#ifndef _BGC_VERSOR_H_
#define _BGC_VERSOR_H_

#include <stdint.h>

#include "utilities.h"
#include "angle.h"
#include "vector3.h"
#include "rotation3.h"
#include "matrix3x3.h"
#include "quaternion.h"

#define BGC_SOME_TURN 1
#define BGC_ZERO_TURN 0
#define BGC_OPPOSITE -1

#define BGC_ERROR_PRIMARY_DIRECTION_UNKNOWN -3001
#define BGC_ERROR_PRIMARY_VECTOR_IS_ZERO -3002

#define BGC_ERROR_AUXILIARY_DIRECTION_UNKNOWN -3011
#define BGC_ERROR_AUXILIARY_VECTOR_IS_ZERO -3012

#define BGC_ERROR_DIRECTIONS_PARALLEL -3021
#define BGC_ERROR_VECTORS_PARALLEL -3022

// =================== Types ==================== //

typedef struct {
    float _s0, _x1, _x2, _x3;
} BGC_FP32_Versor;

typedef struct {
    double _s0, _x1, _x2, _x3;
} BGC_FP64_Versor;

// ================= Constants ================== //

extern const BGC_FP32_Versor BGC_FP32_IDLE_VERSOR;
extern const BGC_FP64_Versor BGC_FP64_IDLE_VERSOR;

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

inline void bgc_fp32_versor_reset(BGC_FP32_Versor* versor)
{
    versor->_s0 = 1.0f;
    versor->_x1 = 0.0f;
    versor->_x2 = 0.0f;
    versor->_x3 = 0.0f;
}

inline void bgc_fp64_versor_reset(BGC_FP64_Versor* versor)
{
    versor->_s0 = 1.0;
    versor->_x1 = 0.0;
    versor->_x2 = 0.0;
    versor->_x3 = 0.0;
}

// ==================== Set ===================== //

void _bgc_fp32_versor_normalize(BGC_FP32_Versor* twin);

void _bgc_fp64_versor_normalize(BGC_FP64_Versor* twin);

inline void bgc_fp32_versor_make(BGC_FP32_Versor* versor, const float s0, const float x1, const float x2, const float x3)
{
    versor->_s0 = s0;
    versor->_x1 = x1;
    versor->_x2 = x2;
    versor->_x3 = x3;

    const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_versor_normalize(versor);
    }
}

inline void bgc_fp64_versor_make(BGC_FP64_Versor* versor, const double s0, const double x1, const double x2, const double x3)
{
    versor->_s0 = s0;
    versor->_x1 = x1;
    versor->_x2 = x2;
    versor->_x3 = x3;

    const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_versor_normalize(versor);
    }
}

// ================== Set Turn ================== //

void bgc_fp32_versor_make_for_turn(BGC_FP32_Versor* versor, const float x1, const float x2, const float x3, const float angle, const int unit);

void bgc_fp64_versor_make_for_turn(BGC_FP64_Versor* versor, const double x1, const double x2, const double x3, const double angle, const int unit);

// ================ Set Rotation ================ //

inline void bgc_fp32_versor_make_for_rotation(BGC_FP32_Versor* versor, const BGC_FP32_Rotation3* rotation)
{
    bgc_fp32_versor_make_for_turn(versor, rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS);
}

inline void bgc_fp64_versor_make_for_rotation(BGC_FP64_Versor* versor, const BGC_FP64_Rotation3* rotation)
{
    bgc_fp64_versor_make_for_turn(versor, rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS);
}

// ========= Make Direction Difference ========== //

int bgc_fp32_versor_make_direction_difference(BGC_FP32_Versor* difference, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end);

int bgc_fp64_versor_make_direction_difference(BGC_FP64_Versor* difference, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end);

