mirror of https://github.com/ArduPilot/ardupilot
283 lines
9.2 KiB
C++
283 lines
9.2 KiB
C++
/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
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/*
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* matrix3.cpp
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* Copyright (C) Andrew Tridgell 2012
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*
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* This file is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by the
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* Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This file is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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* See the GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#pragma GCC optimize("O3")
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#include "AP_Math.h"
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// create a rotation matrix given some euler angles
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// this is based on http://gentlenav.googlecode.com/files/EulerAngles.pdf
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template <typename T>
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void Matrix3<T>::from_euler(float roll, float pitch, float yaw)
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{
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float cp = cosf(pitch);
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float sp = sinf(pitch);
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float sr = sinf(roll);
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float cr = cosf(roll);
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float sy = sinf(yaw);
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float cy = cosf(yaw);
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a.x = cp * cy;
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a.y = (sr * sp * cy) - (cr * sy);
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a.z = (cr * sp * cy) + (sr * sy);
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b.x = cp * sy;
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b.y = (sr * sp * sy) + (cr * cy);
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b.z = (cr * sp * sy) - (sr * cy);
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c.x = -sp;
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c.y = sr * cp;
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c.z = cr * cp;
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}
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// calculate euler angles from a rotation matrix
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// this is based on http://gentlenav.googlecode.com/files/EulerAngles.pdf
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template <typename T>
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void Matrix3<T>::to_euler(float *roll, float *pitch, float *yaw) const
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{
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if (pitch != NULL) {
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*pitch = -safe_asin(c.x);
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}
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if (roll != NULL) {
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*roll = atan2f(c.y, c.z);
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}
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if (yaw != NULL) {
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*yaw = atan2f(b.x, a.x);
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}
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}
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/*
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calculate Euler angles (312 convention) for the matrix.
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See http://www.atacolorado.com/eulersequences.doc
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vector is returned in r, p, y order
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*/
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template <typename T>
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Vector3<T> Matrix3<T>::to_euler312() const
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{
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return Vector3<T>(asinf(c.y),
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atan2f(-c.x, c.z),
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atan2f(-a.y, b.y));
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}
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/*
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fill the matrix from Euler angles in radians in 312 convention
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*/
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template <typename T>
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void Matrix3<T>::from_euler312(float roll, float pitch, float yaw)
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{
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float c3 = cosf(pitch);
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float s3 = sinf(pitch);
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float s2 = sinf(roll);
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float c2 = cosf(roll);
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float s1 = sinf(yaw);
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float c1 = cosf(yaw);
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a.x = c1 * c3 - s1 * s2 * s3;
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b.y = c1 * c2;
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c.z = c3 * c2;
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a.y = -c2*s1;
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a.z = s3*c1 + c3*s2*s1;
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b.x = c3*s1 + s3*s2*c1;
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b.z = s1*s3 - s2*c1*c3;
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c.x = -s3*c2;
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c.y = s2;
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}
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// apply an additional rotation from a body frame gyro vector
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// to a rotation matrix.
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template <typename T>
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void Matrix3<T>::rotate(const Vector3<T> &g)
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{
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Matrix3<T> temp_matrix;
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temp_matrix.a.x = a.y * g.z - a.z * g.y;
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temp_matrix.a.y = a.z * g.x - a.x * g.z;
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temp_matrix.a.z = a.x * g.y - a.y * g.x;
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temp_matrix.b.x = b.y * g.z - b.z * g.y;
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temp_matrix.b.y = b.z * g.x - b.x * g.z;
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temp_matrix.b.z = b.x * g.y - b.y * g.x;
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temp_matrix.c.x = c.y * g.z - c.z * g.y;
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temp_matrix.c.y = c.z * g.x - c.x * g.z;
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temp_matrix.c.z = c.x * g.y - c.y * g.x;
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(*this) += temp_matrix;
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}
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// apply an additional rotation from a body frame gyro vector
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// to a rotation matrix.
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template <typename T>
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void Matrix3<T>::rotateXY(const Vector3<T> &g)
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{
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Matrix3<T> temp_matrix;
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temp_matrix.a.x = -a.z * g.y;
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temp_matrix.a.y = a.z * g.x;
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temp_matrix.a.z = a.x * g.y - a.y * g.x;
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temp_matrix.b.x = -b.z * g.y;
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temp_matrix.b.y = b.z * g.x;
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temp_matrix.b.z = b.x * g.y - b.y * g.x;
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temp_matrix.c.x = -c.z * g.y;
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temp_matrix.c.y = c.z * g.x;
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temp_matrix.c.z = c.x * g.y - c.y * g.x;
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(*this) += temp_matrix;
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}
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// apply an additional inverse rotation to a rotation matrix but
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// only use X, Y elements from rotation vector
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template <typename T>
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void Matrix3<T>::rotateXYinv(const Vector3<T> &g)
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{
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Matrix3<T> temp_matrix;
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temp_matrix.a.x = a.z * g.y;
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temp_matrix.a.y = - a.z * g.x;
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temp_matrix.a.z = - a.x * g.y + a.y * g.x;
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temp_matrix.b.x = b.z * g.y;
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temp_matrix.b.y = - b.z * g.x;
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temp_matrix.b.z = - b.x * g.y + b.y * g.x;
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temp_matrix.c.x = c.z * g.y;
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temp_matrix.c.y = - c.z * g.x;
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temp_matrix.c.z = - c.x * g.y + c.y * g.x;
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(*this) += temp_matrix;
