0dd9a4a576
Is based on Google style which was used in the Libmv project before, but is now consistently applied for the sources of the library itself and to C-API. With some time C-API will likely be removed, and it makes it easier to make it follow Libmv style, hence the diversion from Blender's style. There are quite some exceptions (clang-format off) in the code around Eigen matrix initialization. It is rather annoying, and there could be some neat way to make initialization readable without such exception. Could be some places where loss of readability in matrix initialization got lost as the change is quite big. If this has happened it is easier to address readability once actually working on the code. This change allowed to spot some missing header guards, so that's nice. Doing it in bundled version, as the upstream library needs to have some of the recent development ported over from bundle to upstream. There should be no functional changes.
495 lines
16 KiB
C++
495 lines
16 KiB
C++
// Copyright (c) 2007, 2008_WIN32 libmv authors.
|
|
//
|
|
// Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
// of this software and associated documentation files (the "Software"), to
|
|
// deal in the Software without restriction, including without limitation the
|
|
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
|
// sell copies of the Software, and to permit persons to whom the Software is
|
|
// furnished to do so, subject to the following conditions:
|
|
//
|
|
// The above copyright notice and this permission notice shall be included in
|
|
// all copies or substantial portions of the Software.
|
|
//
|
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
|
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
|
// IN THE SOFTWARE.
|
|
//
|
|
// Matrix and vector classes, based on Eigen2.
|
|
//
|
|
// Avoid using Eigen2 classes directly; instead typedef them here.
|
|
|
|
#ifndef LIBMV_NUMERIC_NUMERIC_H
|
|
#define LIBMV_NUMERIC_NUMERIC_H
|
|
|
|
#include <Eigen/Cholesky>
|
|
#include <Eigen/Core>
|
|
#include <Eigen/Eigenvalues>
|
|
#include <Eigen/Geometry>
|
|
#include <Eigen/LU>
|
|
#include <Eigen/QR>
|
|
#include <Eigen/SVD>
|
|
|
|
#if !defined(__MINGW64__)
|
|
# if defined(_WIN32) || defined(__APPLE__) || defined(__FreeBSD__) || \
|
|
defined(__NetBSD__) || defined(__HAIKU__)
|
|
inline void sincos(double x, double* sinx, double* cosx) {
|
|
*sinx = sin(x);
|
|
*cosx = cos(x);
|
|
}
|
|
# endif
|
|
#endif // !__MINGW64__
|
|
|
|
#if (defined(WIN32) || defined(WIN64)) && !defined(__MINGW32__)
|
|
inline long lround(double d) {
|
|
return (long)(d > 0 ? d + 0.5 : ceil(d - 0.5));
|
|
}
|
|
# if _MSC_VER < 1800
|
|
inline int round(double d) {
|
|
return (d > 0) ? int(d + 0.5) : int(d - 0.5);
|
|
}
|
|
# endif // _MSC_VER < 1800
|
|
typedef unsigned int uint;
|
|
#endif // _WIN32
|
|
|
|
namespace libmv {
|
|
|
|
typedef Eigen::MatrixXd Mat;
|
|
typedef Eigen::VectorXd Vec;
|
|
|
|
typedef Eigen::MatrixXf Matf;
|
|
typedef Eigen::VectorXf Vecf;
|
|
|
|
typedef Eigen::Matrix<unsigned int, Eigen::Dynamic, Eigen::Dynamic> Matu;
|
|
typedef Eigen::Matrix<unsigned int, Eigen::Dynamic, 1> Vecu;
|
|
typedef Eigen::Matrix<unsigned int, 2, 1> Vec2u;
|
|
|
|
typedef Eigen::Matrix<double, 2, 2> Mat2;
|
|
typedef Eigen::Matrix<double, 2, 3> Mat23;
|
|
typedef Eigen::Matrix<double, 3, 3> Mat3;