// =============== Set Directions =============== //

int bgc_fp32_versor_make_basis_difference(
    BGC_FP32_Versor* versor,
    const BGC_FP32_Vector3* initial_primary_direction,
    const BGC_FP32_Vector3* initial_auxiliary_direction,
    const BGC_FP32_Vector3* final_primary_direction,
    const BGC_FP32_Vector3* final_auxiliary_direction
);

int bgc_fp64_versor_make_basis_difference(
    BGC_FP64_Versor* versor,
    const BGC_FP64_Vector3* initial_primary_direction,
    const BGC_FP64_Vector3* initial_auxiliary_direction,
    const BGC_FP64_Vector3* final_primary_direction,
    const BGC_FP64_Vector3* final_auxiliary_direction
);

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

inline void bgc_fp32_versor_copy(BGC_FP32_Versor* destination, const BGC_FP32_Versor* source)
{
    destination->_s0 = source->_s0;
    destination->_x1 = source->_x1;
    destination->_x2 = source->_x2;
    destination->_x3 = source->_x3;
}

inline void bgc_fp64_versor_copy(BGC_FP64_Versor* destination, const BGC_FP64_Versor* source)
{
    destination->_s0 = source->_s0;
    destination->_x1 = source->_x1;
    destination->_x2 = source->_x2;
    destination->_x3 = source->_x3;
}

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

inline void bgc_fp32_versor_swap(BGC_FP32_Versor* versor1, BGC_FP32_Versor* versor2)
{
    const float s0 = versor1->_s0;
    const float x1 = versor1->_x1;
    const float x2 = versor1->_x2;
    const float x3 = versor1->_x3;

    versor1->_s0 = versor2->_s0;
    versor1->_x1 = versor2->_x1;
    versor1->_x2 = versor2->_x2;
    versor1->_x3 = versor2->_x3;

    versor2->_s0 = s0;
    versor2->_x1 = x1;
    versor2->_x2 = x2;
    versor2->_x3 = x3;
}

inline void bgc_fp64_versor_swap(BGC_FP64_Versor* versor1, BGC_FP64_Versor* versor2)
{
    const double s0 = versor1->_s0;
    const double x1 = versor1->_x1;
    const double x2 = versor1->_x2;
    const double x3 = versor1->_x3;

    versor1->_s0 = versor2->_s0;
    versor1->_x1 = versor2->_x1;
    versor1->_x2 = versor2->_x2;
    versor1->_x3 = versor2->_x3;

    versor2->_s0 = s0;
    versor2->_x1 = x1;
    versor2->_x2 = x2;
    versor2->_x3 = x3;
}

// ================= Comparison ================= //

inline int bgc_fp32_versor_is_idle(const BGC_FP32_Versor* versor)
{
    return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_versor_is_idle(const BGC_FP64_Versor* versor)
{
    return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_FP64_SQUARE_EPSILON;
}

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

inline void bgc_fp32_versor_convert_to_fp64(BGC_FP64_Versor* destination, const BGC_FP32_Versor* source)
{
    bgc_fp64_versor_make(
        destination,
        source->_s0,
        source->_x1,
        source->_x2,
        source->_x3
    );
}

inline void bgc_fp64_versor_convert_to_fp32(BGC_FP32_Versor* destination, const BGC_FP64_Versor* source)
{
    bgc_fp32_versor_make(
        destination,
        (float)source->_s0,
        (float)source->_x1,
        (float)source->_x2,
        (float)source->_x3
    );
}

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

inline void bgc_fp32_versor_shorten(BGC_FP32_Versor* versor)
{
    if (versor->_s0 < 0.0f) {
        versor->_s0 = -versor->_s0;
        versor->_x1 = -versor->_x1;
        versor->_x2 = -versor->_x2;
        versor->_x3 = -versor->_x3;
    }
}

inline void bgc_fp64_versor_shorten(BGC_FP64_Versor* versor)
{
    if (versor->_s0 < 0.0) {
        versor->_s0 = -versor->_s0;
        versor->_x1 = -versor->_x1;
        versor->_x2 = -versor->_x2;
        versor->_x3 = -versor->_x3;
    }
}

inline void bgc_fp32_versor_get_shortened(BGC_FP32_Versor* shortened, const BGC_FP32_Versor* versor)
{
    if (versor->_s0 >= 0.0f) {
        shortened->_s0 = versor->_s0;
        shortened->_x1 = versor->_x1;
        shortened->_x2 = versor->_x2;
        shortened->_x3 = versor->_x3;
        return;
    }

