public ClusterFit(ColourSet colours, SquishFlags flags)
: base(colours, flags)
{
// set the iteration count
m_iterationCount = ((m_flags & SquishFlags.kColourIterativeClusterFit) != 0) ? kMaxIterations : 1;
// initialise the best error
m_besterror = Vector4.one * float.MaxValue;
// initialise the metric
bool perceptual = ((m_flags & SquishFlags.kColourMetricPerceptual) != 0);
if (perceptual)
{
m_metric = new Vector4(0.2126f, 0.7152f, 0.0722f, 0.0f);
}
else
{
m_metric = Vector4.one;
}
// cache some values
int count = m_colours.GetCount();
Vector3[] values = m_colours.GetPoints();
// get the covariance matrix
Sym3x3 covariance = math.ComputeWeightedCovariance(count, values, m_colours.GetWeights());
// compute the principle component
m_principle = math.ComputePrincipleComponent(covariance);
}
public static Sym3x3 ComputeWeightedCovariance(int n, Vector3[] points, float[] weights)
{
// compute the centroid
float total = 0.0f;
Vector3 centroid = Vector3.zero;
for (int i = 0; i < n; ++i)
{
total += weights[i];
centroid += weights[i] * points[i];
}
centroid /= total;
// accumulate the covariance matrix
Sym3x3 covariance = new Sym3x3();
for (int i = 0; i < n; ++i)
{
Vector3 a = points[i] - centroid;
Vector3 b = weights[i] * a;
covariance[0] += a.x * b.x;
covariance[1] += a.x * b.y;
covariance[2] += a.x * b.z;
covariance[3] += a.y * b.y;
covariance[4] += a.y * b.z;
covariance[5] += a.z * b.z;
}
// return it
return(covariance);
}
public static Vector3 GetMultiplicity1Evector(Sym3x3 matrix, float evalue)
{
// compute M
Sym3x3 m = new Sym3x3();
m[0] = matrix[0] - evalue;
m[1] = matrix[1];
m[2] = matrix[2];
m[3] = matrix[3] - evalue;
m[4] = matrix[4];
m[5] = matrix[5] - evalue;
// compute U
Sym3x3 u = new Sym3x3();
u[0] = m[3] * m[5] - m[4] * m[4];
u[1] = m[2] * m[4] - m[1] * m[5];
u[2] = m[1] * m[4] - m[2] * m[3];
u[3] = m[0] * m[5] - m[2] * m[2];
u[4] = m[1] * m[2] - m[4] * m[0];
u[5] = m[0] * m[3] - m[1] * m[1];
// find the largest component
float mc = Mathf.Abs(u[0]);
int mi = 0;
for (int i = 1; i < 6; ++i)
{
float c = Mathf.Abs(u[i]);
if (c > mc)
{
mc = c;
mi = i;
}
}
// pick the column with this component
switch (mi)
{
case 0:
return(new Vector3(u[0], u[1], u[2]));
case 1:
case 3:
return(new Vector3(u[1], u[3], u[4]));
default:
return(new Vector3(u[2], u[4], u[5]));
}
}
public static Vector3 GetMultiplicity2Evector(Sym3x3 matrix, float evalue)
{
// compute M
Sym3x3 m = new Sym3x3();
m[0] = matrix[0] - evalue;
m[1] = matrix[1];
m[2] = matrix[2];
m[3] = matrix[3] - evalue;
m[4] = matrix[4];
m[5] = matrix[5] - evalue;
// find the largest component
float mc = Mathf.Abs(m[0]);
int mi = 0;
for (int i = 1; i < 6; ++i)
{
float c = Mathf.Abs(m[i]);
if (c > mc)
{
mc = c;
mi = i;
}
}
// pick the first eigenvector based on this index
switch (mi)
{
case 0:
case 1:
return(new Vector3(-m[1], m[0], 0.0f));
case 2:
return(new Vector3(m[2], 0.0f, -m[0]));
case 3:
case 4:
return(new Vector3(0.0f, -m[4], m[3]));
default:
return(new Vector3(0.0f, -m[5], m[4]));
}
}
public RangeFit(ColourSet colours, SquishFlags flags)
: base(colours, flags)
{
// initialise the metric
bool perceptual = ((m_flags & SquishFlags.kColourMetricPerceptual) != 0);
if (perceptual)
{
m_metric = new Vector3(0.2126f, 0.7152f, 0.0722f);
}
else
{
m_metric = Vector3.one;
}
// initialise the best error
m_besterror = float.MaxValue;
// cache some values
int count = m_colours.GetCount();
Vector3[] values = m_colours.GetPoints();
float[] weights = m_colours.GetWeights();
// get the covariance matrix
