mirror of https://github.com/ArduPilot/ardupilot
668 lines
16 KiB
C++
668 lines
16 KiB
C++
/*
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* quaternion.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("O2")
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#include "AP_Math.h"
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#include <AP_InternalError/AP_InternalError.h>
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// return the rotation matrix equivalent for this quaternion
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void Quaternion::rotation_matrix(Matrix3f &m) const
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{
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const float q3q3 = q3 * q3;
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const float q3q4 = q3 * q4;
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const float q2q2 = q2 * q2;
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const float q2q3 = q2 * q3;
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const float q2q4 = q2 * q4;
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const float q1q2 = q1 * q2;
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const float q1q3 = q1 * q3;
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const float q1q4 = q1 * q4;
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const float q4q4 = q4 * q4;
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m.a.x = 1.0f-2.0f*(q3q3 + q4q4);
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m.a.y = 2.0f*(q2q3 - q1q4);
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m.a.z = 2.0f*(q2q4 + q1q3);
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m.b.x = 2.0f*(q2q3 + q1q4);
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m.b.y = 1.0f-2.0f*(q2q2 + q4q4);
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m.b.z = 2.0f*(q3q4 - q1q2);
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m.c.x = 2.0f*(q2q4 - q1q3);
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m.c.y = 2.0f*(q3q4 + q1q2);
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m.c.z = 1.0f-2.0f*(q2q2 + q3q3);
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}
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// return the rotation matrix equivalent for this quaternion after normalization
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void Quaternion::rotation_matrix_norm(Matrix3f &m) const
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{
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const float q1q1 = q1 * q1;
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const float q1q2 = q1 * q2;
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const float q1q3 = q1 * q3;
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const float q1q4 = q1 * q4;
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const float q2q2 = q2 * q2;
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const float q2q3 = q2 * q3;
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const float q2q4 = q2 * q4;
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const float q3q3 = q3 * q3;
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const float q3q4 = q3 * q4;
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const float q4q4 = q4 * q4;
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const float invs = 1.0f / (q1q1 + q2q2 + q3q3 + q4q4);
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m.a.x = ( q2q2 - q3q3 - q4q4 + q1q1)*invs;
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m.a.y = 2.0f*(q2q3 - q1q4)*invs;
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m.a.z = 2.0f*(q2q4 + q1q3)*invs;
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m.b.x = 2.0f*(q2q3 + q1q4)*invs;
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m.b.y = (-q2q2 + q3q3 - q4q4 + q1q1)*invs;
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m.b.z = 2.0f*(q3q4 - q1q2)*invs;
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m.c.x = 2.0f*(q2q4 - q1q3)*invs;
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m.c.y = 2.0f*(q3q4 + q1q2)*invs;
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m.c.z = (-q2q2 - q3q3 + q4q4 + q1q1)*invs;
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}
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// return the rotation matrix equivalent for this quaternion
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// Thanks to Martin John Baker
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// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
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void Quaternion::from_rotation_matrix(const Matrix3f &m)
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{
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const float &m00 = m.a.x;
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const float &m11 = m.b.y;
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const float &m22 = m.c.z;
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const float &m10 = m.b.x;
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const float &m01 = m.a.y;
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const float &m20 = m.c.x;
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const float &m02 = m.a.z;
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const float &m21 = m.c.y;
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const float &m12 = m.b.z;
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float &qw = q1;
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float &qx = q2;
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float &qy = q3;
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float &qz = q4;
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const float tr = m00 + m11 + m22;
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if (tr > 0) {
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const float S = sqrtf(tr+1) * 2;
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qw = 0.25f * S;
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qx = (m21 - m12) / S;
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qy = (m02 - m20) / S;
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qz = (m10 - m01) / S;
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} else if ((m00 > m11) && (m00 > m22)) {
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const float S = sqrtf(1.0f + m00 - m11 - m22) * 2.0f;
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qw = (m21 - m12) / S;
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qx = 0.25f * S;
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qy = (m01 + m10) / S;
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qz = (m02 + m20) / S;
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} else if (m11 > m22) {
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const float S = sqrtf(1.0f + m11 - m00 - m22) * 2.0f;
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qw = (m02 - m20) / S;
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qx = (m01 + m10) / S;
