11#pragma warning(disable: 4804)
12#pragma warning(disable: 4146)
36 static constexpr Matrix3 scale( T s )
noexcept {
return Matrix3( { s, T(0), T(0) }, { T(0), s, T(0) }, { T(0), T(0), s } ); }
38 static constexpr Matrix3 scale( T sx, T sy, T sz )
noexcept {
return Matrix3( { sx, T(0), T(0) }, { T(0), sy, T(0) }, { T(0), T(0), sz } ); }
63 constexpr T
trace() const noexcept {
return x.x +
y.y +
z.z; }
65 constexpr T
normSq() const noexcept {
return x.lengthSq() +
y.lengthSq() +
z.lengthSq(); }
66 constexpr auto norm() const noexcept
74 constexpr T
det() const noexcept;
89 [[nodiscard]] friend constexpr
bool operator ==( const
Matrix3<T> & a, const
Matrix3<T> & b ) {
return a.x == b.x && a.y == b.y && a.z == b.z; }
100 if constexpr ( std::is_integral_v<T> )
101 return { b.x / a, b.y / a, b.z / a };
103 return b * ( 1 / a );
111 if constexpr ( std::is_integral_v<T> )
112 { a.
x /= b; a.y /= b; a.z /= b;
return a; }
114 return a *= ( 1 / b );
120 return {
dot( a.x, b ),
dot( a.y, b ),
dot( a.z, b ) };
127 for (
int i = 0; i < 3; ++i )
128 for (
int j = 0; j < 3; ++j )
129 res[i][j] =
dot( a[i], b.col(j) );
141 return dot( a.x, b.x ) + dot( a.y, b.y ) + dot( a.z, b.z );
148 return { a.
x * b, a.
y * b, a.
z * b };
155 auto u = axis.normalized();
160 { c + u.x * u.x * oc, u.x * u.y * oc - u.z * s, u.x * u.z * oc + u.y * s },
161 { u.y * u.x * oc + u.z * s, c + u.y * u.y * oc, u.y * u.z * oc - u.x * s },
162 { u.z * u.x * oc - u.y * s, u.z * u.y * oc + u.x * s, c + u.z * u.z * oc }
169 auto axis =
cross( from, to );
170 if ( axis.lengthSq() > 0 )
171 return rotation( axis,
angle( from, to ) );
172 if (
dot( from, to ) >= 0 )
174 return rotation(
cross( from, from.furthestBasisVector() ), T( PI ) );
181 const auto cx = std::cos( eulerAngles.x );
182 const auto cy = std::cos( eulerAngles.y );
183 const auto cz = std::cos( eulerAngles.z );
184 const auto sx = std::sin( eulerAngles.x );
185 const auto sy = std::sin( eulerAngles.y );
186 const auto sz = std::sin( eulerAngles.z );
188 { cy * cz, cz * sx * sy - cx * sz, cx * cz * sy + sx * sz },
189 { cy * sz, cx * cz + sx * sy * sz, -cz * sx + cx * sy * sz },
190 { -sy, cy * sx, cx * cy }
197 const auto alpha = eulerAngles.
x;
198 const auto beta = eulerAngles.y;
199 const auto gamma = eulerAngles.z;
201 { T(1), -gamma, beta },
202 { gamma, T(1), -alpha },
203 { -beta, alpha, T(1) }
211 x.x * ( y.y * z.z - y.z * z.y )
212 - x.y * ( y.x * z.z - y.z * z.x )
213 + x.z * ( y.x * z.y - y.y * z.x );
219 auto det = this->det();
224 { y.y * z.z - y.z * z.y, x.z * z.y - x.y * z.z, x.y * y.z - x.z * y.y },
225 { y.z * z.x - y.x * z.z, x.x * z.z - x.z * z.x, x.z * y.x - x.x * y.z },
226 { y.x * z.y - y.y * z.x, x.y * z.x - x.x * z.y, x.x * y.y - x.y * y.x }
246 std::atan2( z.y, z.z ),
247 std::atan2( -z.x, std::sqrt( z.y * z.y + z.z * z.z ) ),
248 std::atan2( y.x, x.x )
256 const auto a0 = col( 0 );
259 const auto r00 = a0.length();
260 const auto e0 = r00 > 0 ? a0 / r00 :
Vector3<T>{};
261 const auto r01 =
dot( e0, a1 );
262 const auto r02 =
dot( e0, a2 );
264 const auto r11 = a1.length();
265 const auto e1 = r11 > 0 ? a1 / r11 :
Vector3<T>{};
266 const auto r12 =
dot( e1, a2 );
267 a2 -= r02 * e0 + r12 * e1;
268 const auto r22 = a2.length();
269 const auto e2 = r22 > 0 ? a2 / r22 :
Vector3<T>{};
#define MR_REQUIRES_IF_SUPPORTED(...)