Sym3x3 covariance = math.ComputeWeightedCovariance(count, values, weights);
// compute the principle component
Vector3 principle = math.ComputePrincipleComponent(covariance);
// get the min and max range as the codebook endpoints
Vector3 start = Vector3.zero;
Vector3 end = Vector3.zero;
if (count > 0)
{
float min, max;
// compute the range
start = end = values[0];
min = max = Vector3.Dot(values[0], principle);
for (int i = 1; i < count; ++i)
{
float val = Vector3.Dot(values[i], principle);
if (val < min)
{
start = values[i];
min = val;
}
else if (val > max)
{
end = values[i];
max = val;
}
}
}
// clamp the output to [0, 1]
start = Vector3.Min(Vector3.one, Vector3.Max(Vector3.zero, start));
end = Vector3.Min(Vector3.one, Vector3.Max(Vector3.zero, end));
// clamp to the grid and save
Vector3 half = Vector3.one * (0.5f);
m_start = Vector3.Scale(math.Truncate(Vector3.Scale(grid, start) + half), gridrcp);
m_end = Vector3.Scale(math.Truncate(Vector3.Scale(grid, end) + half), gridrcp);
}
public static Vector3 ComputePrincipleComponent(Sym3x3 matrix)
{
// compute the cubic coefficients
float c0 = matrix[0] * matrix[3] * matrix[5]
+ 2.0f * matrix[1] * matrix[2] * matrix[4]
- matrix[0] * matrix[4] * matrix[4]
- matrix[3] * matrix[2] * matrix[2]
- matrix[5] * matrix[1] * matrix[1];
float c1 = matrix[0] * matrix[3] + matrix[0] * matrix[5] + matrix[3] * matrix[5]
- matrix[1] * matrix[1] - matrix[2] * matrix[2] - matrix[4] * matrix[4];
float c2 = matrix[0] + matrix[3] + matrix[5];
// compute the quadratic coefficients
float a = c1 - (1.0f / 3.0f) * c2 * c2;
float b = (-2.0f / 27.0f) * c2 * c2 * c2 + (1.0f / 3.0f) * c1 * c2 - c0;
// compute the root count check
float Q = 0.25f * b * b + (1.0f / 27.0f) * a * a * a;
// test the multiplicity
if (float.Epsilon < Q)
{
// only one root, which implies we have a multiple of the identity
return Vector3.one;
}
else if (Q < -float.Epsilon)
{
// three distinct roots
float theta = Mathf.Atan2(Mathf.Sqrt(-Q), -0.5f * b);
float rho = Mathf.Sqrt(0.25f * b * b - Q);
float rt = Mathf.Pow(rho, 1.0f / 3.0f);
float ct = Mathf.Cos(theta / 3.0f);
float st = Mathf.Sin(theta / 3.0f);
float l1 = (1.0f / 3.0f) * c2 + 2.0f * rt * ct;
float l2 = (1.0f / 3.0f) * c2 - rt * (ct + (float)Mathf.Sqrt(3.0f) * st);
float l3 = (1.0f / 3.0f) * c2 - rt * (ct - (float)Mathf.Sqrt(3.0f) * st);
// pick the larger
if (Mathf.Abs(l2) > Mathf.Abs(l1))
l1 = l2;
if (Mathf.Abs(l3) > Mathf.Abs(l1))
l1 = l3;
// get the eigenvector
return GetMultiplicity1Evector(matrix, l1);
}
else // if( -FLT_EPSILON <= Q && Q <= FLT_EPSILON )
{
// two roots
float rt;
if (b < 0.0f)
rt = -Mathf.Pow(-0.5f * b, 1.0f / 3.0f);
else
rt = Mathf.Pow(0.5f * b, 1.0f / 3.0f);
float l1 = (1.0f / 3.0f) * c2 + rt; // repeated
float l2 = (1.0f / 3.0f) * c2 - 2.0f * rt;
// get the eigenvector
if (Mathf.Abs(l1) > Mathf.Abs(l2))
return GetMultiplicity2Evector(matrix, l1);
else
return GetMultiplicity1Evector(matrix, l2);
}
}
public static Vector3 GetMultiplicity2Evector(Sym3x3 matrix, float evalue)
{
// compute M
Sym3x3 m = new Sym3x3();
m[0] = matrix[0] - evalue;
m[1] = matrix[1];
m[2] = matrix[2];
m[3] = matrix[3] - evalue;
m[4] = matrix[4];
m[5] = matrix[5] - evalue;
// find the largest component
float mc = Mathf.Abs(m[0]);
int mi = 0;
for (int i = 1; i < 6; ++i)
{
float c = Mathf.Abs(m[i]);
if (c > mc)
{
mc = c;
mi = i;
}
}
// pick the first eigenvector based on this index
switch (mi)
{
case 0:
case 1:
return new Vector3(-m[1], m[0], 0.0f);
case 2:
return new Vector3(m[2], 0.0f, -m[0]);
case 3:
case 4:
return new Vector3(0.0f, -m[4], m[3]);
