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* pose)
{
    pose->_versor.real_part.s0 = 1.0f;
    pose->_versor.real_part.x1 = 0.0f;
    pose->_versor.real_part.x2 = 0.0f;
    pose->_versor.real_part.x3 = 0.0f;

    pose->_versor.dual_part.s0 = 0.0f;
    pose->_versor.dual_part.x1 = 0.0f;
    pose->_versor.dual_part.x2 = 0.0f;
    pose->_versor.dual_part.x3 = 0.0f;
}

inline void bgc_fp64_rigid_pose3_reset(BGC_FP64_RigidPose3* pose)
{
    pose->_versor.real_part.s0 = 1.0;
    pose->_versor.real_part.x1 = 0.0;
    pose->_versor.real_part.x2 = 0.0;
    pose->_versor.real_part.x3 = 0.0;

    pose->_versor.dual_part.s0 = 0.0;
    pose->_versor.dual_part.x1 = 0.0;
    pose->_versor.dual_part.x2 = 0.0;
    pose->_versor.dual_part.x3 = 0.0;
}

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

inline void _bgc_fp32_rigid_pose3_normalize(BGC_FP32_RigidPose3* 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* 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* 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* 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* 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* 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* 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* 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* 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* 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* 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* 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* pose1, BGC_FP32_RigidPose3* pose2)
{
    bgc_fp32_dual_quaternion_swap(&pose1->_versor, &pose2->_versor);
}

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

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

inline void bgc_fp32_rigid_pose3_convert_to_fp64(BGC_FP64_RigidPose3* 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* 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* pose)
{
    if (pose->_versor.real_part.s0 < 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* pose)
{
    if (pose->_versor.real_part.s0 < 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* shortened, const BGC_FP32_RigidPose3* const pose)
{
    if (pose->_versor.real_part.s0 < 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* shortened, const BGC_FP64_RigidPose3* const pose)
{
    if (pose->_versor.real_part.s0 < 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* 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* 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* 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* 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* 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* pose)
{
    bgc_fp64_quaternion_conjugate(&pose->_versor.real_part);
    bgc_fp64_quaternion_conjugate(&pose->_versor.dual_part);
}

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

inline void bgc_fp32_rigid_pose3_get_reverse(BGC_FP32_RigidPose3* 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(BGC_FP64_RigidPose3* 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* 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* 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* difference, const BGC_FP32_RigidPose3* const base, const BGC_FP32_RigidPose3* const excludant)
{
    BGC_FP32_Quaternion dual_part1, dual_part2;

    _bgc_fp32_restrict_quaternion_multiply_by_conjugate(&dual_part1, &base->_versor.real_part, &excludant->_versor.dual_part);
    _bgc_fp32_restrict_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* difference, const BGC_FP64_RigidPose3* const base, const BGC_FP64_RigidPose3* const excludant)
{
    BGC_FP64_Quaternion dual_part1, dual_part2;

    _bgc_fp64_restrict_quaternion_multiply_by_conjugate(&dual_part1, &base->_versor.real_part, &excludant->_versor.dual_part);
    _bgc_fp64_restrict_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 Outward Matrix ============= //

inline void bgc_fp32_rigid_pose3_get_outward_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_RigidPose3* const pose)
{
    _bgc_fp32_versor_get_rotation_matrix(matrix, &pose->_versor.real_part);
}

inline void bgc_fp64_rigid_pose3_get_outward_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_RigidPose3* const pose)
{
    _bgc_fp64_versor_get_rotation_matrix(matrix, &pose->_versor.real_part);
}

// ============= Get Inward Matrix ============== //

inline void bgc_fp32_rigid_pose3_get_inward_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_RigidPose3* const pose)
{
    _bgc_fp32_versor_get_reverse_matrix(matrix, &pose->_versor.real_part);
}

inline void bgc_fp64_rigid_pose3_get_inward_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_RigidPose3* const pose)
{
    _bgc_fp64_versor_get_reverse_matrix(matrix, &pose->_versor.real_part);
}

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

inline void bgc_fp32_rigid_pose3_get_outer_shift(BGC_FP32_Vector3* 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->x1 = 2.0f * ((dual->x1 * real->s0 + dual->x3 * real->x2) - (dual->s0 * real->x1 + dual->x2 * real->x3));
    shift->x2 = 2.0f * ((dual->x2 * real->s0 + dual->x1 * real->x3) - (dual->s0 * real->x2 + dual->x3 * real->x1));
    shift->x3 = 2.0f * ((dual->x3 * real->s0 + dual->x2 * real->x1) - (dual->s0 * real->x3 + dual->x1 * real->x2));
}

inline void bgc_fp64_rigid_pose3_get_outer_shift(BGC_FP64_Vector3* 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->x1 = 2.0 * ((dual->x1 * real->s0 + dual->x3 * real->x2) - (dual->s0 * real->x1 + dual->x2 * real->x3));
    shift->x2 = 2.0 * ((dual->x2 * real->s0 + dual->x1 * real->x3) - (dual->s0 * real->x2 + dual->x3 * real->x1));
    shift->x3 = 2.0 * ((dual->x3 * real->s0 + dual->x2 * real->x1) - (dual->s0 * real->x3 + dual->x1 * real->x2));
}