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}
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/*
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re-normalise a rotation matrix
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*/
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template <typename T>
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void Matrix3<T>::normalize(void)
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{
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float error = a * b;
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Vector3<T> t0 = a - (b * (0.5f * error));
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Vector3<T> t1 = b - (a * (0.5f * error));
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Vector3<T> t2 = t0 % t1;
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a = t0 * (1.0f / t0.length());
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b = t1 * (1.0f / t1.length());
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c = t2 * (1.0f / t2.length());
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}
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// multiplication by a vector
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template <typename T>
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Vector3<T> Matrix3<T>::operator *(const Vector3<T> &v) const
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{
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return Vector3<T>(a.x * v.x + a.y * v.y + a.z * v.z,
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b.x * v.x + b.y * v.y + b.z * v.z,
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c.x * v.x + c.y * v.y + c.z * v.z);
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}
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// multiplication by a vector, extracting only the xy components
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template <typename T>
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Vector2<T> Matrix3<T>::mulXY(const Vector3<T> &v) const
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{
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return Vector2<T>(a.x * v.x + a.y * v.y + a.z * v.z,
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b.x * v.x + b.y * v.y + b.z * v.z);
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}
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// multiplication of transpose by a vector
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template <typename T>
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Vector3<T> Matrix3<T>::mul_transpose(const Vector3<T> &v) const
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{
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return Vector3<T>(a.x * v.x + b.x * v.y + c.x * v.z,
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a.y * v.x + b.y * v.y + c.y * v.z,
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a.z * v.x + b.z * v.y + c.z * v.z);
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}
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// multiplication by another Matrix3<T>
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template <typename T>
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Matrix3<T> Matrix3<T>::operator *(const Matrix3<T> &m) const
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{
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Matrix3<T> temp (Vector3<T>(a.x * m.a.x + a.y * m.b.x + a.z * m.c.x,
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a.x * m.a.y + a.y * m.b.y + a.z * m.c.y,
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a.x * m.a.z + a.y * m.b.z + a.z * m.c.z),
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Vector3<T>(b.x * m.a.x + b.y * m.b.x + b.z * m.c.x,
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b.x * m.a.y + b.y * m.b.y + b.z * m.c.y,
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b.x * m.a.z + b.y * m.b.z + b.z * m.c.z),
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Vector3<T>(c.x * m.a.x + c.y * m.b.x + c.z * m.c.x,
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c.x * m.a.y + c.y * m.b.y + c.z * m.c.y,
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c.x * m.a.z + c.y * m.b.z + c.z * m.c.z));
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return temp;
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}
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template <typename T>
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Matrix3<T> Matrix3<T>::transposed(void) const
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{
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return Matrix3<T>(Vector3<T>(a.x, b.x, c.x),
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Vector3<T>(a.y, b.y, c.y),
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Vector3<T>(a.z, b.z, c.z));
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}
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template <typename T>
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void Matrix3<T>::zero(void)
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{
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a.x = a.y = a.z = 0;
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b.x = b.y = b.z = 0;
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c.x = c.y = c.z = 0;
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}
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// create rotation matrix for rotation about the vector v by angle theta
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// See: http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToMatrix/
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template <typename T>
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void Matrix3<T>::from_axis_angle(const Vector3<T> &v, float theta)
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{
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float C = cosf(theta);
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float S = sinf(theta);
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float t = 1.0f - C;
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Vector3f normv = v.normalized();
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float x = normv.x;
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float y = normv.y;
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float z = normv.z;
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a.x = t*x*x + C;
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a.y = t*x*y - z*S;
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a.z = t*x*z + y*S;
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b.x = t*x*y + z*S;
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b.y = t*y*y + C;
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b.z = t*y*z - x*S;
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c.x = t*x*z - y*S;
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c.y = t*y*z + x*S;
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c.z = t*z*z + C;
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}
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// only define for float
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template void Matrix3<float>::zero(void);
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template void Matrix3<float>::rotate(const Vector3<float> &g);
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template void Matrix3<float>::rotateXY(const Vector3<float> &g);
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template void Matrix3<float>::rotateXYinv(const Vector3<float> &g);
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template void Matrix3<float>::normalize(void);
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template void Matrix3<float>::from_euler(float roll, float pitch, float yaw);
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template void Matrix3<float>::to_euler(float *roll, float *pitch, float *yaw) const;
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template void Matrix3<float>::from_euler312(float roll, float pitch, float yaw);
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template void Matrix3<float>::from_axis_angle(const Vector3<float> &v, float theta);
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template Vector3<float> Matrix3<float>::to_euler312(void) const;
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template Vector3<float> Matrix3<float>::operator *(const Vector3<float> &v) const;
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template Vector3<float> Matrix3<float>::mul_transpose(const Vector3<float> &v) const;
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template Matrix3<float> Matrix3<float>::operator *(const Matrix3<float> &m) const;
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template Matrix3<float> Matrix3<float>::transposed(void) const;
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template Vector2<float> Matrix3<float>::mulXY(const Vector3<float> &v) const;
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template void Matrix3<double>::zero(void);
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template void Matrix3<double>::rotate(const Vector3<double> &g);
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template void Matrix3<double>::rotateXY(const Vector3<double> &g);
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template void Matrix3<double>::rotateXYinv(const Vector3<double> &g);
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template void Matrix3<double>::from_euler(float roll, float pitch, float yaw);
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template void Matrix3<double>::to_euler(float *roll, float *pitch, float *yaw) const;
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template Vector3<double> Matrix3<double>::operator *(const Vector3<double> &v) const;
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template Vector3<double> Matrix3<double>::mul_transpose(const Vector3<double> &v) const;
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template Matrix3<double> Matrix3<double>::operator *(const Matrix3<double> &m) const;
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template Matrix3<double> Matrix3<double>::transposed(void) const;
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template Vector2<double> Matrix3<double>::mulXY(const Vector3<double> &v) const;
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