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quaternion.c
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////////////////////////////////////////////////////////////////////////////
//
// This file is part of linux-mpu9150
//
// Copyright (c) 2013 Pansenti, LLC
//
// 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.
#include "quaternion.h"
void quaternionNorm(quaternion_t q, double *n)
{
*n = sqrtf(q[QUAT_W] * q[QUAT_W] + q[QUAT_X] * q[QUAT_X] +
q[QUAT_Y] * q[QUAT_Y] + q[QUAT_Z] * q[QUAT_Z]);
}
void quaternionNormalize(quaternion_t q)
{
double length;
quaternionNorm(q, &length);
if (length == 0)
return;
q[QUAT_W] /= length;
q[QUAT_X] /= length;
q[QUAT_Y] /= length;
q[QUAT_Z] /= length;
}
void quaternionToEuler(quaternion_t q, vector3d_t v)
{
// fix roll near poles with this tolerance
double pole = (double)M_PI / 2.0 - 0.05;
double qysqr = q[QUAT_Y] * q[QUAT_Y];
double sinr_cosp = 2.0 * (q[QUAT_W] * q[QUAT_X] + q[QUAT_Y] * q[QUAT_Z]);
double cosr_cosp = 1.0 - 2.0 * (q[QUAT_X] * q[QUAT_X] + qysqr);
double sinp = 2.0 * (q[QUAT_W] * q[QUAT_Y] - q[QUAT_Z] * q[QUAT_X]);
double siny_cosp = 2.0 * (q[QUAT_W] * q[QUAT_Z] + q[QUAT_X] * q[QUAT_Y]);
double cosy_cosp = 1.0 - 2.0 * (qysqr + q[QUAT_Z] * q[QUAT_Z]);
// Keep sinp within range of asin (-1, 1)
sinp = sinp > 1.0 ? 1.0 : sinp;
sinp = sinp < -1.0 ? -1.0 : sinp;
v[VEC3_Y] = asin(sinp);
if ((v[VEC3_Y] < pole) && (v[VEC3_Y] > -pole)) {
v[VEC3_X] = atan2(sinr_cosp, cosr_cosp);
}
v[VEC3_Z] = atan2(siny_cosp, cosy_cosp);
}
void eulerToQuaternion(vector3d_t v, quaternion_t q)
{
double cosX2 = cos(v[VEC3_X] / 2.0);
double sinX2 = sin(v[VEC3_X] / 2.0);
double cosY2 = cos(v[VEC3_Y] / 2.0);
double sinY2 = sin(v[VEC3_Y] / 2.0);
double cosZ2 = cos(v[VEC3_Z] / 2.0);
double sinZ2 = sin(v[VEC3_Z] / 2.0);
q[QUAT_W] = cosX2 * cosY2 * cosZ2 + sinX2 * sinY2 * sinZ2;
q[QUAT_X] = sinX2 * cosY2 * cosZ2 - cosX2 * sinY2 * sinZ2;
q[QUAT_Y] = cosX2 * sinY2 * cosZ2 + sinX2 * cosY2 * sinZ2;
q[QUAT_Z] = cosX2 * cosY2 * sinZ2 - sinX2 * sinY2 * cosZ2;
quaternionNormalize(q);
}
void quaternionConjugate(quaternion_t s, quaternion_t d)
{
d[QUAT_W] = s[QUAT_W];
d[QUAT_X] = -s[QUAT_X];
d[QUAT_Y] = -s[QUAT_Y];
d[QUAT_Z] = -s[QUAT_Z];
}
void quaternionMultiply(quaternion_t qa, quaternion_t qb, quaternion_t qd)
{
vector3d_t va;
vector3d_t vb;
double dotAB;
vector3d_t crossAB;
va[VEC3_X] = qa[QUAT_X];
va[VEC3_Y] = qa[QUAT_Y];
va[VEC3_Z] = qa[QUAT_Z];
vb[VEC3_X] = qb[QUAT_X];
vb[VEC3_Y] = qb[QUAT_Y];
vb[VEC3_Z] = qb[QUAT_Z];
vector3DotProduct(va, vb, &dotAB);
vector3CrossProduct(va, vb, crossAB);
qd[QUAT_W] = qa[QUAT_W] * qb[QUAT_W] - dotAB;
qd[QUAT_X] = qa[QUAT_W] * vb[VEC3_X] + qb[QUAT_W] * va[VEC3_X] + crossAB[VEC3_X];
qd[QUAT_Y] = qa[QUAT_W] * vb[VEC3_Y] + qb[QUAT_W] * va[VEC3_Y] + crossAB[VEC3_Y];
qd[QUAT_Z] = qa[QUAT_W] * vb[VEC3_Z] + qb[QUAT_W] * va[VEC3_Z] + crossAB[VEC3_Z];
}
void tiltCompensate(quaternion_t magQ, quaternion_t unfusedQ)
{
quaternion_t unfusedConjugateQ;
quaternion_t tempQ;
quaternionConjugate(unfusedQ, unfusedConjugateQ);
quaternionMultiply(magQ, unfusedConjugateQ, tempQ);
quaternionMultiply(unfusedQ, tempQ, magQ);
}
void quaternionLERP(quaternion_t a, const quaternion_t b, const double t)
{
double t_ = 1 - t;
a[QUAT_X] = t_*a[QUAT_X] + t*b[QUAT_X];
a[QUAT_Y] = t_*a[QUAT_Y] + t*b[QUAT_Y];
a[QUAT_Z] = t_*a[QUAT_Z] + t*b[QUAT_Z];
a[QUAT_W] = t_*a[QUAT_W] + t*b[QUAT_W];
quaternionNormalize(a);
}
void quaternionSLERP(quaternion_t a, const quaternion_t b, const double t)
{
double t_ = 1 - t;
double Wa, Wb;
double theta = acos(a[QUAT_X]*b[QUAT_X] + a[QUAT_Y]*b[QUAT_Y] + a[QUAT_Z]*b[QUAT_Z] + a[QUAT_W]*b[QUAT_W]);
double sn = sin(theta);
Wa = sin(t_*theta) / sn;
Wb = sin(t*theta) / sn;
a[QUAT_X] = Wa*a[QUAT_X] + Wb*b[QUAT_X];
a[QUAT_Y] = Wa*a[QUAT_Y] + Wb*b[QUAT_Y];
a[QUAT_Z] = Wa*a[QUAT_Z] + Wb*b[QUAT_Z];
a[QUAT_W] = Wa*a[QUAT_W] + Wb*b[QUAT_W];
quaternionNormalize(a);
}