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

inline void bgc_fp32_rigid_pose3_get_inner_shift(BGC_FP32_Vector3* 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->x1 = 2.0f * ((dual->s0 * real->x1 - dual->x1 * real->s0) + (dual->x3 * real->x2 - dual->x2 * real->x3));
    shift->x2 = 2.0f * ((dual->s0 * real->x2 - dual->x2 * real->s0) + (dual->x1 * real->x3 - dual->x3 * real->x1));
    shift->x3 = 2.0f * ((dual->s0 * real->x3 - dual->x3 * real->s0) + (dual->x2 * real->x1 - dual->x1 * real->x2));
}

inline void bgc_fp64_rigid_pose3_get_inner_shift(BGC_FP64_Vector3* 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->x1 = 2.0 * ((dual->s0 * real->x1 - dual->x1 * real->s0) + (dual->x3 * real->x2 - dual->x2 * real->x3));
    shift->x2 = 2.0 * ((dual->s0 * real->x2 - dual->x2 * real->s0) + (dual->x1 * real->x3 - dual->x3 * real->x1));
    shift->x3 = 2.0 * ((dual->s0 * real->x3 - dual->x3 * real->s0) + (dual->x2 * real->x1 - dual->x1 * real->x2));
}

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

inline void bgc_fp32_rigid_pose3_get_outward_affine(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* const pose)
{
    _bgc_fp32_versor_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_outer_shift(&affine_map->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_outward_affine(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* const pose)
{
    _bgc_fp64_versor_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_outer_shift(&affine_map->shift, pose);
}

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

inline void bgc_fp32_rigid_pose3_get_inward_affine(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* const pose)
{
    _bgc_fp32_versor_get_reverse_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_inner_shift(&affine_map->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_inward_affine(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* const pose)
{
    _bgc_fp64_versor_get_reverse_matrix(&affine_map->distortion, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_inner_shift(&affine_map->shift, pose);
}

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

inline void bgc_fp32_rigid_pose3_get_outer_position(BGC_FP32_Position3* position, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_copy(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_outer_shift(&position->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_outer_position(BGC_FP64_Position3* position, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_copy(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_outer_shift(&position->shift, pose);
}

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

inline void bgc_fp32_rigid_pose3_set_outer_position(BGC_FP32_RigidPose3* 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.s0 = -0.5f * (shift->x1 * versor->x1 + shift->x2 * versor->x2 + shift->x3 * versor->x3);
    pose->_versor.dual_part.x1 = -0.5f * (shift->x3 * versor->x2 - shift->x2 * versor->x3 - shift->x1 * versor->s0);
    pose->_versor.dual_part.x2 = -0.5f * (shift->x1 * versor->x3 - shift->x3 * versor->x1 - shift->x2 * versor->s0);
    pose->_versor.dual_part.x3 = -0.5f * (shift->x2 * versor->x1 - shift->x1 * versor->x2 - shift->x3 * versor->s0);
}

inline void bgc_fp64_rigid_pose3_set_outer_position(BGC_FP64_RigidPose3* 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.s0 = -0.5 * (shift->x1 * versor->x1 + shift->x2 * versor->x2 + shift->x3 * versor->x3);
    pose->_versor.dual_part.x1 = -0.5 * (shift->x3 * versor->x2 - shift->x2 * versor->x3 - shift->x1 * versor->s0);
    pose->_versor.dual_part.x2 = -0.5 * (shift->x1 * versor->x3 - shift->x3 * versor->x1 - shift->x2 * versor->s0);
    pose->_versor.dual_part.x3 = -0.5 * (shift->x2 * versor->x1 - shift->x1 * versor->x2 - shift->x3 * versor->s0);
}

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

inline void bgc_fp32_rigid_pose3_get_inner_position(BGC_FP32_Position3* position, const BGC_FP32_RigidPose3* const pose)
{
    bgc_fp32_quaternion_get_conjugate(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp32_rigid_pose3_get_inner_shift(&position->shift, pose);
}

inline void bgc_fp64_rigid_pose3_get_inner_position(BGC_FP64_Position3* position, const BGC_FP64_RigidPose3* const pose)
{
    bgc_fp64_quaternion_get_conjugate(&position->turn._versor, &pose->_versor.real_part);
    bgc_fp64_rigid_pose3_get_inner_shift(&position->shift, pose);
}

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

inline void bgc_fp32_rigid_pose3_set_inner_position(BGC_FP32_RigidPose3* 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.s0 = -0.5f * (versor->x1 * shift->x1 + versor->x2 * shift->x2 + versor->x3 * shift->x3);
    pose->_versor.dual_part.x1 = -0.5f * (versor->s0 * shift->x1 + versor->x3 * shift->x2 - versor->x2 * shift->x3);
    pose->_versor.dual_part.x2 = -0.5f * (versor->s0 * shift->x2 + versor->x1 * shift->x3 - versor->x3 * shift->x1);
    pose->_versor.dual_part.x3 = -0.5f * (versor->s0 * shift->x3 + versor->x2 * shift->x1 - versor->x1 * shift->x2);
}

inline void bgc_fp64_rigid_pose3_set_inner_position(BGC_FP64_RigidPose3* 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.s0 = -0.5f * (versor->x1 * shift->x1 + versor->x2 * shift->x2 + versor->x3 * shift->x3);
    pose->_versor.dual_part.x1 = -0.5f * (versor->s0 * shift->x1 + versor->x3 * shift->x2 - versor->x2 * shift->x3);
    pose->_versor.dual_part.x2 = -0.5f * (versor->s0 * shift->x2 + versor->x1 * shift->x3 - versor->x3 * shift->x1);
    pose->_versor.dual_part.x3 = -0.5f * (versor->s0 * shift->x3 + versor->x2 * shift->x1 - versor->x1 * shift->x2);
}

#endif