|
|
typedef Eigen::Matrix<double, 3, 4> Mat34;
|
|
typedef Eigen::Matrix<double, 3, 5> Mat35;
|
|
typedef Eigen::Matrix<double, 4, 1> Mat41;
|
|
typedef Eigen::Matrix<double, 4, 3> Mat43;
|
|
typedef Eigen::Matrix<double, 4, 4> Mat4;
|
|
typedef Eigen::Matrix<double, 4, 6> Mat46;
|
|
typedef Eigen::Matrix<float, 2, 2> Mat2f;
|
|
typedef Eigen::Matrix<float, 2, 3> Mat23f;
|
|
typedef Eigen::Matrix<float, 3, 3> Mat3f;
|
|
typedef Eigen::Matrix<float, 3, 4> Mat34f;
|
|
typedef Eigen::Matrix<float, 3, 5> Mat35f;
|
|
typedef Eigen::Matrix<float, 4, 3> Mat43f;
|
|
typedef Eigen::Matrix<float, 4, 4> Mat4f;
|
|
typedef Eigen::Matrix<float, 4, 6> Mat46f;
|
|
|
|
typedef Eigen::Matrix<double, 3, 3, Eigen::RowMajor> RMat3;
|
|
typedef Eigen::Matrix<double, 4, 4, Eigen::RowMajor> RMat4;
|
|
|
|
typedef Eigen::Matrix<double, 2, Eigen::Dynamic> Mat2X;
|
|
typedef Eigen::Matrix<double, 3, Eigen::Dynamic> Mat3X;
|
|
typedef Eigen::Matrix<double, 4, Eigen::Dynamic> Mat4X;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 2> MatX2;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 3> MatX3;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 4> MatX4;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 5> MatX5;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 6> MatX6;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 7> MatX7;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 8> MatX8;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 9> MatX9;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 15> MatX15;
|
|
typedef Eigen::Matrix<double, Eigen::Dynamic, 16> MatX16;
|
|
|
|
typedef Eigen::Vector2d Vec2;
|
|
typedef Eigen::Vector3d Vec3;
|
|
typedef Eigen::Vector4d Vec4;
|
|
typedef Eigen::Matrix<double, 5, 1> Vec5;
|
|
typedef Eigen::Matrix<double, 6, 1> Vec6;
|
|
typedef Eigen::Matrix<double, 7, 1> Vec7;
|
|
typedef Eigen::Matrix<double, 8, 1> Vec8;
|
|
typedef Eigen::Matrix<double, 9, 1> Vec9;
|
|
typedef Eigen::Matrix<double, 10, 1> Vec10;
|
|
typedef Eigen::Matrix<double, 11, 1> Vec11;
|
|
typedef Eigen::Matrix<double, 12, 1> Vec12;
|
|
typedef Eigen::Matrix<double, 13, 1> Vec13;
|
|
typedef Eigen::Matrix<double, 14, 1> Vec14;
|
|
typedef Eigen::Matrix<double, 15, 1> Vec15;
|
|
typedef Eigen::Matrix<double, 16, 1> Vec16;
|
|
typedef Eigen::Matrix<double, 17, 1> Vec17;
|
|
typedef Eigen::Matrix<double, 18, 1> Vec18;
|
|
typedef Eigen::Matrix<double, 19, 1> Vec19;
|
|
typedef Eigen::Matrix<double, 20, 1> Vec20;
|
|
|
|
typedef Eigen::Vector2f Vec2f;
|
|
typedef Eigen::Vector3f Vec3f;
|
|
typedef Eigen::Vector4f Vec4f;
|
|
|
|
typedef Eigen::VectorXi VecXi;
|
|
|
|
typedef Eigen::Vector2i Vec2i;
|
|
typedef Eigen::Vector3i Vec3i;
|
|
typedef Eigen::Vector4i Vec4i;
|
|
|
|
typedef Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>
|
|
RMatf;
|
|
|
|
typedef Eigen::NumTraits<double> EigenDouble;
|
|
|
|
using Eigen::Dynamic;
|
|
using Eigen::Map;
|
|
using Eigen::Matrix;
|
|
|
|
// Find U, s, and VT such that
|
|
//
|
|
// A = U * diag(s) * VT
|
|
//
|
|
template <typename TMat, typename TVec>
|
|
inline void SVD(TMat* /*A*/, Vec* /*s*/, Mat* /*U*/, Mat* /*VT*/) {
|
|
assert(0);
|
|
}
|
|
|
|
// Solve the linear system Ax = 0 via SVD. Store the solution in x, such that
|
|
// ||x|| = 1.0. Return the singluar value corresponding to the solution.
