bgc-c/basic-geometry/turn3.h

#ifndef _BGC_VERSOR_H_
#define _BGC_VERSOR_H_

#include <stdint.h>

#include "utilities.h"
#include "angle.h"
#include "vector3.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 {
    BGC_FP32_Quaternion _versor;
} BGC_FP32_Turn3;

typedef struct {
    BGC_FP64_Quaternion _versor;
} BGC_FP64_Turn3;

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

extern const BGC_FP32_Turn3 BGC_FP32_IDLE_TURN3;
extern const BGC_FP64_Turn3 BGC_FP64_IDLE_TURN3;

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

inline void bgc_fp32_turn3_reset(BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_make(&turn->_versor, 1.0f, 0.0f, 0.0f, 0.0f);
}

inline void bgc_fp64_turn3_reset(BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_make(&turn->_versor, 1.0, 0.0, 0.0, 0.0);
}

// ============= Private: Normalize ============= //

void _bgc_fp32_turn3_normalize(BGC_FP32_Turn3* turn, const float square_modulus);

void _bgc_fp64_turn3_normalize(BGC_FP64_Turn3* turn, const double square_modulus);

// ================= Set Values ================= //

inline void bgc_fp32_turn3_set_raw_values(BGC_FP32_Turn3* turn, const float s0, const float x1, const float x2, const float x3)
{
    bgc_fp32_quaternion_make(&turn->_versor, s0, x1, x2, x3);

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

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_turn3_normalize(turn, square_modulus);
    }
}

inline void bgc_fp64_turn3_set_raw_values(BGC_FP64_Turn3* turn, const double s0, const double x1, const double x2, const double x3)
{
    bgc_fp64_quaternion_make(&turn->_versor, s0, x1, x2, x3);

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

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_turn3_normalize(turn, square_modulus);
    }
}

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

inline void bgc_fp32_turn3_get_quaternion(BGC_FP32_Quaternion* quaternion, const BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_copy(quaternion, &turn->_versor);
}

inline void bgc_fp64_turn3_get_quaternion(BGC_FP64_Quaternion* quaternion, const BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_copy(quaternion, &turn->_versor);
}

// =============== Set Quaternion =============== //

inline void bgc_fp32_turn3_set_quaternion(BGC_FP32_Turn3* turn, const BGC_FP32_Quaternion* quaternion)
{
    bgc_fp32_quaternion_copy(&turn->_versor, quaternion);

    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_turn3_normalize(turn, square_modulus);
    }
}

inline void bgc_fp64_turn3_set_quaternion(BGC_FP64_Turn3* turn, const BGC_FP64_Quaternion* quaternion)
{
    bgc_fp64_quaternion_copy(&turn->_versor, quaternion);

    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_turn3_normalize(turn, square_modulus);
    }
}

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

float bgc_fp32_turn3_get_rotation(BGC_FP32_Vector3* axis, const BGC_FP32_Turn3* turn, const int angle_unit);

double bgc_fp64_turn3_get_rotation(BGC_FP64_Vector3* axis, const BGC_FP64_Turn3* turn, const int angle_unit);

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

void bgc_fp32_turn3_set_rotation(BGC_FP32_Turn3* turn, const float x1, const float x2, const float x3, const float angle, const int angle_unit);

void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* turn, const double x1, const double x2, const double x3, const double angle, const int angle_unit);

// ========= Find Direction Difference ========== //

int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* difference, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end);

int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* difference, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end);

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

int bgc_fp32_turn3_make_basis_difference(
    BGC_FP32_Turn3* turn,
    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_turn3_make_basis_difference(
    BGC_FP64_Turn3* turn,
    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_turn3_copy(BGC_FP32_Turn3* destination, const BGC_FP32_Turn3* source)
{
    bgc_fp32_quaternion_copy(&destination->_versor, &source->_versor);
}

inline void bgc_fp64_turn3_copy(BGC_FP64_Turn3* destination, const BGC_FP64_Turn3* source)
{
    bgc_fp64_quaternion_copy(&destination->_versor, &source->_versor);
}

