public ClusterFit(ColourSet colours, SquishFlags flags)
: base(colours, flags)
{
// set the iteration count
m_iterationCount = ((m_flags & SquishFlags.ColourIterativeClusterFit) != 0) ? kMaxIterations : 1;
// initialise the best error
m_besterror = new Vec4(float.MaxValue);
// initialise the metric
bool perceptual = ((m_flags & SquishFlags.ColourMetricPerceptual) != 0);
if (perceptual)
m_metric = new Vec4(0.2126f, 0.7152f, 0.0722f, 0.0f);
else
m_metric = new Vec4(1.0f);
// cache some values
int count = m_colours.GetCount();
Vec3[] values = m_colours.GetPoints();
// get the covariance matrix
Sym3x3 covariance = Sym3x3.ComputeWeightedCovariance(count, values, m_colours.GetWeights());
// compute the principle component
m_principle = Sym3x3.ComputePrincipleComponent(covariance);
}
public static bool CompareAnyLessThan(Vec4 a, Vec4 b)
{
return a.X() < b.X()
|| a.Y() < b.Y()
|| a.Z() < b.Z()
|| a.W() < b.W();
}
public static Vec4 Truncate(Vec4 v)
{
return new Vec4(
v.X() > 0.0f ? CMath.Floor(v.X()) : CMath.Ceil(v.X()),
v.Y() > 0.0f ? CMath.Floor(v.Y()) : CMath.Ceil(v.Y()),
v.Z() > 0.0f ? CMath.Floor(v.Z()) : CMath.Ceil(v.Z()),
v.W() > 0.0f ? CMath.Floor(v.W()) : CMath.Ceil(v.W())
);
}
public static Vec4 Max(Vec4 a, Vec4 b)
{
return new Vec4(
Math.Max(a.X(), b.X()),
Math.Max(a.Y(), b.Y()),
Math.Max(a.Z(), b.Z()),
Math.Max(a.W(), b.W())
);
}
public static Vec4 Reciprocal(Vec4 v)
{
return new Vec4(
1.0f / v.X(),
1.0f / v.Y(),
1.0f / v.Z(),
1.0f / v.W()
);
}
public static Vec4 NegativeMultiplySubtract(Vec4 a, Vec4 b, Vec4 c)
{
return c - a * b;
}
public static Vec4 MultiplyAdd(Vec4 a, Vec4 b, Vec4 c)
{
return a * b + c;
}
protected override unsafe void Compress3(byte* block)
{
// declare variables
int count = m_colours.GetCount();
Vec4 two = new Vec4(2.0f);
Vec4 one = new Vec4(1.0f);
Vec4 half_half2 = new Vec4(0.5f, 0.5f, 0.5f, 0.25f);
Vec4 zero = new Vec4(0.0f);
Vec4 half = new Vec4(0.5f);
Vec4 grid = new Vec4(31.0f, 63.0f, 31.0f, 0.0f);
Vec4 gridrcp = new Vec4(1.0f / 31.0f, 1.0f / 63.0f, 1.0f / 31.0f, 0.0f);
// prepare an ordering using the principle axis
ConstructOrdering(m_principle, 0);
// check all possible clusters and iterate on the total order
Vec4 beststart = new Vec4(0.0f);
Vec4 bestend = new Vec4(0.0f);
Vec4 besterror = m_besterror;
byte[] bestindices = new byte[16];
int bestiteration = 0;
int besti = 0, bestj = 0;
// loop over iterations (we avoid the case that all points in first or last cluster)
for (int iterationIndex = 0; ; )
{
// first cluster [0,i) is at the start
Vec4 part0 = new Vec4(0.0f);
for (int i = 0; i < count; ++i)
{
// second cluster [i,j) is half along
Vec4 part1 = (i == 0) ? m_points_weights[0] : new Vec4(0.0f);
int jmin = (i == 0) ? 1 : i;
for (int j = jmin; ; )
{
// last cluster [j,count) is at the end
Vec4 part2 = m_xsum_wsum - part1 - part0;
// compute least squares terms directly
Vec4 alphax_sum = Vec4.MultiplyAdd(part1, half_half2, part0);
Vec4 alpha2_sum = alphax_sum.SplatW();
Vec4 betax_sum = Vec4.MultiplyAdd(part1, half_half2, part2);
Vec4 beta2_sum = betax_sum.SplatW();
Vec4 alphabeta_sum = (part1 * half_half2).SplatW();
// compute the least-squares optimal points
Vec4 factor = Vec4.Reciprocal(Vec4.NegativeMultiplySubtract(alphabeta_sum, alphabeta_sum, alpha2_sum * beta2_sum));
Vec4 a = Vec4.NegativeMultiplySubtract(betax_sum, alphabeta_sum, alphax_sum * beta2_sum) * factor;