|
|
// Destroys A and resizes x if necessary.
|
|
// TODO(maclean): Take the SVD of the transpose instead of this zero padding.
|
|
template <typename TMat, typename TVec>
|
|
double Nullspace(TMat* A, TVec* nullspace) {
|
|
Eigen::JacobiSVD<TMat> svd(*A, Eigen::ComputeFullV);
|
|
(*nullspace) = svd.matrixV().col(A->cols() - 1);
|
|
if (A->rows() >= A->cols())
|
|
return svd.singularValues()(A->cols() - 1);
|
|
else
|
|
return 0.0;
|
|
}
|
|
|
|
// Solve the linear system Ax = 0 via SVD. Finds two solutions, x1 and x2, such
|
|
// that x1 is the best solution and x2 is the next best solution (in the L2
|
|
// norm sense). Store the solution in x1 and x2, such that ||x|| = 1.0. Return
|
|
// the singluar value corresponding to the solution x1. Destroys A and resizes
|
|
// x if necessary.
|
|
template <typename TMat, typename TVec1, typename TVec2>
|
|
double Nullspace2(TMat* A, TVec1* x1, TVec2* x2) {
|
|
Eigen::JacobiSVD<TMat> svd(*A, Eigen::ComputeFullV);
|
|
*x1 = svd.matrixV().col(A->cols() - 1);
|
|
*x2 = svd.matrixV().col(A->cols() - 2);
|
|
if (A->rows() >= A->cols())
|
|
return svd.singularValues()(A->cols() - 1);
|
|
else
|
|
return 0.0;
|
|
}
|
|
|
|
// In place transpose for square matrices.
|
|
template <class TA>
|
|
inline void TransposeInPlace(TA* A) {
|
|
*A = A->transpose().eval();
|
|
}
|
|
|
|
template <typename TVec>
|
|
inline double NormL1(const TVec& x) {
|
|
return x.array().abs().sum();
|
|
}
|
|
|
|
template <typename TVec>
|
|
inline double NormL2(const TVec& x) {
|
|
return x.norm();
|
|
}
|
|
|
|
template <typename TVec>
|
|
inline double NormLInfinity(const TVec& x) {
|
|
return x.array().abs().maxCoeff();
|
|
}
|
|
|
|
template <typename TVec>
|
|
inline double DistanceL1(const TVec& x, const TVec& y) {
|
|
return (x - y).array().abs().sum();
|
|
}
|
|
|
|
template <typename TVec>
|
|
inline double DistanceL2(const TVec& x, const TVec& y) {
|
|
return (x - y).norm();
|
|
}
|
|
template <typename TVec>
|
|
inline double DistanceLInfinity(const TVec& x, const TVec& y) {
|
|
return (x - y).array().abs().maxCoeff();
|
|
}
|
|
|
|
// Normalize a vector with the L1 norm, and return the norm before it was
|
|
// normalized.
|
|
template <typename TVec>
|
|
inline double NormalizeL1(TVec* x) {
|
|
double norm = NormL1(*x);
|
|
*x /= norm;
|
|
return norm;
|
|
}
|
|
|
|
// Normalize a vector with the L2 norm, and return the norm before it was
|
|
// normalized.
|
|
template <typename TVec>
|
|
inline double NormalizeL2(TVec* x) {
|
|
double norm = NormL2(*x);
|
|
*x /= norm;
|
|
return norm;
|
|
}
|
|
|
|
// Normalize a vector with the L^Infinity norm, and return the norm before it
|
|
// was normalized.