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

inline void bgc_fp32_turn3_swap(BGC_FP32_Turn3* turn1, BGC_FP32_Turn3* turn2)
{
    bgc_fp32_quaternion_swap(&turn1->_versor, &turn2->_versor);
}

inline void bgc_fp64_turn3_swap(BGC_FP64_Turn3* turn1, BGC_FP64_Turn3* turn2)
{
    bgc_fp64_quaternion_swap(&turn1->_versor, &turn2->_versor);
}

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

inline int bgc_fp32_turn3_is_idle(const BGC_FP32_Turn3* turn)
{
    return turn->_versor.x1 * turn->_versor.x1 + turn->_versor.x2 * turn->_versor.x2 + turn->_versor.x3 * turn->_versor.x3 <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_turn3_is_idle(const BGC_FP64_Turn3* turn)
{
    return turn->_versor.x1 * turn->_versor.x1 + turn->_versor.x2 * turn->_versor.x2 + turn->_versor.x3 * turn->_versor.x3 <= BGC_FP64_SQUARE_EPSILON;
}

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

inline void bgc_fp32_turn3_convert_to_fp64(BGC_FP64_Turn3* destination, const BGC_FP32_Turn3* source)
{
    bgc_fp32_quaternion_convert_to_fp64(&destination->_versor, &source->_versor);

    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&destination->_versor);

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_turn3_normalize(destination, square_modulus);
    }
}

inline void bgc_fp64_turn3_convert_to_fp32(BGC_FP32_Turn3* destination, const BGC_FP64_Turn3* source)
{
    bgc_fp64_quaternion_convert_to_fp32(&destination->_versor, &source->_versor);

    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&destination->_versor);

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_turn3_normalize(destination, square_modulus);
    }
}

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

inline void bgc_fp32_turn3_shorten(BGC_FP32_Turn3* turn)
{
    if (turn->_versor.s0 < 0.0f) {
        bgc_fp32_quaternion_revert(&turn->_versor);
    }
}

inline void bgc_fp64_turn3_shorten(BGC_FP64_Turn3* turn)
{
    if (turn->_versor.s0 < 0.0) {
        bgc_fp64_quaternion_revert(&turn->_versor);
    }
}

inline void bgc_fp32_turn3_get_shortened(BGC_FP32_Turn3* shortened, const BGC_FP32_Turn3* turn)
{
    if (turn->_versor.s0 >= 0.0f) {
        bgc_fp32_quaternion_copy(&shortened->_versor, &turn->_versor);
    }
    else {
        bgc_fp32_quaternion_get_reverse(&shortened->_versor, &turn->_versor);
    }
}

inline void bgc_fp64_turn3_get_shortened(BGC_FP64_Turn3* shortened, const BGC_FP64_Turn3* turn)
{
    if (turn->_versor.s0 >= 0.0) {
        bgc_fp64_quaternion_copy(&shortened->_versor, &turn->_versor);
    }
    else {
        bgc_fp64_quaternion_get_reverse(&shortened->_versor, &turn->_versor);
    }
}

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

inline void bgc_fp32_turn3_alternate(BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_revert(&turn->_versor);
}

inline void bgc_fp64_turn3_alternate(BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_revert(&turn->_versor);
}

inline void bgc_fp32_turn3_get_alternative(BGC_FP32_Turn3* alternative, const BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_get_reverse(&alternative->_versor, &turn->_versor);
}

inline void bgc_fp64_turn3_get_alternative(BGC_FP64_Turn3* alternative, const BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_get_reverse(&alternative->_versor, &turn->_versor);
}

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

inline void bgc_fp32_turn3_revert(BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_conjugate(&turn->_versor);
}

inline void bgc_fp64_turn3_revert(BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_conjugate(&turn->_versor);
}

inline void bgc_fp32_turn3_get_reverse(BGC_FP32_Turn3* inverse, const BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_get_conjugate(&inverse->_versor, &turn->_versor);
}

inline void bgc_fp64_turn3_get_reverse(BGC_FP64_Turn3* inverse, const BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_get_conjugate(&inverse->_versor, &turn->_versor);
}