    shortened->_s0 = -versor->_s0;
    shortened->_x1 = -versor->_x1;
    shortened->_x2 = -versor->_x2;
    shortened->_x3 = -versor->_x3;
}

inline void bgc_fp64_versor_get_shortened(BGC_FP64_Versor* shortened, const BGC_FP64_Versor* versor)
{
    if (versor->_s0 >= 0.0) {
        shortened->_s0 = versor->_s0;
        shortened->_x1 = versor->_x1;
        shortened->_x2 = versor->_x2;
        shortened->_x3 = versor->_x3;
        return;
    }

    shortened->_s0 = -versor->_s0;
    shortened->_x1 = -versor->_x1;
    shortened->_x2 = -versor->_x2;
    shortened->_x3 = -versor->_x3;
}

// ================== Negative ================== //

inline void bgc_fp32_versor_alternate(BGC_FP32_Versor* versor)
{
    versor->_s0 = -versor->_s0;
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_fp64_versor_alternate(BGC_FP64_Versor* versor)
{
    versor->_s0 = -versor->_s0;
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_fp32_versor_get_alternative(BGC_FP32_Versor* alternative, const BGC_FP32_Versor* versor)
{
    alternative->_s0 = -versor->_s0;
    alternative->_x1 = -versor->_x1;
    alternative->_x2 = -versor->_x2;
    alternative->_x3 = -versor->_x3;
}

inline void bgc_fp64_versor_get_alternative(BGC_FP64_Versor* alternative, const BGC_FP64_Versor* versor)
{
    alternative->_s0 = -versor->_s0;
    alternative->_x1 = -versor->_x1;
    alternative->_x2 = -versor->_x2;
    alternative->_x3 = -versor->_x3;
}

// =================== Invert =================== //

inline void bgc_fp32_versor_revert(BGC_FP32_Versor* versor)
{
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_fp64_versor_revert(BGC_FP64_Versor* versor)
{
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_fp32_versor_get_reverse(BGC_FP32_Versor* inverse, const BGC_FP32_Versor* versor)
{
    inverse->_s0 = versor->_s0;
    inverse->_x1 = -versor->_x1;
    inverse->_x2 = -versor->_x2;
    inverse->_x3 = -versor->_x3;
}

inline void bgc_fp64_versor_get_reverse(BGC_FP64_Versor* inverse, const BGC_FP64_Versor* versor)
{
    inverse->_s0 = versor->_s0;
    inverse->_x1 = -versor->_x1;
    inverse->_x2 = -versor->_x2;
    inverse->_x3 = -versor->_x3;
}

// =============== Get Exponation =============== //

void bgc_fp32_versor_get_exponation(BGC_FP32_Versor* power, const BGC_FP32_Versor* base, const float exponent);

void bgc_fp64_versor_get_exponation(BGC_FP64_Versor* power, const BGC_FP64_Versor* base, const double exponent);

// ================ Combination ================= //

inline void bgc_fp32_versor_combine(BGC_FP32_Versor* combination, const BGC_FP32_Versor* first, const BGC_FP32_Versor* second)
{
    bgc_fp32_versor_make(
        combination,
        (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
        (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
        (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
        (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2)
    );
}

inline void bgc_fp64_versor_combine(BGC_FP64_Versor* combination, const BGC_FP64_Versor* first, const BGC_FP64_Versor* second)
{
    bgc_fp64_versor_make(
        combination,
        (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
        (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
        (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
        (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2)
    );
}

// ============ Combination of three ============ //

inline void bgc_fp32_versor_combine3(BGC_FP32_Versor* combination, const BGC_FP32_Versor* first, const BGC_FP32_Versor* second, const BGC_FP32_Versor* third)
{
    const float s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
    const float x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
    const float x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
    const float x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);

    bgc_fp32_versor_make(
        combination,
        (third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
        (third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
        (third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
        (third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2)
    );
}

inline void bgc_fp64_versor_combine3(BGC_FP64_Versor* combination, const BGC_FP64_Versor* first, const BGC_FP64_Versor* second, const BGC_FP64_Versor* third)
{
    const double s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
    const double x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
    const double x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
    const double x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);

    bgc_fp64_versor_make(
        combination,
        (third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
        (third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
        (third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
        (third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2)
    );
}

