bgc-c/basic-geometry/rigid-pose3.h

#ifndef _BGC_RIGID_POSE3_H_INCLUDED_
#define _BGC_RIGID_POSE3_H_INCLUDED_

#include <math.h>

#include "types.h"
#include "affine3.h"
#include "quaternion.h"
#include "dual-quaternion.h"

// ==================== Reset =================== //

inline void bgc_fp32_rigid_pose3_reset(BGC_FP32_RigidPose3* const pose)
{
    pose->_versor.real_part.s = 1.0f;
    pose->_versor.real_part.x = 0.0f;
    pose->_versor.real_part.y = 0.0f;
    pose->_versor.real_part.z = 0.0f;

    pose->_versor.dual_part.s = 0.0f;
    pose->_versor.dual_part.x = 0.0f;
    pose->_versor.dual_part.y = 0.0f;
    pose->_versor.dual_part.z = 0.0f;
}

inline void bgc_fp64_rigid_pose3_reset(BGC_FP64_RigidPose3* const pose)
{
    pose->_versor.real_part.s = 1.0;
    pose->_versor.real_part.x = 0.0;
    pose->_versor.real_part.y = 0.0;
    pose->_versor.real_part.z = 0.0;

    pose->_versor.dual_part.s = 0.0;
    pose->_versor.dual_part.x = 0.0;
    pose->_versor.dual_part.y = 0.0;
    pose->_versor.dual_part.z = 0.0;
}

// ================= Normalize ================== //

inline void _bgc_fp32_rigid_pose3_normalize(BGC_FP32_RigidPose3* const pose)
{
    const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(&pose->_versor.real_part);

    if (square_magnitude <= BGC_FP32_SQUARE_EPSILON || isnan(square_magnitude)) {
        bgc_fp32_rigid_pose3_reset(pose);
        return;
    }

    if (!bgc_fp32_is_square_unit(square_magnitude)) {
        const float multiplier = sqrtf(1.0f / square_magnitude);

        bgc_fp32_dual_quaternion_multiply_by_real_number(&pose->_versor, &pose->_versor, multiplier);
    }

    const float dot_product = bgc_fp32_quaternion_get_dot_product(&pose->_versor.real_part, &pose->_versor.dual_part);

    bgc_fp32_quaternion_subtract_scaled(&pose->_versor.dual_part, &pose->_versor.dual_part, &pose->_versor.real_part, dot_product);
}

inline void _bgc_fp64_rigid_pose3_normalize(BGC_FP64_RigidPose3* const pose)
{
    const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(&pose->_versor.real_part);

    if (square_magnitude <= BGC_FP64_SQUARE_EPSILON || isnan(square_magnitude)) {
        bgc_fp64_rigid_pose3_reset(pose);
        return;
    }

    if (!bgc_fp64_is_square_unit(square_magnitude)) {
        const double multiplier = sqrt(1.0 / square_magnitude);

        bgc_fp64_dual_quaternion_multiply_by_real_number(&pose->_versor, &pose->_versor, multiplier);
    }

    const double dot_product = bgc_fp64_quaternion_get_dot_product(&pose->_versor.real_part, &pose->_versor.dual_part);

    bgc_fp64_quaternion_subtract_scaled(&pose->_versor.dual_part, &pose->_versor.dual_part, &pose->_versor.real_part, dot_product);
}

// ============ Get Dual Quaternion ============= //

inline void bgc_fp32_rigid_pose3_get_dual_quaternion(BGC_FP32_DualQuaternion* const quaternion, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_dual_quaternion_copy(quaternion, &pose->_versor);
}

inline void bgc_fp64_rigid_pose3_get_dual_quaternion(BGC_FP64_DualQuaternion* const quaternion, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_dual_quaternion_copy(quaternion, &pose->_versor);
}