|
|
template <typename TVec>
|
|
inline double NormalizeLInfinity(TVec* x) {
|
|
double norm = NormLInfinity(*x);
|
|
*x /= norm;
|
|
return norm;
|
|
}
|
|
|
|
// Return the square of a number.
|
|
template <typename T>
|
|
inline T Square(T x) {
|
|
return x * x;
|
|
}
|
|
|
|
Mat3 RotationAroundX(double angle);
|
|
Mat3 RotationAroundY(double angle);
|
|
Mat3 RotationAroundZ(double angle);
|
|
|
|
// Returns the rotation matrix of a rotation of angle |axis| around axis.
|
|
// This is computed using the Rodrigues formula, see:
|
|
// http://mathworld.wolfram.com/RodriguesRotationFormula.html
|
|
Mat3 RotationRodrigues(const Vec3& axis);
|
|
|
|
// Make a rotation matrix such that center becomes the direction of the
|
|
// positive z-axis, and y is oriented close to up.
|
|
Mat3 LookAt(Vec3 center);
|
|
|
|
// Return a diagonal matrix from a vector containg the diagonal values.
|
|
template <typename TVec>
|
|
inline Mat Diag(const TVec& x) {
|
|
return x.asDiagonal();
|
|
}
|
|
|
|
template <typename TMat>
|
|
inline double FrobeniusNorm(const TMat& A) {
|
|
return sqrt(A.array().abs2().sum());
|
|
}
|
|
|
|
template <typename TMat>
|
|
inline double FrobeniusDistance(const TMat& A, const TMat& B) {
|
|
return FrobeniusNorm(A - B);
|
|
}
|
|
|
|
inline Vec3 CrossProduct(const Vec3& x, const Vec3& y) {
|
|
return x.cross(y);
|
|
}
|
|
|
|
Mat3 CrossProductMatrix(const Vec3& x);
|
|
|
|
void MeanAndVarianceAlongRows(const Mat& A,
|
|
Vec* mean_pointer,
|
|
Vec* variance_pointer);
|
|
|
|
#if defined(_WIN32)
|
|
// TODO(bomboze): un-#if this for both platforms once tested under Windows
|
|
/* This solution was extensively discussed here
|
|
http://forum.kde.org/viewtopic.php?f=74&t=61940 */
|
|
# define SUM_OR_DYNAMIC(x, y) \
|
|
(x == Eigen::Dynamic || y == Eigen::Dynamic) ? Eigen::Dynamic : (x + y)
|
|
|
|
template <typename Derived1, typename Derived2>
|
|
struct hstack_return {
|
|
typedef typename Derived1::Scalar Scalar;
|
|
enum {
|
|
RowsAtCompileTime = Derived1::RowsAtCompileTime,
|
|
ColsAtCompileTime = SUM_OR_DYNAMIC(Derived1::ColsAtCompileTime,
|
|
Derived2::ColsAtCompileTime),
|
|
Options = Derived1::Flags & Eigen::RowMajorBit ? Eigen::RowMajor : 0,
|
|
MaxRowsAtCompileTime = Derived1::MaxRowsAtCompileTime,
|
|
MaxColsAtCompileTime = SUM_OR_DYNAMIC(Derived1::MaxColsAtCompileTime,
|
|
Derived2::MaxColsAtCompileTime)
|
|
};
|
|
typedef Eigen::Matrix<Scalar,
|
|
RowsAtCompileTime,
|
|
ColsAtCompileTime,
|
|
Options,
|
|
MaxRowsAtCompileTime,
|
|
MaxColsAtCompileTime>
|
|
type;
|
|
};
|
|
|
|
template <typename Derived1, typename Derived2>
|
|
typename hstack_return<Derived1, Derived2>::type HStack(
|
|
const Eigen::MatrixBase<Derived1>& lhs,
|
|
