private static Vector3 ApplyWeights(Vector4 w, PositionedQuad root)
{
return
(w.X * root.P0 +
w.Y * root.P1 +
w.Z * root.P2 +
w.W * root.P3);
}
public PositionedQuad AsPositionedQuad(PositionedQuad root)
{
return(new PositionedQuad(
ApplyWeights(W0, root),
ApplyWeights(W1, root),
ApplyWeights(W2, root),
ApplyWeights(W3, root)
));
}
public void TestIntegrateOverQuad()
{
var profile = new ScatteringProfile(1, 0.1);
Vector3 receiverPosition = new Vector3(0, 0, 0);
float sideLength = 100;
var quad = new PositionedQuad(
new Vector3(sideLength, sideLength, 0),
new Vector3(0, sideLength, 0),
new Vector3(0, 0, 0),
new Vector3(sideLength, 0, 0)
);
Vector4 contribution = profile.IntegrateOverQuad(receiverPosition, quad);
//quad should cover 1/4 of total area
//only vertex 2 is close, so contributions from other vertices should be negligible
Assert.AreEqual(0.25, contribution[2], 5e-3);
Assert.AreEqual(0, contribution[0], 5e-3);
Assert.AreEqual(0, contribution[1], 5e-3);
Assert.AreEqual(0, contribution[3], 5e-3);
}
private static Vector4 IntegrateOverSubQuad(ScatteringProfile profile, Vector3 receiverPosition, PositionedQuad root, SubQuad subQuad)
{
var quad = subQuad.AsPositionedQuad(root);
double area = quad.Area;
//this assume that P0 is the closest point to the receiver
double closestDistance = Vector3.Distance(receiverPosition, quad.P0);
double maximumContribution = profile.CalculateMaximumContribution(closestDistance, area);
if (maximumContribution < SubdivisionThreshold)
{
double distance = Vector3.Distance(receiverPosition, quad.Center);
return(subQuad.CenterWeight * (float)(area * profile.CalculateDiffuseReflectance(distance)));
}
else
{
Vector4 total = Vector4.Zero;
foreach (SubQuad subSubQuad in subQuad.Split())
{
total += IntegrateOverSubQuad(profile, receiverPosition, root, subSubQuad);
}
return(total);
}
}
public static Vector4 IntegrateOverQuad(this ScatteringProfile profile, Vector3 receiverPosition, PositionedQuad quad)
{
int nearestIdx = quad.FindClosestCorner(receiverPosition);
SubQuad orientedSubQuad = SubQuad.MakeRotatedWhole(nearestIdx);
return(IntegrateOverSubQuad(profile, receiverPosition, quad, orientedSubQuad));
}
/**
* Returns form factors unnormalized by receiver
*/
private double[][] CalculateRawFormFactors(ScatteringProfile[] profilesBySurface)
{
double[][] formFactors = new double[vertexCount][]; //indexed by (receiver, transmitter)
for (int receiverIdx = 0; receiverIdx < vertexCount; receiverIdx++)
{
formFactors[receiverIdx] = new double[vertexCount];
}
var stopwatch = Stopwatch.StartNew();
int transmitterCount = faces.Length;
for (int transmitterIdx = 0; transmitterIdx < transmitterCount; ++transmitterIdx)
{
if (transmitterIdx % 1000 == 0)
{
double fractionComplete = transmitterIdx / (double)transmitterCount;
double estimatedRemainingSeconds = stopwatch.ElapsedMilliseconds / 1000.0 / fractionComplete;
Console.WriteLine(fractionComplete + ": " + estimatedRemainingSeconds);
}
int transmitterLabel = connectedComponentLabels.FaceLabels[transmitterIdx];
int surfaceIdx = surfaceMap[transmitterIdx];
ScatteringProfile profile = profilesBySurface[surfaceIdx];
if (profile == null)
{
//not a scattering surface
continue;
}
Quad transmitter = faces[transmitterIdx];
PositionedQuad positionedTransmitter = PositionedQuad.Make(vertexPositions, transmitter);
double transmitterArea = positionedTransmitter.Area;
if (profile.meanFreePath == 0)
{
//edge case: no scattering
//split the face contribution evenly amongst its four corners
double contribution = 0.25 * profile.surfaceAlbedo * transmitterArea;
formFactors[transmitter.Index0][transmitter.Index0] = contribution;
formFactors[transmitter.Index1][transmitter.Index1] = contribution;
formFactors[transmitter.Index2][transmitter.Index2] = contribution;
formFactors[transmitter.Index3][transmitter.Index3] = contribution;
continue;
}
double imperceptibleDistance = profile.FindImperceptibleDistance(transmitterArea);
var transmitterBoundingSphere = positionedTransmitter.BoundingSphere;
var receiverBoundingSphere = new BoundingSphere(transmitterBoundingSphere.Center, (float)(transmitterBoundingSphere.Radius + imperceptibleDistance));
List <int> receiverIndices = receiverCollisionTree.GetPointsInSphere(receiverBoundingSphere);
Vector4[] contributions = receiverIndices
.Select(receiverIdx => {
int receiverLabel = connectedComponentLabels.VertexLabels[receiverIdx];
if (receiverLabel != transmitterLabel)
{
return(Vector4.Zero);
}
Vector3 receiverPosition = vertexPositions[receiverIdx];
Vector4 contribution = profile.IntegrateOverQuad(receiverPosition, positionedTransmitter);
return(contribution);
}).ToArray();
double totalContribution = contributions.Sum(v => v.X + v.Y + v.Z + v.W);
double normalizationFactor = profile.surfaceAlbedo * transmitterArea / totalContribution;
for (int i = 0; i < contributions.Length; ++i)
{
int receiverIdx = receiverIndices[i];
Vector4 contribution = contributions[i];
formFactors[receiverIdx][transmitter.Index0] += normalizationFactor * contribution[0];
formFactors[receiverIdx][transmitter.Index1] += normalizationFactor * contribution[1];
formFactors[receiverIdx][transmitter.Index2] += normalizationFactor * contribution[2];
formFactors[receiverIdx][transmitter.Index3] += normalizationFactor * contribution[3];
}
}
return(formFactors);
}
