// 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/ApprQuery.h> #include <Mathematics/OrientedBox.h> #include <Mathematics/SymmetricEigensolver2x2.h> #include <Mathematics/Vector2.h> // Fit points with a Gaussian distribution. The center is the mean of the // points, the axes are the eigenvectors of the covariance matrix and the // extents are the eigenvalues of the covariance matrix and are returned in // increasing order. An oriented box is used to store the mean, axes and // extents. namespace WwiseGTE { template <typename Real> class ApprGaussian2 : public ApprQuery<Real, Vector2<Real>> { public: // Initialize the model parameters to zero. ApprGaussian2() { mParameters.center = Vector2<Real>::Zero(); mParameters.axis[0] = Vector2<Real>::Zero(); mParameters.axis[1] = Vector2<Real>::Zero(); mParameters.extent = Vector2<Real>::Zero(); } // Basic fitting algorithm. See ApprQuery.h for the various Fit(...) // functions that you can call. virtual bool FitIndexed( size_t numPoints, Vector2<Real> const* points, size_t numIndices, int const* indices) override { if (this->ValidIndices(numPoints, points, numIndices, indices)) { // Compute the mean of the points. Vector2<Real> mean = Vector2<Real>::Zero(); int const* currentIndex = indices; for (size_t i = 0; i < numIndices; ++i) { mean += points[*currentIndex++]; } Real invSize = (Real)1 / (Real)numIndices; mean *= invSize; if (std::isfinite(mean[0]) && std::isfinite(mean[1])) { // Compute the covariance matrix of the points. Real covar00 = (Real)0, covar01 = (Real)0, covar11 = (Real)0; currentIndex = indices; for (size_t i = 0; i < numIndices; ++i) { Vector2<Real> diff = points[*currentIndex++] - mean; covar00 += diff[0] * diff[0]; covar01 += diff[0] * diff[1]; covar11 += diff[1] * diff[1]; } covar00 *= invSize; covar01 *= invSize; covar11 *= invSize; // Solve the eigensystem. SymmetricEigensolver2x2<Real> es; std::array<Real, 2> eval; std::array<std::array<Real, 2>, 2> evec; es(covar00, covar01, covar11, +1, eval, evec); mParameters.center = mean; mParameters.axis[0] = evec[0]; mParameters.axis[1] = evec[1]; mParameters.extent = eval; return true; } } mParameters.center = Vector2<Real>::Zero(); mParameters.axis[0] = Vector2<Real>::Zero(); mParameters.axis[1] = Vector2<Real>::Zero(); mParameters.extent = Vector2<Real>::Zero(); return false; } // Get the parameters for the best fit. OrientedBox2<Real> const& GetParameters() const { return mParameters; } virtual size_t GetMinimumRequired() const override { return 2; } virtual Real Error(Vector2<Real> const& point) const override { Vector2<Real> diff = point - mParameters.center; Real error = (Real)0; for (int i = 0; i < 2; ++i) { if (mParameters.extent[i] > (Real)0) { Real ratio = Dot(diff, mParameters.axis[i]) / mParameters.extent[i]; error += ratio * ratio; } } return error; } virtual void CopyParameters(ApprQuery<Real, Vector2<Real>> const* input) override { auto source = dynamic_cast<ApprGaussian2 const*>(input); if (source) { *this = *source; } } private: OrientedBox2<Real> mParameters; }; }