default:
return new Vector3(0.0f, -m[5], m[4]);
}
}
public static Vector3 GetMultiplicity1Evector(Sym3x3 matrix, float evalue)
{
// compute M
Sym3x3 m = new Sym3x3();
m[0] = matrix[0] - evalue;
m[1] = matrix[1];
m[2] = matrix[2];
m[3] = matrix[3] - evalue;
m[4] = matrix[4];
m[5] = matrix[5] - evalue;
// compute U
Sym3x3 u = new Sym3x3();
u[0] = m[3] * m[5] - m[4] * m[4];
u[1] = m[2] * m[4] - m[1] * m[5];
u[2] = m[1] * m[4] - m[2] * m[3];
u[3] = m[0] * m[5] - m[2] * m[2];
u[4] = m[1] * m[2] - m[4] * m[0];
u[5] = m[0] * m[3] - m[1] * m[1];
// find the largest component
float mc = Mathf.Abs(u[0]);
int mi = 0;
for (int i = 1; i < 6; ++i)
{
float c = Mathf.Abs(u[i]);
if (c > mc)
{
mc = c;
mi = i;
}
}
// pick the column with this component
switch (mi)
{
case 0:
return new Vector3(u[0], u[1], u[2]);
case 1:
case 3:
return new Vector3(u[1], u[3], u[4]);
default:
return new Vector3(u[2], u[4], u[5]);
}
}
public static Sym3x3 ComputeWeightedCovariance(int n, Vector3[] points, float[] weights)
{
// compute the centroid
float total = 0.0f;
Vector3 centroid = Vector3.zero;
for (int i = 0; i < n; ++i)
{
total += weights[i];
centroid += weights[i] * points[i];
}
centroid /= total;
// accumulate the covariance matrix
Sym3x3 covariance = new Sym3x3();
for (int i = 0; i < n; ++i)
{
Vector3 a = points[i] - centroid;
Vector3 b = weights[i] * a;
covariance[0] += a.x * b.x;
covariance[1] += a.x * b.y;
covariance[2] += a.x * b.z;
covariance[3] += a.y * b.y;
covariance[4] += a.y * b.z;
covariance[5] += a.z * b.z;
}
// return it
return covariance;
}
public static Vector3 ComputePrincipleComponent(Sym3x3 matrix)
{
// compute the cubic coefficients
float c0 = matrix[0] * matrix[3] * matrix[5]
+ 2.0f * matrix[1] * matrix[2] * matrix[4]
- matrix[0] * matrix[4] * matrix[4]
- matrix[3] * matrix[2] * matrix[2]
- matrix[5] * matrix[1] * matrix[1];
float c1 = matrix[0] * matrix[3] + matrix[0] * matrix[5] + matrix[3] * matrix[5]
- matrix[1] * matrix[1] - matrix[2] * matrix[2] - matrix[4] * matrix[4];
float c2 = matrix[0] + matrix[3] + matrix[5];
// compute the quadratic coefficients
float a = c1 - (1.0f / 3.0f) * c2 * c2;
float b = (-2.0f / 27.0f) * c2 * c2 * c2 + (1.0f / 3.0f) * c1 * c2 - c0;
// compute the root count check
float Q = 0.25f * b * b + (1.0f / 27.0f) * a * a * a;
// test the multiplicity
if (float.Epsilon < Q)
{
// only one root, which implies we have a multiple of the identity
return(Vector3.one);
}
else if (Q < -float.Epsilon)
{
// three distinct roots
float theta = Mathf.Atan2(Mathf.Sqrt(-Q), -0.5f * b);
float rho = Mathf.Sqrt(0.25f * b * b - Q);
float rt = Mathf.Pow(rho, 1.0f / 3.0f);
float ct = Mathf.Cos(theta / 3.0f);
float st = Mathf.Sin(theta / 3.0f);
float l1 = (1.0f / 3.0f) * c2 + 2.0f * rt * ct;
float l2 = (1.0f / 3.0f) * c2 - rt * (ct + (float)Mathf.Sqrt(3.0f) * st);
float l3 = (1.0f / 3.0f) * c2 - rt * (ct - (float)Mathf.Sqrt(3.0f) * st);
// pick the larger
if (Mathf.Abs(l2) > Mathf.Abs(l1))
{
l1 = l2;
}
if (Mathf.Abs(l3) > Mathf.Abs(l1))
{
l1 = l3;
}
// get the eigenvector
return(GetMultiplicity1Evector(matrix, l1));
}
else // if( -FLT_EPSILON <= Q && Q <= FLT_EPSILON )
{
// two roots
float rt;
if (b < 0.0f)
{
rt = -Mathf.Pow(-0.5f * b, 1.0f / 3.0f);
}
else
{
rt = Mathf.Pow(0.5f * b, 1.0f / 3.0f);
}
float l1 = (1.0f / 3.0f) * c2 + rt; // repeated
float l2 = (1.0f / 3.0f) * c2 - 2.0f * rt;
// get the eigenvector
if (Mathf.Abs(l1) > Mathf.Abs(l2))
{
return(GetMultiplicity2Evector(matrix, l1));
}
else
{
return(GetMultiplicity1Evector(matrix, l2));
}
}
}