const Eigen::MatrixBase<Derived2>& rhs) {
|
|
typename hstack_return<Derived1, Derived2>::type res;
|
|
res.resize(lhs.rows(), lhs.cols() + rhs.cols());
|
|
res << lhs, rhs;
|
|
return res;
|
|
};
|
|
|
|
template <typename Derived1, typename Derived2>
|
|
struct vstack_return {
|
|
typedef typename Derived1::Scalar Scalar;
|
|
enum {
|
|
RowsAtCompileTime = SUM_OR_DYNAMIC(Derived1::RowsAtCompileTime,
|
|
Derived2::RowsAtCompileTime),
|
|
ColsAtCompileTime = Derived1::ColsAtCompileTime,
|
|
Options = Derived1::Flags & Eigen::RowMajorBit ? Eigen::RowMajor : 0,
|
|
MaxRowsAtCompileTime = SUM_OR_DYNAMIC(Derived1::MaxRowsAtCompileTime,
|
|
Derived2::MaxRowsAtCompileTime),
|
|
MaxColsAtCompileTime = Derived1::MaxColsAtCompileTime
|
|
};
|
|
typedef Eigen::Matrix<Scalar,
|
|
RowsAtCompileTime,
|
|
ColsAtCompileTime,
|
|
Options,
|
|
MaxRowsAtCompileTime,
|
|
MaxColsAtCompileTime>
|
|
type;
|
|
};
|
|
|
|
template <typename Derived1, typename Derived2>
|
|
typename vstack_return<Derived1, Derived2>::type VStack(
|
|
const Eigen::MatrixBase<Derived1>& lhs,
|
|
const Eigen::MatrixBase<Derived2>& rhs) {
|
|
typename vstack_return<Derived1, Derived2>::type res;
|
|
res.resize(lhs.rows() + rhs.rows(), lhs.cols());
|
|
res << lhs, rhs;
|
|
return res;
|
|
};
|
|
|
|
#else // _WIN32
|
|
|
|
// Since it is not possible to typedef privately here, use a macro.
|
|
// Always take dynamic columns if either side is dynamic.
|
|
# define COLS \
|
|
((ColsLeft == Eigen::Dynamic || ColsRight == Eigen::Dynamic) \
|
|
? Eigen::Dynamic \
|
|
: (ColsLeft + ColsRight))
|
|
|
|
// Same as above, except that prefer fixed size if either is fixed.
|
|
# define ROWS \
|
|
((RowsLeft == Eigen::Dynamic && RowsRight == Eigen::Dynamic) \
|
|
? Eigen::Dynamic \
|
|
: ((RowsLeft == Eigen::Dynamic) ? RowsRight : RowsLeft))
|
|
|
|
// TODO(keir): Add a static assert if both rows are at compiletime.
|
|
template <typename T, int RowsLeft, int RowsRight, int ColsLeft, int ColsRight>
|
|
Eigen::Matrix<T, ROWS, COLS> HStack(
|
|
const Eigen::Matrix<T, RowsLeft, ColsLeft>& left,
|
|
const Eigen::Matrix<T, RowsRight, ColsRight>& right) {
|
|
assert(left.rows() == right.rows());
|
|
int n = left.rows();
|
|
int m1 = left.cols();
|
|
int m2 = right.cols();
|
|
|
|
Eigen::Matrix<T, ROWS, COLS> stacked(n, m1 + m2);
|
|
stacked.block(0, 0, n, m1) = left;
|
|
stacked.block(0, m1, n, m2) = right;
|
|
return stacked;
|
|
}
|
|
|
|
// Reuse the above macros by swapping the order of Rows and Cols. Nasty, but
|
|
// the duplication is worse.
|
|
// TODO(keir): Add a static assert if both rows are at compiletime.
|
|
// TODO(keir): Mail eigen list about making this work for general expressions
|
|
// rather than only matrix types.
