/* * matrix3.cpp * Copyright (C) Andrew Tridgell 2012 * * This file is free software: you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This file is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * See the GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program. If not, see <http://www.gnu.org/licenses/>. */ #pragma GCC optimize("O2") #include "AP_Math.h" // create a rotation matrix given some euler angles // this is based on http://gentlenav.googlecode.com/files/EulerAngles.pdf template <typename T> void Matrix3<T>::from_euler(float roll, float pitch, float yaw) { const float cp = cosf(pitch); const float sp = sinf(pitch); const float sr = sinf(roll); const float cr = cosf(roll); const float sy = sinf(yaw); const float cy = cosf(yaw); a.x = cp * cy; a.y = (sr * sp * cy) - (cr * sy); a.z = (cr * sp * cy) + (sr * sy); b.x = cp * sy; b.y = (sr * sp * sy) + (cr * cy); b.z = (cr * sp * sy) - (sr * cy); c.x = -sp; c.y = sr * cp; c.z = cr * cp; } // calculate euler angles from a rotation matrix // this is based on http://gentlenav.googlecode.com/files/EulerAngles.pdf template <typename T> void Matrix3<T>::to_euler(float *roll, float *pitch, float *yaw) const { if (pitch != nullptr) { *pitch = -safe_asin(c.x); } if (roll != nullptr) { *roll = atan2f(c.y, c.z); } if (yaw != nullptr) { *yaw = atan2f(b.x, a.x); } } template <typename T> void Matrix3<T>::from_rotation(enum Rotation rotation) { (*this).a(1,0,0); (*this).b(0,1,0); (*this).c(0,0,1); (*this).a.rotate(rotation); (*this).b.rotate(rotation); (*this).c.rotate(rotation); (*this).transpose(); } /* calculate Euler angles (312 convention) for the matrix. See http://www.atacolorado.com/eulersequences.doc vector is returned in r, p, y order */ template <typename T> Vector3<T> Matrix3<T>::to_euler312() const { return Vector3<T>(asinf(c.y), atan2f(-c.x, c.z), atan2f(-a.y, b.y)); } /* fill the matrix from Euler angles in radians in 312 convention */ template <typename T> void Matrix3<T>::from_euler312(float roll, float pitch, float yaw) { const float c3 = cosf(pitch); const float s3 = sinf(pitch); const float s2 = sinf(roll); const float c2 = cosf(roll); const float s1 = sinf(yaw); const float c1 = cosf(yaw); a.x = c1 * c3 - s1 * s2 * s3; b.y = c1 * c2; c.z = c3 * c2; a.y = -c2*s1; a.z = s3*c1 + c3*s2*s1; b.x = c3*s1 + s3*s2*c1; b.z = s1*s3 - s2*c1*c3; c.x = -s3*c2; c.y = s2; } // apply an additional rotation from a body frame gyro vector // to a rotation matrix. template <typename T> void Matrix3<T>::rotate(const Vector3<T> &g) { (*this) += Matrix3<T>{ a.y * g.z - a.z * g.y, a.z * g.x - a.x * g.z, a.x * g.y - a.y * g.x, b.y * g.z - b.z * g.y, b.z * g.x - b.x * g.z, b.x * g.y - b.y * g.x, c.y * g.z - c.z * g.y, c.z * g.x - c.x * g.z, c.x * g.y - c.y * g.x }; } /* re-normalise a rotation matrix */ template <typename T> void Matrix3<T>::normalize(void) { const float error = a * b; const Vector3<T> t0 = a - (b * (0.5f * error)); const Vector3<T> t1 = b - (a * (0.5f * error)); const Vector3<T> t2 = t0 % t1; a = t0 * (1.0f / t0.length()); b = t1 * (1.0f / t1.length()); c = t2 * (1.0f / t2.length()); } // multiplication by a vector template <typename T> Vector3<T> Matrix3<T>::operator *(const Vector3<T> &v) const { return Vector3<T>(a.x * v.x + a.y * v.y + a.z * v.z, b.x * v.x + b.y * v.y + b.z * v.z, c.x * v.x + c.y * v.y + c.z * v.z); } // multiplication by a vector, extracting only the xy components template <typename T> Vector2<T> Matrix3<T>::mulXY(const Vector3<T> &v) const { return Vector2<T>(a.x * v.x + a.y * v.y + a.z * v.z, b.x * v.x + b.y * v.y + b.z * v.z); } // multiplication of transpose by a vector template <typename T> Vector3<T> Matrix3<T>::mul_transpose(const Vector3<T> &v) const { return Vector3<T>(a.x * v.x + b.x * v.y + c.x * v.z, a.y * v.x + b.y * v.y + c.y * v.z, a.z * v.x + b.z * v.y + c.z * v.z); } // multiplication by another Matrix3<T> template <typename T> Matrix3<T> Matrix3<T>::operator *(const Matrix3<T> &m) const { Matrix3<T> temp (Vector3<T>(a.x * m.a.x + a.y * m.b.x + a.z * m.c.x, a.x * m.a.y + a.y * m.b.y + a.z * m.c.y, a.x * m.a.z + a.y * m.b.z + a.z * m.c.z), Vector3<T>(b.x * m.a.x + b.y * m.b.x + b.z * m.c.x, b.x * m.a.y + b.y * m.b.y + b.z * m.c.y, b.x * m.a.z + b.y * m.b.z + b.z * m.c.z), Vector3<T>(c.x * m.a.x + c.y * m.b.x + c.z * m.c.x, c.x * m.a.y + c.y * m.b.y + c.z * m.c.y, c.x * m.a.z + c.y * m.b.z + c.z * m.c.z)); return temp; } template <typename T> Matrix3<T> Matrix3<T>::transposed(void) const { return Matrix3<T>(Vector3<T>(a.x, b.x, c.x), Vector3<T>(a.y, b.y, c.y), Vector3<T>(a.z, b.z, c.z)); } template <typename T> T Matrix3<T>::det() const { return a.x * (b.y * c.z - b.z * c.y) + a.y * (b.z * c.x - b.x * c.z) + a.z * (b.x * c.y - b.y * c.x); } template <typename T> bool Matrix3<T>::inverse(Matrix3<T>& inv) const { const T d = det(); if (is_zero(d)) { return false; } inv.a.x = (b.y * c.z - c.y * b.z) / d; inv.a.y = (a.z * c.y - a.y * c.z) / d; inv.a.z = (a.y * b.z - a.z * b.y) / d; inv.b.x = (b.z * c.x - b.x * c.z) / d; inv.b.y = (a.x * c.z - a.z * c.x) / d; inv.b.z = (b.x * a.z - a.x * b.z) / d; inv.c.x = (b.x * c.y - c.x * b.y) / d; inv.c.y = (c.x * a.y - a.x * c.y) / d; inv.c.z = (a.x * b.y - b.x * a.y) / d; return true; } template <typename T> bool Matrix3<T>::invert() { Matrix3<T> inv; bool success = inverse(inv); if (success) { *this = inv; } return success; } template <typename T> void Matrix3<T>::zero(void) { a.x = a.y = a.z = 0; b.x = b.y = b.z = 0; c.x = c.y = c.z = 0; } // create rotation matrix for rotation about the vector v by angle theta // See: http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToMatrix/ template <typename T> void Matrix3<T>::from_axis_angle(const Vector3<T> &v, float theta) { const float C = cosf(theta); const float S = sinf(theta); const float t = 1.0f - C; const Vector3f normv = v.normalized(); const float x = normv.x; const float y = normv.y; const float z = normv.z; a.x = t*x*x + C; a.y = t*x*y - z*S; a.z = t*x*z + y*S; b.x = t*x*y + z*S; b.y = t*y*y + C; b.z = t*y*z - x*S; c.x = t*x*z - y*S; c.y = t*y*z + x*S; c.z = t*z*z + C; } // only define for float template void Matrix3<float>::zero(void); template void Matrix3<float>::rotate(const Vector3<float> &g); template void Matrix3<float>::normalize(void); template void Matrix3<float>::from_euler(float roll, float pitch, float yaw); template void Matrix3<float>::to_euler(float *roll, float *pitch, float *yaw) const; template void Matrix3<float>::from_rotation(enum Rotation rotation); template void Matrix3<float>::from_euler312(float roll, float pitch, float yaw); template void Matrix3<float>::from_axis_angle(const Vector3<float> &v, float theta); template Vector3<float> Matrix3<float>::to_euler312(void) const; template Vector3<float> Matrix3<float>::operator *(const Vector3<float> &v) const; template Vector3<float> Matrix3<float>::mul_transpose(const Vector3<float> &v) const; template Matrix3<float> Matrix3<float>::operator *(const Matrix3<float> &m) const; template Matrix3<float> Matrix3<float>::transposed(void) const; template float Matrix3<float>::det() const; template bool Matrix3<float>::inverse(Matrix3<float>& inv) const; template bool Matrix3<float>::invert(); template Vector2<float> Matrix3<float>::mulXY(const Vector3<float> &v) const; template void Matrix3<double>::zero(void); template void Matrix3<double>::rotate(const Vector3<double> &g); template void Matrix3<double>::from_euler(float roll, float pitch, float yaw); template void Matrix3<double>::to_euler(float *roll, float *pitch, float *yaw) const; template Vector3<double> Matrix3<double>::operator *(const Vector3<double> &v) const; template Vector3<double> Matrix3<double>::mul_transpose(const Vector3<double> &v) const; template Matrix3<double> Matrix3<double>::operator *(const Matrix3<double> &m) const; template Matrix3<double> Matrix3<double>::transposed(void) const; template double Matrix3<double>::det() const; template bool Matrix3<double>::inverse(Matrix3<double>& inv) const; template bool Matrix3<double>::invert(); template Vector2<double> Matrix3<double>::mulXY(const Vector3<double> &v) const;