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qy = 0.25f * S;
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qz = (m12 + m21) / S;
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} else {
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const float S = sqrtf(1.0f + m22 - m00 - m11) * 2.0f;
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qw = (m10 - m01) / S;
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qx = (m02 + m20) / S;
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qy = (m12 + m21) / S;
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qz = 0.25f * S;
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}
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}
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// create a quaternion from a given rotation
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void Quaternion::from_rotation(enum Rotation rotation)
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{
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// the constants below can be calculated using the following formula:
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// Matrix3f m_from_rot;
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// m_from_rot.from_rotation(rotation);
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// Quaternion q_from_m;
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// from_rotation_matrix(m_from_rot);
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switch (rotation) {
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case ROTATION_NONE:
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q1 = 1;
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q2 = q3 = q4 = 0;
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return;
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case ROTATION_YAW_45:
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q1 = 0.92387956f;
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q2 = q3 = 0;
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q4 = 0.38268343f;
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return;
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case ROTATION_YAW_90:
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q1 = HALF_SQRT_2;
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q2 = q3 = 0;
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q4 = HALF_SQRT_2;
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return;
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case ROTATION_YAW_135:
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q1 = 0.38268343f;
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q2 = q3 = 0;
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q4 = 0.92387956f;
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return;
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case ROTATION_YAW_180:
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q1 = q2 = q3 = 0;
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q4=1;
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return;
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case ROTATION_YAW_225:
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q1 = -0.38268343f;
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q2 = q3 = 0;
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q4 = 0.92387956f;
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return;
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case ROTATION_YAW_270:
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q1 = HALF_SQRT_2;
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q2 = q3 = 0;
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q4 = -HALF_SQRT_2;
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return;
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case ROTATION_YAW_315:
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q1 = 0.92387956f;
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q2 = q3 = 0;
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q4 = -0.38268343f;
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return;
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case ROTATION_ROLL_180:
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q1 = q3 = q4 = 0;
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q2 = 1;
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return;
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case ROTATION_ROLL_180_YAW_45:
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q1 = q4 = 0;
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q2 = 0.92387956f;
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q3 = 0.38268343f;
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return;
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case ROTATION_ROLL_180_YAW_90:
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q1 = q4 = 0;
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q2 = q3 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_180_YAW_135:
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q1 = q4 = 0;
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q2 = 0.38268343f;
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q3 = 0.92387956f;
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return;
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case ROTATION_PITCH_180:
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q1 = q2 = q4 = 0;
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q3 = 1;
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return;
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case ROTATION_ROLL_180_YAW_225:
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q1 = q4 = 0;
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q2 = -0.38268343f;
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q3 = 0.92387956f;
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return;
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case ROTATION_ROLL_180_YAW_270:
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q1 = q4 = 0;
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q2 = -HALF_SQRT_2;
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q3 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_180_YAW_315:
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q1 = q4 = 0;
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q2 = 0.92387956f;
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q3 = -0.38268343f;
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return;
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case ROTATION_ROLL_90:
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q1 = q2 = HALF_SQRT_2;
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q3 = q4 = 0;
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return;
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case ROTATION_ROLL_90_YAW_45:
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q1 = 0.65328151f;
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q2 = 0.65328145f;