// ============ Get Dual Quaternion ============= //

inline void bgc_fp32_rigid_pose3_set_dual_quaternion(BGC_FP32_RigidPose3* const pose, const BGC_FP32_DualQuaternion* const quaternion)
{
    bgc_fp32_dual_quaternion_copy(&pose->_versor, quaternion);
    _bgc_fp32_rigid_pose3_normalize(pose);
}

inline void bgc_fp64_rigid_pose3_set_dual_quaternion(BGC_FP64_RigidPose3* const pose, const BGC_FP64_DualQuaternion* const quaternion)
{
    bgc_fp64_dual_quaternion_copy(&pose->_versor, quaternion);
    _bgc_fp64_rigid_pose3_normalize(pose);
}

// =============== Get Real Part ================ //

inline void bgc_fp32_rigid_pose3_get_real_part(BGC_FP32_Quaternion* const quaternion, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_copy(quaternion, &pose->_versor.real_part);
}

inline void bgc_fp64_rigid_pose3_get_real_part(BGC_FP64_Quaternion* const quaternion, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_copy(quaternion, &pose->_versor.real_part);
}

// =============== Get Dual Part ================ //

inline void bgc_fp32_rigid_pose3_get_dual_part(BGC_FP32_Quaternion* const quaternion, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_copy(quaternion, &pose->_versor.dual_part);
}

inline void bgc_fp64_rigid_pose3_get_dual_part(BGC_FP64_Quaternion* const quaternion, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_copy(quaternion, &pose->_versor.dual_part);
}

// ==================== Copy ==================== //

inline void bgc_fp32_rigid_pose3_copy(BGC_FP32_RigidPose3* const destination, const BGC_FP32_RigidPose3* const source)
{
    bgc_fp32_dual_quaternion_copy(&destination->_versor, &source->_versor);
}

inline void bgc_fp64_rigid_pose3_copy(BGC_FP64_RigidPose3* const destination, const BGC_FP64_RigidPose3* const source)
{
    bgc_fp64_dual_quaternion_copy(&destination->_versor, &source->_versor);
}

// ==================== Swap ==================== //

inline void bgc_fp32_rigid_pose3_swap(BGC_FP32_RigidPose3* const pose1, BGC_FP32_RigidPose3* const pose2)
{
    bgc_fp32_dual_quaternion_swap(&pose1->_versor, &pose2->_versor);
}

inline void bgc_fp64_rigid_pose3_swap(BGC_FP64_RigidPose3* const pose1, BGC_FP64_RigidPose3* const pose2)
{
    bgc_fp64_dual_quaternion_swap(&pose1->_versor, &pose2->_versor);
}

// ================== Is Idle =================== //

inline int bgc_fp32_rigid_pose3_is_idle(const BGC_FP32_RigidPose3* const pose)
{
    return bgc_fp32_quaternion_is_real(&pose->_versor.real_part) && bgc_fp32_quaternion_is_zero(&pose->_versor.dual_part);
}

inline int bgc_fp64_rigid_pose3_is_idle(const BGC_FP64_RigidPose3* const pose)
{
    return bgc_fp64_quaternion_is_real(&pose->_versor.real_part) && bgc_fp64_quaternion_is_zero(&pose->_versor.dual_part);
}

// ================== Convert =================== //

inline void bgc_fp32_rigid_pose3_convert_to_fp64(BGC_FP64_RigidPose3* const destination, const BGC_FP32_RigidPose3* const source)
{
    bgc_fp32_dual_quaternion_convert_to_fp64(&destination->_versor, &source->_versor);
    _bgc_fp64_rigid_pose3_normalize(destination);
}

inline void bgc_fp64_rigid_pose3_convert_to_fp32(BGC_FP32_RigidPose3* const destination, const BGC_FP64_RigidPose3* const source)
{
    bgc_fp64_dual_quaternion_convert_to_fp32(&destination->_versor, &source->_versor);
    _bgc_fp32_rigid_pose3_normalize(destination);
}

// ================== Shorten =================== //

inline void bgc_fp32_rigid_pose3_shorten(BGC_FP32_RigidPose3* const pose)
{
    if (pose->_versor.real_part.s < 0.0f) {
        bgc_fp32_quaternion_revert(&pose->_versor.real_part);
        bgc_fp32_quaternion_revert(&pose->_versor.dual_part);
    }
}

inline void bgc_fp64_rigid_pose3_shorten(BGC_FP64_RigidPose3* const pose)
{
    if (pose->_versor.real_part.s < 0.0) {
        bgc_fp64_quaternion_revert(&pose->_versor.real_part);
        bgc_fp64_quaternion_revert(&pose->_versor.dual_part);
    }
}