Vec4 b = Vec4.NegativeMultiplySubtract(alphax_sum, alphabeta_sum, betax_sum * alpha2_sum) * factor;
// clamp to the grid
a = Vec4.Min(one, Vec4.Max(zero, a));
b = Vec4.Min(one, Vec4.Max(zero, b));
a = Vec4.Truncate(Vec4.MultiplyAdd(grid, a, half)) * gridrcp;
b = Vec4.Truncate(Vec4.MultiplyAdd(grid, b, half)) * gridrcp;
// compute the error (we skip the constant xxsum)
Vec4 e1 = Vec4.MultiplyAdd(a * a, alpha2_sum, b * b * beta2_sum);
Vec4 e2 = Vec4.NegativeMultiplySubtract(a, alphax_sum, a * b * alphabeta_sum);
Vec4 e3 = Vec4.NegativeMultiplySubtract(b, betax_sum, e2);
Vec4 e4 = Vec4.MultiplyAdd(two, e3, e1);
// apply the metric to the error term
Vec4 e5 = e4 * m_metric;
Vec4 error = e5.SplatX() + e5.SplatY() + e5.SplatZ();
// keep the solution if it wins
if (Vec4.CompareAnyLessThan(error, besterror))
{
beststart = a;
bestend = b;
besti = i;
bestj = j;
besterror = error;
bestiteration = iterationIndex;
}
// advance
if (j == count)
break;
part1 += m_points_weights[j];
++j;
}
// advance
part0 += m_points_weights[i];
}
// stop if we didn't improve in this iteration
if (bestiteration != iterationIndex)
break;
// advance if possible
++iterationIndex;
if (iterationIndex == m_iterationCount)
break;
// stop if a new iteration is an ordering that has already been tried
Vec3 axis = (bestend - beststart).GetVec3();
if (!ConstructOrdering(axis, iterationIndex))
break;
}
// save the block if necessary
if (Vec4.CompareAnyLessThan(besterror, m_besterror))
{
// remap the indices
int orderIndex = 16 * bestiteration;
byte[] unordered = new byte[16];
for (int m = 0; m < besti; ++m)
unordered[m_order[orderIndex + m]] = 0;
for (int m = besti; m < bestj; ++m)
unordered[m_order[orderIndex + m]] = 2;
for (int m = bestj; m < count; ++m)
unordered[m_order[orderIndex + m]] = 1;
fixed (byte* fixUnordered = unordered, fixBestIndices = bestindices)
{
m_colours.RemapIndices(fixUnordered, fixBestIndices);
// save the block
ColourBlock.WriteColourBlock3(beststart.GetVec3(), bestend.GetVec3(), fixBestIndices, block);
}
// save the error
m_besterror = besterror;
}
}
private bool ConstructOrdering(Vec3 axis, int iteration)
{
// cache some values
int count = m_colours.GetCount();
Vec3[] values = m_colours.GetPoints();
// build the list of dot products
float[] dps = new float[16];
int orderIndex = 16 * iteration;
for (int i = 0; i < count; ++i)
{
dps[i] = Vec3.Dot(values[i], axis);
m_order[orderIndex + i] = (byte)i;
}
// stable sort using them
for (int i = 0; i < count; ++i)
{
for (int j = i; j > 0 && dps[j] < dps[j - 1]; --j)
{
CMath.Swap<float>(ref dps[j], ref dps[j - 1]);
CMath.Swap<byte>(ref m_order[orderIndex + j], ref m_order[orderIndex + (j - 1)]);
}
}
// check this ordering is unique
for (int it = 0; it < iteration; ++it)
{
int prevIndex = 16 * it;
bool same = true;
for (int i = 0; i < count; ++i)
{
if (m_order[orderIndex + i] != m_order[prevIndex + i])
{
same = false;
break;
}
}
if (same)
return false;
}
// copy the ordering and weight all the points
Vec3[] unweighted = m_colours.GetPoints();
float[] weights = m_colours.GetWeights();
m_xsum_wsum = new Vec4(0.0f);
for (int i = 0; i < count; ++i)
{
int j = m_order[orderIndex + i];
Vec4 p = new Vec4(unweighted[j].X(), unweighted[j].Y(), unweighted[j].Z(), 1.0f);
Vec4 w = new Vec4(weights[j]);
Vec4 x = p * w;
m_points_weights[i] = x;
m_xsum_wsum += x;
}
return true;
}