunction = () =>
{
SphericalManifoldUtility.RelaxVertexPositionsForRegularity(sphericalSurface, topology, vertexPositions, lockBoundaryPositions, relaxedVertexPositions);
var relaxationAmount = SphericalManifoldUtility.CalculateRelaxationAmount(vertexPositions, relaxedVertexPositions);
for (int i = 0; i < vertexPositions.Count; ++i)
{
vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
}
else if (relaxForRegularityWeight <= 0.0f)
{
var relaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
var faceCentroids = PositionalFaceAttribute.Create(surface, topology.internalFaces.Count);
var faceCentroidAngles = new float[topology.faceEdges.Count].AsEdgeAttribute();
var vertexAreas = new float[topology.vertices.Count].AsVertexAttribute();
relaxIterationFunction = () =>
{
SphericalManifoldUtility.RelaxVertexPositionsForEqualArea(sphericalSurface, topology, vertexPositions, lockBoundaryPositions, relaxedVertexPositions, faceCentroids, faceCentroidAngles, vertexAreas);
var relaxationAmount = SphericalManifoldUtility.CalculateRelaxationAmount(vertexPositions, relaxedVertexPositions);
for (int i = 0; i < vertexPositions.Count; ++i)
{
vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
}
else
{
var regularityWeight = Mathf.Clamp01(relaxForRegularityWeight);
var equalAreaWeight = 1f - regularityWeight;
var regularityRelaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
var equalAreaRelaxedVertexPositions = new Vector3[topology.vertices.Count].AsVertexAttribute();
var relaxedVertexPositions = regularityRelaxedVertexPositions;
var faceCentroids = PositionalFaceAttribute.Create(surface, topology.internalFaces.Count);
var faceCentroidAngles = new float[topology.faceEdges.Count].AsEdgeAttribute();
var vertexAreas = new float[topology.vertices.Count].AsVertexAttribute();
relaxIterationFunction = () =>
{
SphericalManifoldUtility.RelaxVertexPositionsForRegularity(sphericalSurface, topology, vertexPositions, lockBoundaryPositions, regularityRelaxedVertexPositions);
SphericalManifoldUtility.RelaxVertexPositionsForEqualArea(sphericalSurface, topology, vertexPositions, lockBoundaryPositions, equalAreaRelaxedVertexPositions, faceCentroids, faceCentroidAngles, vertexAreas);
for (int i = 0; i < relaxedVertexPositions.Count; ++i)
{
relaxedVertexPositions[i] = regularityRelaxedVertexPositions[i] * regularityWeight + equalAreaRelaxedVertexPositions[i] * equalAreaWeight;
}
var relaxationAmount = SphericalManifoldUtility.CalculateRelaxationAmount(vertexPositions, relaxedVertexPositions);
for (int i = 0; i < vertexPositions.Count; ++i)
{
vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
}
repairFunction = () =>
{
return(SphericalManifoldUtility.ValidateAndRepair(sphericalSurface, topology, vertexPositions, repairRate, lockBoundaryPositions));
};
relaxationLoopFunction = TopologyRandomizer.CreateRelaxationLoopFunction(maxRelaxIterations, maxRepairIterations, relaxRelativePrecision, relaxIterationFunction, repairFunction);
}
}
yield return(executive.GenerateConcurrently(() =>
{
TopologyRandomizer.Randomize(topology, passCount, frequency,
minVertexNeighbors, maxVertexNeighbors, minFaceNeighbors, maxFaceNeighbors,
lockBoundaryPositions, random, relaxationLoopFunction);
}));
EditorUtility.SetDirty(topology);
if (vertexPositions != null)
{
EditorUtility.SetDirty((Object)vertexPositions);
}
yield break;
}