// =============== Get Shortened ================ //

inline void bgc_fp32_rigid_pose3_get_shortened(BGC_FP32_RigidPose3* const shortened, const BGC_FP32_RigidPose3* const pose)
{
    if (pose->_versor.real_part.s < 0.0f) {
        bgc_fp32_quaternion_get_reverse(&shortened->_versor.real_part, &pose->_versor.real_part);
        bgc_fp32_quaternion_get_reverse(&shortened->_versor.dual_part, &pose->_versor.dual_part);
    }
    else {
        bgc_fp32_quaternion_copy(&shortened->_versor.real_part, &pose->_versor.real_part);
        bgc_fp32_quaternion_copy(&shortened->_versor.dual_part, &pose->_versor.dual_part);
    }
}

inline void bgc_fp64_rigid_pose3_get_shortened(BGC_FP64_RigidPose3* const shortened, const BGC_FP64_RigidPose3* const pose)
{
    if (pose->_versor.real_part.s < 0.0) {
        bgc_fp64_quaternion_get_reverse(&shortened->_versor.real_part, &pose->_versor.real_part);
        bgc_fp64_quaternion_get_reverse(&shortened->_versor.dual_part, &pose->_versor.dual_part);
    }
    else {
        bgc_fp64_quaternion_copy(&shortened->_versor.real_part, &pose->_versor.real_part);
        bgc_fp64_quaternion_copy(&shortened->_versor.dual_part, &pose->_versor.dual_part);
    }
}

// ================= Alternate ================== //

inline void bgc_fp32_rigid_pose3_alternate(BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_revert(&pose->_versor.real_part);
    bgc_fp32_quaternion_revert(&pose->_versor.dual_part);
}

inline void bgc_fp64_rigid_pose3_alternate(BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_revert(&pose->_versor.real_part);
    bgc_fp64_quaternion_revert(&pose->_versor.dual_part);
}

// ============== Get Alternative =============== //

inline void bgc_fp32_rigid_pose3_get_alternative(BGC_FP32_RigidPose3* const alternative, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_reverse(&alternative->_versor.real_part, &pose->_versor.real_part);
    bgc_fp32_quaternion_get_reverse(&alternative->_versor.dual_part, &pose->_versor.dual_part);
}

inline void bgc_fp64_rigid_pose3_get_alternative(BGC_FP64_RigidPose3* const alternative, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_reverse(&alternative->_versor.real_part, &pose->_versor.real_part);
    bgc_fp64_quaternion_get_reverse(&alternative->_versor.dual_part, &pose->_versor.dual_part);
}

// =================== Revert =================== //

inline void bgc_fp32_rigid_pose3_revert(BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_conjugate(&pose->_versor.real_part);
    bgc_fp32_quaternion_conjugate(&pose->_versor.dual_part);
}

inline void bgc_fp64_rigid_pose3_revert(BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_conjugate(&pose->_versor.real_part);
    bgc_fp64_quaternion_conjugate(&pose->_versor.dual_part);
}

// ============== Get Reverse Pose ============== //

inline void bgc_fp32_rigid_pose3_get_reverse_pose(BGC_FP32_RigidPose3* const reverse, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_conjugate(&reverse->_versor.real_part, &pose->_versor.real_part);
    bgc_fp32_quaternion_get_conjugate(&reverse->_versor.dual_part, &pose->_versor.dual_part);
}

inline void bgc_fp64_rigid_pose3_get_reverse_pose(BGC_FP64_RigidPose3* const reverse, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_conjugate(&reverse->_versor.real_part, &pose->_versor.real_part);
    bgc_fp64_quaternion_get_conjugate(&reverse->_versor.dual_part, &pose->_versor.dual_part);
}