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q3 = q4 = 0.27059802f;
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return;
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case ROTATION_ROLL_90_YAW_90:
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q1 = q2 = q3 = q4 = 0.5f;
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return;
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case ROTATION_ROLL_90_YAW_135:
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q1 = q2 = 0.27059802f;
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q3 = 0.65328145f;
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q4 = 0.65328151f;
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return;
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case ROTATION_ROLL_270:
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q1 = HALF_SQRT_2;
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q2 = -HALF_SQRT_2;
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q3 = q4 = 0;
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return;
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case ROTATION_ROLL_270_YAW_45:
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q1 = 0.65328151f;
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q2 = -0.65328145f;
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q3 = -0.27059802f;
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q4 = 0.27059802f;
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return;
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case ROTATION_ROLL_270_YAW_90:
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q1 = q4 = 0.5f;
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q2 = q3 = -0.5f;
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return;
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case ROTATION_ROLL_270_YAW_135:
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q1 = 0.27059802f;
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q2 = -0.27059802f;
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q3 = -0.65328145f;
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q4 = 0.65328151f;
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return;
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case ROTATION_PITCH_90:
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q1 = q3 = HALF_SQRT_2;
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q2 = q4 = 0;
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return;
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case ROTATION_PITCH_270:
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q1 = HALF_SQRT_2;
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q2 = q4 = 0;
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q3 = -HALF_SQRT_2;
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return;
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case ROTATION_PITCH_180_YAW_90:
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q1 = q4 = 0;
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q2 = -HALF_SQRT_2;
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q3 = HALF_SQRT_2;
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return;
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case ROTATION_PITCH_180_YAW_270:
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q1 = q4 = 0;
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q2 = q3 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_90_PITCH_90:
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q1 = q2 = q3 = -0.5f;
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q4 = 0.5f;
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return;
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case ROTATION_ROLL_180_PITCH_90:
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q1 = q3 = 0;
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q2 = -HALF_SQRT_2;
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q4 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_270_PITCH_90:
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q1 = q3 = q4 = 0.5f;
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q2 = -0.5f;
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return;
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case ROTATION_ROLL_90_PITCH_180:
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q1 = q2 = 0;
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q3 = -HALF_SQRT_2;
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q4 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_270_PITCH_180:
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q1 = q2 = 0;
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q3 = q4 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_90_PITCH_270:
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q1 = q2 = q4 = 0.5f;
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q3 = -0.5;
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return;
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case ROTATION_ROLL_180_PITCH_270:
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q1 = q3 = 0;
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q2 = q4 = HALF_SQRT_2;
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return;
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case ROTATION_ROLL_270_PITCH_270:
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q1 = -0.5f;
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q2 = q3 = q4 = 0.5f;
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return;
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case ROTATION_ROLL_90_PITCH_180_YAW_90:
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q1 = q3 = -0.5f;
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q2 = q4 = 0.5f;
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return;
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case ROTATION_ROLL_90_YAW_270:
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q1 = q2 = -0.5f;
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q3 = q4 = 0.5f;
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return;
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case ROTATION_ROLL_90_PITCH_68_YAW_293:
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q1 = 0.26774535f;
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q2 = 0.70698798f;
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q3 = 0.01295743f;
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q4 = -0.65445596f;
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return;
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case ROTATION_PITCH_315:
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q1 = 0.92387956f;
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q2 = q4 = 0;
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q3 = -0.38268343f;
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return;
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case ROTATION_ROLL_90_PITCH_315:
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q1 = 0.65328151f;
