// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2020
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2019.08.13
#pragma once
#include <Mathematics/BasisFunction.h>
#include <Mathematics/BandedMatrix.h>
// The algorithm implemented here is based on the document
// https://www.geometrictools.com/Documentation/BSplineCurveLeastSquaresFit.pdf
namespace WwiseGTE
{
template <typename Real>
class BSplineCurveFit
{
public:
// Construction. The preconditions for calling the constructor are
// 1 <= degree && degree < numControls <= numSamples
// The samples points are contiguous blocks of 'dimension' real values
// stored in sampleData.
BSplineCurveFit(int dimension, int numSamples, Real const* sampleData,
int degree, int numControls)
:
mDimension(dimension),
mNumSamples(numSamples),
mSampleData(sampleData),
mDegree(degree),
mNumControls(numControls),
mControlData(dimension * numControls)
{
LogAssert(dimension >= 1, "Invalid dimension.");
LogAssert(1 <= degree && degree < numControls, "Invalid degree.");
LogAssert(sampleData, "Invalid sample data.");
LogAssert(numControls <= numSamples, "Invalid number of controls.");
BasisFunctionInput<Real> input;
input.numControls = numControls;
input.degree = degree;
input.uniform = true;
input.periodic = false;
input.numUniqueKnots = numControls - degree + 1;
input.uniqueKnots.resize(input.numUniqueKnots);
input.uniqueKnots[0].t = (Real)0;
input.uniqueKnots[0].multiplicity = degree + 1;
int last = input.numUniqueKnots - 1;
Real factor = ((Real)1) / (Real)last;
for (int i = 1; i < last; ++i)
{
input.uniqueKnots[i].t = factor * (Real)i;
input.uniqueKnots[i].multiplicity = 1;
}
input.uniqueKnots[last].t = (Real)1;
input.uniqueKnots[last].multiplicity = degree + 1;
mBasis.Create(input);
// Fit the data points with a B-spline curve using a least-squares
// error metric. The problem is of the form A^T*A*Q = A^T*P,
// where A^T*A is a banded matrix, P contains the sample data, and
// Q is the unknown vector of control points.
Real tMultiplier = ((Real)1) / (Real)(mNumSamples - 1);
Real t;
int i0, i1, i2, imin, imax, j;
// Construct the matrix A^T*A.
int degp1 = mDegree + 1;
int numBands = (mNumControls > degp1 ? degp1 : mDegree);
BandedMatrix<Real> ATAMat(mNumControls, numBands, numBands);
for (i0 = 0; i0 < mNumControls; ++i0)
{
for (i1 = 0; i1 < i0; ++i1)
{
ATAMat(i0, i1) = ATAMat(i1, i0);
}
int i1Max = i0 + mDegree;
if (i1Max >= mNumControls)
{
i1Max = mNumControls - 1;
}
for (i1 = i0; i1 <= i1Max; ++i1)
{
Real value = (Real)0;
for (i2 = 0; i2 < mNumSamples; ++i2)
{
t = tMultiplier * (Real)i2;
mBasis.Evaluate(t, 0, imin, imax);
if (imin <= i0 && i0 <= imax && imin <= i1 && i1 <= imax)
{
Real b0 = mBasis.GetValue(0, i0);
Real b1 = mBasis.GetValue(0, i1);
value += b0 * b1;
}
}
ATAMat(i0, i1) = value;
}
}
// Construct the matrix A^T.
Array2<Real> ATMat(mNumSamples, mNumControls);
std::memset(ATMat[0], 0, mNumControls * mNumSamples * sizeof(Real));
for (i0 = 0; i0 < mNumControls; ++i0)
{
for (i1 = 0; i1 < mNumSamples; ++i1)
{
t = tMultiplier * (Real)i1;
mBasis.Evaluate(t, 0, imin, imax);
if (imin <= i0 && i0 <= imax)
{
ATMat[i0][i1] = mBasis.GetValue(0, i0);
}
}
}
// Compute X0 = (A^T*A)^{-1}*A^T by solving the linear system
// A^T*A*X = A^T.
bool solved = ATAMat.template SolveSystem<true>(ATMat[0], mNumSamples);
LogAssert(solved, "Failed to solve linear system.");
// The control points for the fitted curve are stored in the
// vector Q = X0*P, where P is the vector of sample data.
std::fill(mControlData.begin(), mControlData.end(), (Real)0);
for (i0 = 0; i0 < mNumControls; ++i0)
{
Real* Q = &mControlData[i0 * mDimension];
for (i1 = 0; i1 < mNumSamples; ++i1)
{
Real const* P = mSampleData + i1 * mDimension;
Real xValue = ATMat[i0][i1];
for (j = 0; j < mDimension; ++j)
{
Q[j] += xValue * P[j];
}
}
}
// Set the first and last output control points to match the first
// and last input samples. This supports the application of
// fitting keyframe data with B-spline curves. The user expects
// that the curve passes through the first and last positions in
// order to support matching two consecutive keyframe sequences.
Real* cEnd0 = &mControlData[0];
Real const* sEnd0 = mSampleData;
Real* cEnd1 = &mControlData[mDimension * (mNumControls - 1)];
Real const* sEnd1 = &mSampleData[mDimension * (mNumSamples - 1)];
for (j = 0; j < mDimension; ++j)
{
*cEnd0++ = *sEnd0++;
*cEnd1++ = *sEnd1++;
}
}
// Access to input sample information.
inline int GetDimension() const
{
return mDimension;
}
inline int GetNumSamples() const
{
return mNumSamples;
}
inline Real const* GetSampleData() const
{
return mSampleData;
}
// Access to output control point and curve information.
inline int GetDegree() const
{
return mDegree;
}
inline int GetNumControls() const
{
return mNumControls;
}
inline Real const* GetControlData() const
{
return &mControlData[0];
}
inline BasisFunction<Real> const& GetBasis() const
{
return mBasis;
}
// Evaluation of the B-spline curve. It is defined for 0 <= t <= 1.
// If a t-value is outside [0,1], an open spline clamps it to [0,1].
// The caller must ensure that position[] has at least 'dimension'
// elements.
void Evaluate(Real t, unsigned int order, Real* value) const
{
int imin, imax;
mBasis.Evaluate(t, order, imin, imax);
Real const* source = &mControlData[mDimension * imin];
Real basisValue = mBasis.GetValue(order, imin);
for (int j = 0; j < mDimension; ++j)
{
value[j] = basisValue * (*source++);
}
for (int i = imin + 1; i <= imax; ++i)
{
basisValue = mBasis.GetValue(order, i);
for (int j = 0; j < mDimension; ++j)
{
value[j] += basisValue * (*source++);
}
}
}
void GetPosition(Real t, Real* position) const
{
Evaluate(t, 0, position);
}
private:
// Input sample information.
int mDimension;
int mNumSamples;
Real const* mSampleData;
// The fitted B-spline curve, open and with uniform knots.
int mDegree;
int mNumControls;
std::vector<Real> mControlData;
BasisFunction<Real> mBasis;
};
}