// ================== Combine =================== //

inline void bgc_fp32_rigid_pose3_combine(BGC_FP32_RigidPose3* const combination, const BGC_FP32_RigidPose3* const first, const BGC_FP32_RigidPose3* const second)
{
    bgc_fp32_dual_quaternion_multiply_by_dual_quaternion(&combination->_versor, &second->_versor, &first->_versor);
    _bgc_fp32_rigid_pose3_normalize(combination);
}

inline void bgc_fp64_rigid_pose3_combine(BGC_FP64_RigidPose3* const combination, const BGC_FP64_RigidPose3* const first, const BGC_FP64_RigidPose3* const second)
{
    bgc_fp64_dual_quaternion_multiply_by_dual_quaternion(&combination->_versor, &second->_versor, &first->_versor);
    _bgc_fp64_rigid_pose3_normalize(combination);
}

// ================== Exclude =================== //

inline void bgc_fp32_rigid_pose3_exclude(BGC_FP32_RigidPose3* const difference, const BGC_FP32_RigidPose3* const base, const BGC_FP32_RigidPose3* const excludant)
{
    BGC_FP32_Quaternion dual_part1, dual_part2;

    bgc_fp32_quaternion_multiply_by_conjugate(&dual_part1, &base->_versor.real_part, &excludant->_versor.dual_part);
    bgc_fp32_quaternion_multiply_by_conjugate(&dual_part2, &base->_versor.dual_part, &excludant->_versor.real_part);

    bgc_fp32_quaternion_multiply_by_conjugate(&difference->_versor.real_part, &base->_versor.real_part, &excludant->_versor.real_part);
    bgc_fp32_quaternion_add(&difference->_versor.dual_part, &dual_part1, &dual_part2);

    _bgc_fp32_rigid_pose3_normalize(difference);
}

inline void bgc_fp64_rigid_pose3_exclude(BGC_FP64_RigidPose3* const difference, const BGC_FP64_RigidPose3* const base, const BGC_FP64_RigidPose3* const excludant)
{
    BGC_FP64_Quaternion dual_part1, dual_part2;

    bgc_fp64_quaternion_multiply_by_conjugate(&dual_part1, &base->_versor.real_part, &excludant->_versor.dual_part);
    bgc_fp64_quaternion_multiply_by_conjugate(&dual_part2, &base->_versor.dual_part, &excludant->_versor.real_part);

    bgc_fp64_quaternion_multiply_by_conjugate(&difference->_versor.real_part, &base->_versor.real_part, &excludant->_versor.real_part);
    bgc_fp64_quaternion_add(&difference->_versor.dual_part, &dual_part1, &dual_part2);

    _bgc_fp64_rigid_pose3_normalize(difference);
}

// ============ Get Rotation Matrix ============= //

inline void bgc_fp32_rigid_pose3_get_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_rotation_matrix(matrix, &pose->_versor.real_part);
}

inline void bgc_fp64_rigid_pose3_get_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_rotation_matrix(matrix, &pose->_versor.real_part);
}

// ============= Get Reverse Matrix ============= //

inline void bgc_fp32_rigid_pose3_get_reverse_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_reverse_matrix(matrix, &pose->_versor.real_part);
}

inline void bgc_fp64_rigid_pose3_get_reverse_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_reverse_matrix(matrix, &pose->_versor.real_part);
}

// ================= Get Shift ================== //

inline void bgc_fp32_rigid_pose3_get_shift(BGC_FP32_Vector3* const shift, const BGC_FP32_RigidPose3* const pose)
{
    const BGC_FP32_Quaternion* const real = &pose->_versor.real_part;
    const BGC_FP32_Quaternion* const dual = &pose->_versor.dual_part;

    shift->x = 2.0f * ((dual->x * real->s + dual->z * real->y) - (dual->s * real->x + dual->y * real->z));
    shift->y = 2.0f * ((dual->y * real->s + dual->x * real->z) - (dual->s * real->y + dual->z * real->x));
    shift->z = 2.0f * ((dual->z * real->s + dual->y * real->x) - (dual->s * real->z + dual->x * real->y));
}

inline void bgc_fp64_rigid_pose3_get_shift(BGC_FP64_Vector3* const shift, const BGC_FP64_RigidPose3* const pose)
{
    const BGC_FP64_Quaternion* const real = &pose->_versor.real_part;
    const BGC_FP64_Quaternion* const dual = &pose->_versor.dual_part;

    shift->x = 2.0 * ((dual->x * real->s + dual->z * real->y) - (dual->s * real->x + dual->y * real->z));
    shift->y = 2.0 * ((dual->y * real->s + dual->x * real->z) - (dual->s * real->y + dual->z * real->x));
    shift->z = 2.0 * ((dual->z * real->s + dual->y * real->x) - (dual->s * real->z + dual->x * real->y));
}