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q2 = 0.65328145f;
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q3 = -0.27059802f;
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q4 = 0.27059802f;
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return;
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case ROTATION_PITCH_7:
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q1 = 0.99813479f;
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q2 = q4 = 0;
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q3 = 0.06104854f;
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return;
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case ROTATION_CUSTOM:
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// Error; custom rotations not supported
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INTERNAL_ERROR(AP_InternalError::error_t::flow_of_control);
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return;
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case ROTATION_MAX:
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break;
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}
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// rotation invalid
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INTERNAL_ERROR(AP_InternalError::error_t::bad_rotation);
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}
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// rotate this quaternion by the given rotation
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void Quaternion::rotate(enum Rotation rotation)
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{
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// create quaternion from rotation matrix
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Quaternion q_from_rot;
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q_from_rot.from_rotation(rotation);
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// rotate this quaternion
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*this *= q_from_rot;
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}
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// convert a vector from earth to body frame
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void Quaternion::earth_to_body(Vector3f &v) const
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{
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Matrix3f m;
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rotation_matrix(m);
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v = m * v;
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}
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// create a quaternion from Euler angles
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void Quaternion::from_euler(float roll, float pitch, float yaw)
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{
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const float cr2 = cosf(roll*0.5f);
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const float cp2 = cosf(pitch*0.5f);
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const float cy2 = cosf(yaw*0.5f);
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const float sr2 = sinf(roll*0.5f);
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const float sp2 = sinf(pitch*0.5f);
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const float sy2 = sinf(yaw*0.5f);
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q1 = cr2*cp2*cy2 + sr2*sp2*sy2;
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q2 = sr2*cp2*cy2 - cr2*sp2*sy2;
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q3 = cr2*sp2*cy2 + sr2*cp2*sy2;
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q4 = cr2*cp2*sy2 - sr2*sp2*cy2;
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}
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// create a quaternion from Euler angles applied in yaw, roll, pitch order
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// instead of the normal yaw, pitch, roll order
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void Quaternion::from_vector312(float roll, float pitch, float yaw)
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{
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Matrix3f m;
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m.from_euler312(roll, pitch, yaw);
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from_rotation_matrix(m);
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}
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// create a quaternion from its axis-angle representation
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void Quaternion::from_axis_angle(Vector3f v)
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{
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const float theta = v.length();
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if (is_zero(theta)) {
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q1 = 1.0f;
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q2=q3=q4=0.0f;
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return;
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}
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v /= theta;
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from_axis_angle(v,theta);
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}
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// create a quaternion from its axis-angle representation
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// the axis vector must be length 1, theta is in radians
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void Quaternion::from_axis_angle(const Vector3f &axis, float theta)
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{
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// axis must be a unit vector as there is no check for length
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if (is_zero(theta)) {
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q1 = 1.0f;
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q2=q3=q4=0.0f;
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return;
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}
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const float st2 = sinf(theta/2.0f);
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q1 = cosf(theta/2.0f);
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q2 = axis.x * st2;
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q3 = axis.y * st2;
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q4 = axis.z * st2;
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}
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// rotate by the provided axis angle
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void Quaternion::rotate(const Vector3f &v)
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{
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Quaternion r;
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r.from_axis_angle(v);
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(*this) *= r;