// ================= Exclusion ================== //

inline void bgc_fp32_versor_exclude(BGC_FP32_Versor* difference, const BGC_FP32_Versor* base, const BGC_FP32_Versor* excludant)
{
    bgc_fp32_versor_make(
        difference,
        (base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
        (base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
        (base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
        (base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2)
    );
}

inline void bgc_fp64_versor_exclude(BGC_FP64_Versor* difference, const BGC_FP64_Versor* base, const BGC_FP64_Versor* excludant)
{
    bgc_fp64_versor_make(
        difference,
        (base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
        (base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
        (base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
        (base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2)
    );
}

// ============ Sphere Interpolation ============ //

void bgc_fp32_versor_spherically_interpolate(BGC_FP32_Versor* interpolation, const BGC_FP32_Versor* start, const BGC_FP32_Versor* end, const float phase);

void bgc_fp64_versor_spherically_interpolate(BGC_FP64_Versor* interpolation, const BGC_FP64_Versor* start, const BGC_FP64_Versor* end, const double phase);

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

void bgc_fp32_versor_get_rotation(BGC_FP32_Rotation3* rotation, const BGC_FP32_Versor* versor);

void bgc_fp64_versor_get_rotation(BGC_FP64_Rotation3* rotation, const BGC_FP64_Versor* versor);

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

inline void bgc_fp32_versor_get_rotation_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Versor* versor)
{
    const float s0s0 = versor->_s0 * versor->_s0;
    const float x1x1 = versor->_x1 * versor->_x1;
    const float x2x2 = versor->_x2 * versor->_x2;
    const float x3x3 = versor->_x3 * versor->_x3;

    const float s0x1 = versor->_s0 * versor->_x1;
    const float s0x2 = versor->_s0 * versor->_x2;
    const float s0x3 = versor->_s0 * versor->_x3;
    const float x1x2 = versor->_x1 * versor->_x2;
    const float x1x3 = versor->_x1 * versor->_x3;
    const float x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0f * (x1x2 - s0x3);
    matrix->r2c3 = 2.0f * (x2x3 - s0x1);
    matrix->r3c1 = 2.0f * (x1x3 - s0x2);

    matrix->r2c1 = 2.0f * (x1x2 + s0x3);
    matrix->r3c2 = 2.0f * (x2x3 + s0x1);
    matrix->r1c3 = 2.0f * (x1x3 + s0x2);
}

inline void bgc_fp64_versor_get_rotation_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Versor* versor)
{
    const double s0s0 = versor->_s0 * versor->_s0;
    const double x1x1 = versor->_x1 * versor->_x1;
    const double x2x2 = versor->_x2 * versor->_x2;
    const double x3x3 = versor->_x3 * versor->_x3;

    const double s0x1 = versor->_s0 * versor->_x1;
    const double s0x2 = versor->_s0 * versor->_x2;
    const double s0x3 = versor->_s0 * versor->_x3;
    const double x1x2 = versor->_x1 * versor->_x2;
    const double x1x3 = versor->_x1 * versor->_x3;
    const double x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0 * (x1x2 - s0x3);
    matrix->r2c3 = 2.0 * (x2x3 - s0x1);
    matrix->r3c1 = 2.0 * (x1x3 - s0x2);

    matrix->r2c1 = 2.0 * (x1x2 + s0x3);
    matrix->r3c2 = 2.0 * (x2x3 + s0x1);
    matrix->r1c3 = 2.0 * (x1x3 + s0x2);
}