// ============= Get Reverse Shift ============= //

inline void bgc_fp32_rigid_pose3_get_reverse_shift(BGC_FP32_Vector3* const shift, const BGC_FP32_RigidPose3* const pose)
{
    const BGC_FP32_Quaternion* const real = &pose->_versor.real_part;
    const BGC_FP32_Quaternion* const dual = &pose->_versor.dual_part;

    shift->x = 2.0f * ((dual->s * real->x - dual->x * real->s) + (dual->z * real->y - dual->y * real->z));
    shift->y = 2.0f * ((dual->s * real->y - dual->y * real->s) + (dual->x * real->z - dual->z * real->x));
    shift->z = 2.0f * ((dual->s * real->z - dual->z * real->s) + (dual->y * real->x - dual->x * real->y));
}

inline void bgc_fp64_rigid_pose3_get_reverse_shift(BGC_FP64_Vector3* const shift, const BGC_FP64_RigidPose3* const pose)
{
    const BGC_FP64_Quaternion* const real = &pose->_versor.real_part;
    const BGC_FP64_Quaternion* const dual = &pose->_versor.dual_part;

    shift->x = 2.0 * ((dual->s * real->x - dual->x * real->s) + (dual->z * real->y - dual->y * real->z));
    shift->y = 2.0 * ((dual->s * real->y - dual->y * real->s) + (dual->x * real->z - dual->z * real->x));
    shift->z = 2.0 * ((dual->s * real->z - dual->z * real->s) + (dual->y * real->x - dual->x * real->y));
}

// ================ Get Affine3 ================= //

inline void bgc_fp32_rigid_pose3_get_affine(BGC_FP32_Affine3* const affine_map, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_shift(&affine_map->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_affine(BGC_FP64_Affine3* const affine_map, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_shift(&affine_map->shift, pose);
}

// ============ Get Reverse Affine3 ============= //

inline void bgc_fp32_rigid_pose3_get_reverse_affine(BGC_FP32_Affine3* const affine_map, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_reverse_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_reverse_shift(&affine_map->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_reverse_affine(BGC_FP64_Affine3* const affine_map, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_reverse_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_reverse_shift(&affine_map->shift, pose);
}

// =============== Get Position3 ================ //

inline void bgc_fp32_rigid_pose3_get_position(BGC_FP32_Position3* const position, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_copy(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_shift(&position->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_position(BGC_FP64_Position3* const position, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_copy(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_shift(&position->shift, pose);
}

// =============== Set Position3 ================ //

inline void bgc_fp32_rigid_pose3_set_position(BGC_FP32_RigidPose3* const pose, const BGC_FP32_Position3* const position)
{
    const BGC_FP32_Quaternion* const versor = &position->turn._versor;
    const BGC_FP32_Vector3* const shift = &position->shift;

    bgc_fp32_quaternion_copy(&pose->_versor.real_part, versor);

    pose->_versor.dual_part.s = -0.5f * (shift->x * versor->x + shift->y * versor->y + shift->z * versor->z);
    pose->_versor.dual_part.x = -0.5f * (shift->z * versor->y - shift->y * versor->z - shift->x * versor->s);
    pose->_versor.dual_part.y = -0.5f * (shift->x * versor->z - shift->z * versor->x - shift->y * versor->s);
    pose->_versor.dual_part.z = -0.5f * (shift->y * versor->x - shift->x * versor->y - shift->z * versor->s);
}

inline void bgc_fp64_rigid_pose3_set_position(BGC_FP64_RigidPose3* const pose, const BGC_FP64_Position3* const position)
{
    const BGC_FP64_Quaternion* const versor = &position->turn._versor;
    const BGC_FP64_Vector3* const shift = &position->shift;

