slerp.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2019, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */
#pragma once

#include <mrpt/math/CQuaternion.h>
#include <mrpt/math/TPose3D.h>

namespace mrpt::math
{
/** \addtogroup geometry_grp
 *  @{ */

/** @name SLERP (Spherical Linear Interpolation) functions
    @{ */

/** SLERP interpolation between two quaternions
 * \param[in] q0 The quaternion for t=0
 * \param[in] q1 The quaternion for t=1
 * \param[in] t  A "time" parameter, in the range [0,1].
 * \param[out] q The output, interpolated quaternion.
 * \tparam T  The type of the quaternion (e.g. float, double).
 * \exception std::exception Only in Debug, if t is not in the valid range.
 * \sa http://en.wikipedia.org/wiki/Slerp
 */
template <typename T>
void slerp(
    const CQuaternion<T>& q0, const CQuaternion<T>& q1, const double t,
    CQuaternion<T>& q)
{
    ASSERTDEB_(t >= 0 && t <= 1);
    // See:
    // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/index.htm
    // Angle between q0-q1:
    double cosHalfTheta =
        q0[0] * q1[0] + q0[1] * q1[1] + q0[2] * q1[2] + q0[3] * q1[3];
    // if qa=qb or qa=-qb then theta = 0 and we can return qa
    if (std::abs(cosHalfTheta) >= 1.0)
    {
        q = q0;
        return;
    }
    bool reverse_q1 = false;
    if (cosHalfTheta < 0)  // Always follow the shortest path
    {
        reverse_q1 = true;
        cosHalfTheta = -cosHalfTheta;
    }
    // Calculate temporary values.
    const double halfTheta = acos(cosHalfTheta);
    const double sinHalfTheta = std::sqrt(1.0 - mrpt::square(cosHalfTheta));
    // if theta = 180 degrees then result is not fully defined
    // we could rotate around any axis normal to qa or qb
    if (std::abs(sinHalfTheta) < 0.001)
    {
        if (!reverse_q1)
            for (int i = 0; i < 4; i++) q[i] = (1 - t) * q0[i] + t * q1[i];
        else
            for (int i = 0; i < 4; i++) q[i] = (1 - t) * q0[i] - t * q1[i];
        return;
    }
    const double A = sin((1 - t) * halfTheta) / sinHalfTheta;
    const double B = sin(t * halfTheta) / sinHalfTheta;
    if (!reverse_q1)
        for (int i = 0; i < 4; i++) q[i] = A * q0[i] + B * q1[i];
    else
        for (int i = 0; i < 4; i++) q[i] = A * q0[i] - B * q1[i];
}

/** SLERP interpolation between two 6D poses - like mrpt::math::slerp for
 * quaternions, but interpolates the [X,Y,Z] coordinates as well.
 * \param[in] p0 The pose for t=0
 * \param[in] p1 The pose for t=1
 * \param[in] t  A "time" parameter, in the range [0,1].
 * \param[out] p The output, interpolated pose.
 * \exception std::exception Only in Debug, if t is not in the valid range.
 */
void slerp(const TPose3D& q0, const TPose3D& q1, const double t, TPose3D& p);

/** \overload Interpolates two SO(3) elements (the rotational part only), given
 * as mrpt::math::TPose3D
 * form as yaw,pitch,roll angles. XYZ are ignored.
 */
void slerp_ypr(
    const mrpt::math::TPose3D& q0, const mrpt::math::TPose3D& q1,
    const double t, mrpt::math::TPose3D& p);

/** @} */

/** @} */  // grouping
}  // namespace mrpt::math