|
|
template <typename T, int RowsLeft, int RowsRight, int ColsLeft, int ColsRight>
|
|
Eigen::Matrix<T, COLS, ROWS> VStack(
|
|
const Eigen::Matrix<T, ColsLeft, RowsLeft>& top,
|
|
const Eigen::Matrix<T, ColsRight, RowsRight>& bottom) {
|
|
assert(top.cols() == bottom.cols());
|
|
int n1 = top.rows();
|
|
int n2 = bottom.rows();
|
|
int m = top.cols();
|
|
|
|
Eigen::Matrix<T, COLS, ROWS> stacked(n1 + n2, m);
|
|
stacked.block(0, 0, n1, m) = top;
|
|
stacked.block(n1, 0, n2, m) = bottom;
|
|
return stacked;
|
|
}
|
|
# undef COLS
|
|
# undef ROWS
|
|
#endif // _WIN32
|
|
|
|
void HorizontalStack(const Mat& left, const Mat& right, Mat* stacked);
|
|
|
|
template <typename TTop, typename TBot, typename TStacked>
|
|
void VerticalStack(const TTop& top, const TBot& bottom, TStacked* stacked) {
|
|
assert(top.cols() == bottom.cols());
|
|
int n1 = top.rows();
|
|
int n2 = bottom.rows();
|
|
int m = top.cols();
|
|
|
|
stacked->resize(n1 + n2, m);
|
|
stacked->block(0, 0, n1, m) = top;
|
|
stacked->block(n1, 0, n2, m) = bottom;
|
|
}
|
|
|
|
void MatrixColumn(const Mat& A, int i, Vec2* v);
|
|
void MatrixColumn(const Mat& A, int i, Vec3* v);
|
|
void MatrixColumn(const Mat& A, int i, Vec4* v);
|
|
|
|
template <typename TMat, typename TCols>
|
|
TMat ExtractColumns(const TMat& A, const TCols& columns) {
|
|
TMat compressed(A.rows(), columns.size());
|
|
for (int i = 0; i < columns.size(); ++i) {
|
|
compressed.col(i) = A.col(columns[i]);
|
|
}
|
|
return compressed;
|
|
}
|
|
|
|
template <typename TMat, typename TDest>
|
|
void reshape(const TMat& a, int rows, int cols, TDest* b) {
|
|
assert(a.rows() * a.cols() == rows * cols);
|
|
b->resize(rows, cols);
|
|
for (int i = 0; i < rows; i++) {
|
|
for (int j = 0; j < cols; j++) {
|
|
(*b)(i, j) = a[cols * i + j];
|
|
}
|
|
}
|
|
}
|
|
|
|
inline bool isnan(double i) {
|
|
#ifdef WIN32
|
|
return _isnan(i) > 0;
|
|
#else
|
|
return std::isnan(i);
|
|
#endif
|
|
}
|
|
|
|
/// Ceil function that has the same behavior for positive
|
|
/// and negative values
|
|
template <typename FloatType>
|
|
FloatType ceil0(const FloatType& value) {
|
|
FloatType result = std::ceil(std::fabs(value));
|
|
return (value < 0.0) ? -result : result;
|
|
}
|
|
|
|
/// Returns the skew anti-symmetric matrix of a vector
|
|
inline Mat3 SkewMat(const Vec3& x) {
|
|
Mat3 skew;
|
|
skew << 0, -x(2), x(1), x(2), 0, -x(0), -x(1), x(0), 0;
|
|
return skew;
|
|
}
|
|
/// Returns the skew anti-symmetric matrix of a vector with only
|
|
/// the first two (independent) lines
|
|
inline Mat23 SkewMatMinimal(const Vec2& x) {
|
|
Mat23 skew;
|
|
skew << 0, -1, x(1), 1, 0, -x(0);
|
|
return skew;
|
|
}
|
|
|
|
/// Returns the rotaiton matrix built from given vector of euler angles
|
|
inline Mat3 RotationFromEulerVector(Vec3 euler_vector) {
|
|
double theta = euler_vector.norm();
|
|
if (theta == 0.0) {
|
|
return Mat3::Identity();
|
|
}
|
|
Vec3 w = euler_vector / theta;
|
|
Mat3 w_hat = CrossProductMatrix(w);
|
|
return Mat3::Identity() + w_hat * sin(theta) +
|
|
w_hat * w_hat * (1 - cos(theta));
|
|
}
|
|
} // namespace libmv
|
|
|
|
#endif // LIBMV_NUMERIC_NUMERIC_H
|