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66 lines
3.2 KiB
C++
66 lines
3.2 KiB
C++
/*
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* Copyright (c) Contributors to the Open 3D Engine Project
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*
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* SPDX-License-Identifier: Apache-2.0 OR MIT
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*
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*/
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#pragma once
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namespace NumericalMethods
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{
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class VectorVariable;
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namespace Eigenanalysis
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{
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//! Compute the cross product between two 3D vectors.
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//! @param lhs The left-hand side vector.
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//! @param rhs The right-hand side vector.
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//! @return The 3D vector equal to the cross product if both input vectors are 3-dimensional.
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VectorVariable CrossProduct(const VectorVariable& lhs, const VectorVariable& rhs);
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//! Robustly computes a right-handed orthonormal basis containing a given unit-length 3D input vector.
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//! @param vecW[in] A 3D input vector which must be of unit length.
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//! @param vecU[out] The first of the computed unit-length orthogonal vectors.
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//! @param vecV[out] The second of the computed unit-length orthogonal vectors.
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//! @return {vecU, vecV, vecW} will be a right-handed orthogonal set.
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void ComputeOrthogonalComplement(const VectorVariable& vecW, VectorVariable& vecU, VectorVariable& vecV);
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//! Given elements of a symmetric 3x3 matrix and one of its eigenvalues, computes the corresponding eigenvector.
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//! For numerical stability, this function should only be used to find the eigenvector corresponding to
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//! eigenvalues that are unique and numerically not close to other eigenvalues.
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//! @param a<ij> The element of the matrix in row i, column j.
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//! @param val One of the eigenvalues of the matrix.
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//! @return The corresponding eigenvector.
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VectorVariable ComputeEigenvector0(
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double a00, double a01, double a02, double a11, double a12, double a22, double val
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);
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//! Given elements of a symmetric 3x3 matrix, one of its eigenvalues and an unrelated eigenvector, computes the
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//! eigenvector corresponding to the eigenvalue.
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//! This algorithm is numerically stable even if the eigenvalue is repeated.
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//! @param a<ij> The element of the matrix in row i, column j.
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//! @param val The eigenvalue whose corresponding eigenvector is to be found.
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//! @param vec The unrelated eigenvector that is already known.
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//! @return The eigenvector corresponding to the given eigenvalue.
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VectorVariable ComputeEigenvector1(
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double a00,
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double a01,
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double a02,
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double a11,
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double a12,
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double a22,
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double val,
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const VectorVariable& vec
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);
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// Given two eigenvectors of a symmetric 3x3 matrix, computes the third.
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// The third eigenvector is found by taking the cross product of the known eigenvectors (the eigenvectors of a
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// real symmetric 3x3 matrix are always orthogonal).
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//! @param vec0 The first of the already known eigenvectors.
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//! @param vec1 The second of the already known eigenvectors.
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//! @return The computed eigenvector.
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VectorVariable ComputeEigenvector2(const VectorVariable& vec0, const VectorVariable& vec1);
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} // namespace Eigenanalysis
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} // namespace NumericalMethods
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