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}
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// convert this quaternion to a rotation vector where the direction of the vector represents
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// the axis of rotation and the length of the vector represents the angle of rotation
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void Quaternion::to_axis_angle(Vector3f &v)
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{
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const float l = sqrtf(sq(q2)+sq(q3)+sq(q4));
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v = Vector3f(q2,q3,q4);
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if (!is_zero(l)) {
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v /= l;
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v *= wrap_PI(2.0f * atan2f(l,q1));
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}
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}
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// create a quaternion from its axis-angle representation
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// only use with small angles. I.e. length of v should less than 0.17 radians (i.e. 10 degrees)
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void Quaternion::from_axis_angle_fast(Vector3f v)
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{
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const float theta = v.length();
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if (is_zero(theta)) {
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q1 = 1.0f;
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q2=q3=q4=0.0f;
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return;
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}
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v /= theta;
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from_axis_angle_fast(v,theta);
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|
}
|
|
|
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// create a quaternion from its axis-angle representation
|
|
// theta should less than 0.17 radians (i.e. 10 degrees)
|
|
void Quaternion::from_axis_angle_fast(const Vector3f &axis, float theta)
|
|
{
|
|
const float t2 = theta/2.0f;
|
|
const float sqt2 = sq(t2);
|
|
const float st2 = t2-sqt2*t2/6.0f;
|
|
|
|
q1 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
|
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q2 = axis.x * st2;
|
|
q3 = axis.y * st2;
|
|
q4 = axis.z * st2;
|
|
}
|
|
|
|
// rotate by the provided axis angle
|
|
// only use with small angles. I.e. length of v should less than 0.17 radians (i.e. 10 degrees)
|
|
void Quaternion::rotate_fast(const Vector3f &v)
|
|
{
|
|
const float theta = v.length();
|
|
if (is_zero(theta)) {
|
|
return;
|
|
}
|
|
const float t2 = theta/2.0f;
|
|
const float sqt2 = sq(t2);
|
|
float st2 = t2-sqt2*t2/6.0f;
|
|
st2 /= theta;
|
|
|
|
//"rotation quaternion"
|
|
const float w2 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
|
|
const float x2 = v.x * st2;
|
|
const float y2 = v.y * st2;
|
|
const float z2 = v.z * st2;
|
|
|
|
//copy our quaternion
|
|
const float w1 = q1;
|
|
const float x1 = q2;
|
|
const float y1 = q3;
|
|
const float z1 = q4;
|
|
|
|
//do the multiply into our quaternion
|
|
q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
|
|
q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
|
|
q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
|
|
q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
|
|
}
|
|
|
|
// get euler roll angle
|
|
float Quaternion::get_euler_roll() const
|
|
{
|
|
return (atan2f(2.0f*(q1*q2 + q3*q4), 1.0f - 2.0f*(q2*q2 + q3*q3)));
|
|
}
|
|
|
|
// get euler pitch angle
|
|
float Quaternion::get_euler_pitch() const
|
|
{
|
|
return safe_asin(2.0f*(q1*q3 - q4*q2));
|
|
}
|
|
|
|
// get euler yaw angle
|
|
float Quaternion::get_euler_yaw() const
|
|
{
|
|
return atan2f(2.0f*(q1*q4 + q2*q3), 1.0f - 2.0f*(q3*q3 + q4*q4));
|
|
}
|
|
|
|
// create eulers from a quaternion
|
|
void Quaternion::to_euler(float &roll, float &pitch, float &yaw) const
|
|
{
|
|
roll = get_euler_roll();
|
|
pitch = get_euler_pitch();
|
|
yaw = get_euler_yaw();
|
|
}
|
|
|
|
// create eulers from a quaternion
|
|
Vector3f Quaternion::to_vector312(void) const
|
|
{
|
|
Matrix3f m;
|
|
rotation_matrix(m);
|
|
return m.to_euler312();
|
|
}
|
|
|
|
float Quaternion::length(void) const
|
|
{
|
|
return sqrtf(sq(q1) + sq(q2) + sq(q3) + sq(q4));
|
|
}
|
|
|
|
// return the reverse rotation of this quaternion
|
|
Quaternion Quaternion::inverse(void) const
|
|
{
|
|
return Quaternion(q1, -q2, -q3, -q4);
|
|
}
|
|
|
|
// reverse the rotation of this quaternion
|
|
void Quaternion::invert()
|
|
{
|
|
q2 = -q2;
|
|
q3 = -q3;
|
|
q4 = -q4;
|
|
}
|
|
|
|
void Quaternion::normalize(void)
|
|
{
|
|
const float quatMag = length();
|
|
if (!is_zero(quatMag)) {
|
|
const float quatMagInv = 1.0f/quatMag;
|
|
q1 *= quatMagInv;
|
|
q2 *= quatMagInv;
|
|
q3 *= quatMagInv;
|
|
q4 *= quatMagInv;
|
|
}
|
|
}
|
|
|
|
Quaternion Quaternion::operator*(const Quaternion &v) const
|
|
{
|
|
Quaternion ret;
|
|
const float &w1 = q1;
|
|
const float &x1 = q2;
|
|
const float &y1 = q3;
|
|
const float &z1 = q4;
|
|
|
|
const float w2 = v.q1;
|
|
const float x2 = v.q2;
|
|
const float y2 = v.q3;
|
|
const float z2 = v.q4;
|
|
|
|
ret.q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
|
|
ret.q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
|
|
ret.q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
|
|
ret.q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
|
|
|
|
return ret;
|
|
}
|
|
|
|
Quaternion &Quaternion::operator*=(const Quaternion &v)
|
|
{
|
|
const float w1 = q1;
|
|
const float x1 = q2;
|
|
const float y1 = q3;
|
|
const float z1 = q4;
|
|
|
|
const float w2 = v.q1;
|
|
const float x2 = v.q2;
|
|
const float y2 = v.q3;
|
|
const float z2 = v.q4;
|
|
|
|
q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
|
|
q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
|
|
q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
|
|
q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
|
|
|
|
return *this;
|
|
}
|
|
|
|
Quaternion Quaternion::operator/(const Quaternion &v) const
|
|
{
|
|
Quaternion ret;
|
|
const float &quat0 = q1;
|
|
const float &quat1 = q2;
|
|
const float &quat2 = q3;
|
|
const float &quat3 = q4;
|
|
|
|
const float rquat0 = v.q1;
|
|
const float rquat1 = v.q2;
|
|
const float rquat2 = v.q3;
|
|
const float rquat3 = v.q4;
|
|
|
|
ret.q1 = (rquat0*quat0 + rquat1*quat1 + rquat2*quat2 + rquat3*quat3);
|
|
ret.q2 = (rquat0*quat1 - rquat1*quat0 - rquat2*quat3 + rquat3*quat2);
|
|
ret.q3 = (rquat0*quat2 + rquat1*quat3 - rquat2*quat0 - rquat3*quat1);
|
|
ret.q4 = (rquat0*quat3 - rquat1*quat2 + rquat2*quat1 - rquat3*quat0);
|
|
return ret;
|
|
}
|
|
|
|
// angular difference in radians between quaternions
|
|
Quaternion Quaternion::angular_difference(const Quaternion &v) const
|
|
{
|
|
return v.inverse() * *this;
|
|
}
|