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

inline void bgc_fp32_versor_get_reverse_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Versor* versor)
{
    const float s0s0 = versor->_s0 * versor->_s0;
    const float x1x1 = versor->_x1 * versor->_x1;
    const float x2x2 = versor->_x2 * versor->_x2;
    const float x3x3 = versor->_x3 * versor->_x3;

    const float s0x1 = versor->_s0 * versor->_x1;
    const float s0x2 = versor->_s0 * versor->_x2;
    const float s0x3 = versor->_s0 * versor->_x3;
    const float x1x2 = versor->_x1 * versor->_x2;
    const float x1x3 = versor->_x1 * versor->_x3;
    const float x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0f * (x1x2 + s0x3);
    matrix->r2c3 = 2.0f * (x2x3 + s0x1);
    matrix->r3c1 = 2.0f * (x1x3 + s0x2);

    matrix->r2c1 = 2.0f * (x1x2 - s0x3);
    matrix->r3c2 = 2.0f * (x2x3 - s0x1);
    matrix->r1c3 = 2.0f * (x1x3 - s0x2);
}

inline void bgc_fp64_versor_get_reverse_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Versor* versor)
{
    const double s0s0 = versor->_s0 * versor->_s0;
    const double x1x1 = versor->_x1 * versor->_x1;
    const double x2x2 = versor->_x2 * versor->_x2;
    const double x3x3 = versor->_x3 * versor->_x3;

    const double s0x1 = versor->_s0 * versor->_x1;
    const double s0x2 = versor->_s0 * versor->_x2;
    const double s0x3 = versor->_s0 * versor->_x3;
    const double x1x2 = versor->_x1 * versor->_x2;
    const double x1x3 = versor->_x1 * versor->_x3;
    const double x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0 * (x1x2 + s0x3);
    matrix->r2c3 = 2.0 * (x2x3 + s0x1);
    matrix->r3c1 = 2.0 * (x1x3 + s0x2);

    matrix->r2c1 = 2.0 * (x1x2 - s0x3);
    matrix->r3c2 = 2.0 * (x2x3 - s0x1);
    matrix->r1c3 = 2.0 * (x1x3 - s0x2);
}

// ============= Get Both Matrixes ============== //

inline void bgc_fp32_versor_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Versor* versor)
{
    bgc_fp32_versor_get_reverse_matrix(reverse, versor);
    bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
}

inline void bgc_fp64_versor_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Versor* versor)
{
    bgc_fp64_versor_get_reverse_matrix(reverse, versor);
    bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
}

// ================ Turn Vector ================= //

inline void bgc_fp32_versor_turn_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Versor* versor, const BGC_FP32_Vector3* vector)
{
    const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const float x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const float x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const float x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    turned_vector->x1 = x1;
    turned_vector->x2 = x2;
    turned_vector->x3 = x3;
}

inline void bgc_fp64_versor_turn_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Versor* versor, const BGC_FP64_Vector3* vector)
{
    const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const double x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const double x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const double x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    turned_vector->x1 = x1;
    turned_vector->x2 = x2;
    turned_vector->x3 = x3;
}

// ============== Turn Vector Back ============== //

inline void bgc_fp32_versor_turn_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Versor* versor, const BGC_FP32_Vector3* vector)
{
    const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const float x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const float x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const float x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    turned_vector->x1 = x1;
    turned_vector->x2 = x2;
    turned_vector->x3 = x3;
}

inline void bgc_fp64_versor_turn_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Versor* versor, const BGC_FP64_Vector3* vector)
{
    const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const double x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const double x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const double x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    turned_vector->x1 = x1;
    turned_vector->x2 = x2;
    turned_vector->x3 = x3;
}

// ================== Are Close ================= //

inline int bgc_fp32_versor_are_close(const BGC_FP32_Versor* versor1, const BGC_FP32_Versor* versor2)
{
    const float ds0 = versor1->_s0 - versor2->_s0;
    const float dx1 = versor1->_x1 - versor2->_x1;
    const float dx2 = versor1->_x2 - versor2->_x2;
    const float dx3 = versor1->_x3 - versor2->_x3;

    return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_versor_are_close(const BGC_FP64_Versor* versor1, const BGC_FP64_Versor* versor2)
{
    const double ds0 = versor1->_s0 - versor2->_s0;
    const double dx1 = versor1->_x1 - versor2->_x1;
    const double dx2 = versor1->_x2 - versor2->_x2;
    const double dx3 = versor1->_x3 - versor2->_x3;

    return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_FP64_SQUARE_EPSILON;
}

#endif