    bgc_fp64_quaternion_copy(&pose->_versor.real_part, versor);

    pose->_versor.dual_part.s = -0.5 * (shift->x * versor->x + shift->y * versor->y + shift->z * versor->z);
    pose->_versor.dual_part.x = -0.5 * (shift->z * versor->y - shift->y * versor->z - shift->x * versor->s);
    pose->_versor.dual_part.y = -0.5 * (shift->x * versor->z - shift->z * versor->x - shift->y * versor->s);
    pose->_versor.dual_part.z = -0.5 * (shift->y * versor->x - shift->x * versor->y - shift->z * versor->s);
}

// =========== Get Reverse Position3 ============ //

inline void bgc_fp32_rigid_pose3_get_reverse_position(BGC_FP32_Position3* const position, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_conjugate(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_reverse_shift(&position->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_reverse_position(BGC_FP64_Position3* const position, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_conjugate(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_reverse_shift(&position->shift, pose);
}

// =========== Set Reverse Position3 ============ //

inline void bgc_fp32_rigid_pose3_set_reverse_position(BGC_FP32_RigidPose3* const pose, const BGC_FP32_Position3* const position)
{
    const BGC_FP32_Quaternion* const versor = &position->turn._versor;
    const BGC_FP32_Vector3* const shift = &position->shift;

    bgc_fp32_quaternion_get_conjugate(&pose->_versor.real_part, versor);

    pose->_versor.dual_part.s = -0.5f * (versor->x * shift->x + versor->y * shift->y + versor->z * shift->z);
    pose->_versor.dual_part.x = -0.5f * (versor->s * shift->x + versor->z * shift->y - versor->y * shift->z);
    pose->_versor.dual_part.y = -0.5f * (versor->s * shift->y + versor->x * shift->z - versor->z * shift->x);
    pose->_versor.dual_part.z = -0.5f * (versor->s * shift->z + versor->y * shift->x - versor->x * shift->y);
}

inline void bgc_fp64_rigid_pose3_set_reverse_position(BGC_FP64_RigidPose3* const pose, const BGC_FP64_Position3* const position)
{
    const BGC_FP64_Quaternion* const versor = &position->turn._versor;
    const BGC_FP64_Vector3* const shift = &position->shift;

    bgc_fp64_quaternion_get_conjugate(&pose->_versor.real_part, versor);

    pose->_versor.dual_part.s = -0.5f * (versor->x * shift->x + versor->y * shift->y + versor->z * shift->z);
    pose->_versor.dual_part.x = -0.5f * (versor->s * shift->x + versor->z * shift->y - versor->y * shift->z);
    pose->_versor.dual_part.y = -0.5f * (versor->s * shift->y + versor->x * shift->z - versor->z * shift->x);
    pose->_versor.dual_part.z = -0.5f * (versor->s * shift->z + versor->y * shift->x - versor->x * shift->y);
}

// ============== Transform Vector ============== //

inline void bgc_fp32_rigid_pose3_transform_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_RigidPose3* const pose, const BGC_FP32_Vector3* const original_vector)
{
    _bgc_fp32_versor_turn_vector(turned_vector, &pose->_versor.real_part, original_vector);
}

inline void bgc_fp64_rigid_pose3_transform_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_RigidPose3* const pose, const BGC_FP64_Vector3* const original_vector)
{
    _bgc_fp64_versor_turn_vector(turned_vector, &pose->_versor.real_part, original_vector);
}

// =========== Transform Vector Back ============ //

inline void bgc_fp32_rigid_pose3_transform_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_RigidPose3* const pose, const BGC_FP32_Vector3* const original_vector)
{
    _bgc_fp32_versor_turn_vector_back(turned_vector, &pose->_versor.real_part, original_vector);
}

inline void bgc_fp64_rigid_pose3_transform_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_RigidPose3* const pose, const BGC_FP64_Vector3* const original_vector)
{
    _bgc_fp64_versor_turn_vector_back(turned_vector, &pose->_versor.real_part, original_vector);
}

#endif