private float ComputeLeastSquares(Vec4 alphax_sum, Vec4 betax_sum, Vec4 alphabeta_sum, out Vec4 a, out Vec4 b)
{
Vec4 alpha2_sum = alphax_sum.SplatW();
Vec4 beta2_sum = betax_sum.SplatW();
// compute the least-squares optimal points
Vec4 factor = alphabeta_sum.NegativeMultiplySubtract(alphabeta_sum, alpha2_sum * beta2_sum).Reciprocal();
a = betax_sum.NegativeMultiplySubtract(alphabeta_sum, alphax_sum * beta2_sum) * factor;
b = alphax_sum.NegativeMultiplySubtract(alphabeta_sum, betax_sum * alpha2_sum) * factor;
// clamp to the grid
a = a.Clamp(Vec4.Zero, Vec4.One);
b = b.Clamp(Vec4.Zero, Vec4.One);
a = GRID.MultiplyAdd(a, HALF).Truncate() * GRIDRCP;
b = GRID.MultiplyAdd(b, HALF).Truncate() * GRIDRCP;
// compute the error (we skip the constant xxsum)
Vec4 e1 = (a * a * alpha2_sum) + (b * b * beta2_sum);
Vec4 e2 = a.NegativeMultiplySubtract(alphax_sum, a * b * alphabeta_sum);
Vec4 e3 = b.NegativeMultiplySubtract(betax_sum, e2);
Vec4 e4 = e3 * 2 + e1;
// apply the metric to the error term
Vec4 e5 = e4 * m_metric;
return(e5.X + e5.Y + e5.Z);
}
public static Vec3 ComputePrincipleComponent(Sym3x3 matrix)
{
Vec4 row0 = new Vec4(matrix[0], matrix[1], matrix[2], 0.0f);
Vec4 row1 = new Vec4(matrix[1], matrix[3], matrix[4], 0.0f);
Vec4 row2 = new Vec4(matrix[2], matrix[4], matrix[5], 0.0f);
Vec4 v = new Vec4(1.0f);
for (int i = 0; i < 8; ++i)
{
// matrix multiply
Vec4 w = row0 * v.SplatX();
w = row1.MultiplyAdd(v.SplatY(), w);
w = row2.MultiplyAdd(v.SplatZ(), w);
// get max component from xyz in all channels
Vec4 a = Vec4.Max(w.SplatX(), Vec4.Max(w.SplatY(), w.SplatZ()));
// divide through and advance
v = w * a.Reciprocal();
}
return(v.GetVec3());
}
private float SolveLeastSquares(out Vec4 start, out Vec4 end)
{
// accumulate all the quantities we need
int count = m_colours.Count;
float alpha2_sum = 0;
float beta2_sum = 0;
float alphabeta_sum = 0;
var alphax_sum = Vec4.Zero;
var betax_sum = Vec4.Zero;
for (int i = 0; i < count; ++i)
{
var alpha = m_alpha[i];
var beta = m_beta[i];
var x = m_weighted[i];
alpha2_sum += alpha * alpha;
beta2_sum += beta * beta;
alphabeta_sum += alpha * beta;
alphax_sum += alpha * x;
betax_sum += beta * x;
}
// zero where non-determinate
Vec4 a, b;
if (beta2_sum == 0)
{
a = alphax_sum / alpha2_sum;
b = Vec4.Zero;
}
else if (alpha2_sum == 0)
{
a = Vec4.Zero;
b = betax_sum / beta2_sum;
}
else
{
var factor = 1.0f / (alpha2_sum * beta2_sum - alphabeta_sum * alphabeta_sum);
a = (alphax_sum * beta2_sum - betax_sum * alphabeta_sum) * factor;
b = (betax_sum * alpha2_sum - alphax_sum * alphabeta_sum) * factor;
}
// clamp the output to [0, 1]
a = a.Clamp(Vec4.Zero, Vec4.One);
b = b.Clamp(Vec4.Zero, Vec4.One);
// clamp to the grid
a = GRID.MultiplyAdd(a, HALF).Truncate() * GRIDRCP;
b = GRID.MultiplyAdd(b, HALF).Truncate() * GRIDRCP;
// compute the error
var e1 = a * a * alpha2_sum + b * b * beta2_sum /*+ m_xxsum*/
+ 2 * (a * b * alphabeta_sum - a * alphax_sum - b * betax_sum);
// apply the metric to the error term
float error = Vec4.Dot(e1, m_metricSqr);
// save the start and end
start = a;
end = b;
return(error);
}
protected override void Compress4(BlockWindow block)
{
// declare variables
var count = m_colours.Count;
// prepare an ordering using the principle axis
ConstructOrdering(m_principle, 0);
// check all possible clusters and iterate on the total order
Vec4 beststart = Vec4.Zero;
Vec4 bestend = Vec4.Zero;
float m_besterror = float.MaxValue;
float besterror = m_besterror;
var bestindices = new Byte[16];
int bestiteration = 0;
int besti = 0, bestj = 0, bestk = 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 = Vec4.Zero;
for (int i = 0; i < count; ++i)
{
// second cluster [i,j) is one third along
Vec4 part1 = Vec4.Zero;
for (int j = i; ;)
{
// third cluster [j,k) is two thirds along
Vec4 part2 = (j == 0) ? m_points_weights[0] : Vec4.Zero;
int kmin = (j == 0) ? 1 : j;
for (int k = kmin; ;)
{
// last cluster [k,count) is at the end
Vec4 part3 = m_xsum_wsum - part2 - part1 - part0;
// compute least squares terms directly
Vec4 alphax_sum = ONETHIRD_ONETHIRD2.MultiplyAdd(part2, TWOTHIRDS_TWOTHIRDS2.MultiplyAdd(part1, part0));
Vec4 betax_sum = ONETHIRD_ONETHIRD2.MultiplyAdd(part1, TWOTHIRDS_TWOTHIRDS2.MultiplyAdd(part2, part3));
Vec4 alphabeta_sum = TWONINETHS * (part1 + part2).SplatW();
var error = ComputeLeastSquares(alphax_sum, betax_sum, alphabeta_sum, out Vec4 a, out Vec4 b);
// keep the solution if it wins
if (error < besterror)
{
beststart = a;
bestend = b;
besterror = error;
besti = i;
bestj = j;
bestk = k;
bestiteration = iterationIndex;
}
// advance
if (k == count)
{
break;
}
part2 += m_points_weights[k];
++k;
}
// 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 (besterror < m_besterror)
{
// remap the indices
var orderIndex = 16 * bestiteration;
var 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 < bestk; ++m)
{
unordered[m_order[orderIndex + m]] = 3;
}
for (int m = bestk; m < count; ++m)
{
unordered[m_order[orderIndex + m]] = 1;
}
m_colours.RemapIndices(unordered, bestindices);
// save the block
block.WriteColourBlock4(beststart.GetVec3(), bestend.GetVec3(), bestindices);
// save the error
m_besterror = besterror;
}
}