Definition MRMacros.h:31
MRMESH_CLASS Vector3
Definition MRMesh/MRMeshFwd.h:170
int dot(Vector2i a, Vector2i b)
Vector3f cross(Vector3f a, Vector3f b)
Definition MRMesh/MRMatrix3.h:83
Matrix3 q
Definition MRMesh/MRMatrix3.h:84
Definition MRMesh/MRMatrix3.h:19
static constexpr Matrix3 scale(T sx, T sy, T sz) noexcept
returns a matrix that has its own scale along each axis
Definition MRMesh/MRMatrix3.h:38
Matrix3< T > outer(const Vector3< T > &a, const Vector3< T > &b)
x = a * b^T
Definition MRMesh/MRMatrix3.h:146
T ValueType
Definition MRMesh/MRMatrix3.h:20
static constexpr Matrix3 fromRows(const Vector3< T > &x, const Vector3< T > &y, const Vector3< T > &z) noexcept
constructs a matrix from its 3 rows
Definition MRMesh/MRMatrix3.h:50
static constexpr Matrix3 identity() noexcept
Definition MRMesh/MRMatrix3.h:34
friend constexpr auto operator*(T a, const Matrix3< T > &b) -> Matrix3< decltype(std::declval< T >() *std::declval< T >())>
Definition MRMesh/MRMatrix3.h:96
constexpr Matrix3< T > transposed() const noexcept
computes transposed matrix
constexpr T det() const noexcept
computes determinant of the matrix
static constexpr Matrix3 rotationFromEuler(const Vector3< T > &eulerAngles) noexcept
Vector3< T > x
rows, identity matrix by default
Definition MRMesh/MRMatrix3.h:24
constexpr const Vector3< T > & operator[](int row) const noexcept
row access
Definition MRMesh/MRMatrix3.h:56
friend constexpr Matrix3< T > & operator-=(Matrix3< T > &a, const Matrix3< T > &b)
Definition MRMesh/MRMatrix3.h:107
constexpr Matrix3< T > inverse() const noexcept
computes inverse matrix
constexpr T normSq() const noexcept
compute sum of squared matrix elements
Definition MRMesh/MRMatrix3.h:65
friend constexpr Matrix3< T > & operator*=(Matrix3< T > &a, T b)
Definition MRMesh/MRMatrix3.h:108
static constexpr Matrix3 rotation(const Vector3< T > &axis, T angle) noexcept
creates matrix representing rotation around given axis on given angle
friend constexpr Matrix3< T > & operator+=(Matrix3< T > &a, const Matrix3< T > &b)
Definition MRMesh/MRMatrix3.h:106
constexpr auto norm() const noexcept
Definition MRMesh/MRMatrix3.h:66
constexpr Vector3< T > toEulerAngles() const noexcept
returns 3 Euler angles, assuming this is a rotation matrix composed as follows: R=R(z)*R(y)*R(x)
constexpr Vector3< T > col(int i) const noexcept
column access
Definition MRMesh/MRMatrix3.h:60
static constexpr Matrix3 rotation(const Vector3< T > &from, const Vector3< T > &to) noexcept
creates matrix representing rotation that after application to (from) makes (to) vector
static constexpr Matrix3 scale(T s) noexcept
returns a matrix that scales uniformly
Definition MRMesh/MRMatrix3.h:36
constexpr T trace() const noexcept
computes trace of the matrix
Definition MRMesh/MRMatrix3.h:63
friend constexpr bool operator!=(const Matrix3< T > &a, const Matrix3< T > &b)
Definition MRMesh/MRMatrix3.h:90
static constexpr Matrix3 fromColumns(const Vector3< T > &x, const Vector3< T > &y, const Vector3< T > &z) noexcept
Definition MRMesh/MRMatrix3.h:53
Vector3< T > y
Definition MRMesh/MRMatrix3.h:25
static constexpr Matrix3 zero() noexcept
Definition MRMesh/MRMatrix3.h:33
auto dot(const Matrix3< T > &a, const Matrix3< T > &b) -> decltype(dot(a.x, b.x))
double-dot product: x = a : b
Definition MRMesh/MRMatrix3.h:139
friend constexpr auto operator-(const Matrix3< T > &a, const Matrix3< T > &b) -> Matrix3< decltype(std::declval< T >() - std::declval< T >())>
Definition MRMesh/MRMatrix3.h:95
QR qr() const noexcept
decompose this matrix on the product Q*R, where Q is orthogonal and R is upper triangular
friend constexpr auto operator+(const Matrix3< T > &a, const Matrix3< T > &b) -> Matrix3< decltype(std::declval< T >()+std::declval< T >())>
Definition MRMesh/MRMatrix3.h:94
constexpr Matrix3(const Matrix3< U > &m)
Definition MRMesh/MRMatrix3.h:32
friend constexpr auto operator/(Matrix3< T > b, T a) -> Matrix3< decltype(std::declval< T >()/std::declval< T >())>
Definition MRMesh/MRMatrix3.h:98
Vector3< T > z
Definition MRMesh/MRMatrix3.h:26
friend constexpr Matrix3< T > & operator/=(Matrix3< T > &a, T b)
Definition MRMesh/MRMatrix3.h:109
static constexpr Matrix3 approximateLinearRotationMatrixFromEuler(const Vector3< T > &eulerAngles) noexcept
returns linear by angles approximation of the rotation matrix, which is close to true rotation matrix...
constexpr Matrix3() noexcept=default
static constexpr Matrix3 scale(const Vector3< T > &s) noexcept
Definition MRMesh/MRMatrix3.h:39
Definition MRMesh/MRVector3.h:26
T x
Definition MRMesh/MRVector3.h:32
T y
Definition MRMesh/MRVector3.h:32
T z
Definition MRMesh/MRVector3.h:32