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

void bgc_fp32_turn3_get_exponation(BGC_FP32_Turn3* power, const BGC_FP32_Turn3* base, const float exponent);

void bgc_fp64_turn3_get_exponation(BGC_FP64_Turn3* power, const BGC_FP64_Turn3* base, const double exponent);

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

inline void bgc_fp32_turn3_combine(BGC_FP32_Turn3* combination, const BGC_FP32_Turn3* first, const BGC_FP32_Turn3* second)
{
    bgc_fp32_quaternion_get_product(&combination->_versor, &second->_versor, &first->_versor);

    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&combination->_versor);

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_turn3_normalize(combination, square_modulus);
    }
}

inline void bgc_fp64_turn3_combine(BGC_FP64_Turn3* combination, const BGC_FP64_Turn3* first, const BGC_FP64_Turn3* second)
{
    bgc_fp64_quaternion_get_product(&combination->_versor, &second->_versor, &first->_versor);

    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&combination->_versor);

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_turn3_normalize(combination, square_modulus);
    }
}

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

inline void bgc_fp32_turn3_combine3(BGC_FP32_Turn3* combination, const BGC_FP32_Turn3* first, const BGC_FP32_Turn3* second, const BGC_FP32_Turn3* third)
{
    BGC_FP32_Quaternion product;

    bgc_fp32_quaternion_get_product(&product, &second->_versor, &first->_versor);

    bgc_fp32_quaternion_get_product(&combination->_versor, &third->_versor, &product);

    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&combination->_versor);

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_turn3_normalize(combination, square_modulus);
    }
}

inline void bgc_fp64_turn3_combine3(BGC_FP64_Turn3* combination, const BGC_FP64_Turn3* first, const BGC_FP64_Turn3* second, const BGC_FP64_Turn3* third)
{
    BGC_FP64_Quaternion product;

    bgc_fp64_quaternion_get_product(&product, &second->_versor, &first->_versor);

    bgc_fp64_quaternion_get_product(&combination->_versor, &third->_versor, &product);

    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&combination->_versor);

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_turn3_normalize(combination, square_modulus);
    }
}

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

inline void bgc_fp32_turn3_exclude(BGC_FP32_Turn3* difference, const BGC_FP32_Turn3* base, const BGC_FP32_Turn3* excludant)
{
    bgc_fp32_quaternion_get_product_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor);

    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&difference->_versor);

    if (!bgc_fp32_is_square_unit(square_modulus)) {
        _bgc_fp32_turn3_normalize(difference, square_modulus);
    }
}

inline void bgc_fp64_turn3_exclude(BGC_FP64_Turn3* difference, const BGC_FP64_Turn3* base, const BGC_FP64_Turn3* excludant)
{
    bgc_fp64_quaternion_get_product_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor);

    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&difference->_versor);

    if (!bgc_fp64_is_square_unit(square_modulus)) {
        _bgc_fp64_turn3_normalize(difference, square_modulus);
    }
}

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

void bgc_fp32_turn3_spherically_interpolate(BGC_FP32_Turn3* interpolation, const BGC_FP32_Turn3* start, const BGC_FP32_Turn3* end, const float phase);

void bgc_fp64_turn3_spherically_interpolate(BGC_FP64_Turn3* interpolation, const BGC_FP64_Turn3* start, const BGC_FP64_Turn3* end, const double phase);

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

inline void bgc_fp32_turn3_get_rotation_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_get_rotation_matrix(matrix, &turn->_versor);
}

inline void bgc_fp64_turn3_get_rotation_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_get_rotation_matrix(matrix, &turn->_versor);
}

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

inline void bgc_fp32_turn3_get_reverse_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_get_reverse_matrix(matrix, &turn->_versor);
}

inline void bgc_fp64_turn3_get_reverse_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_get_reverse_matrix(matrix, &turn->_versor);
}

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

inline void bgc_fp32_turn3_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Turn3* turn)
{
    bgc_fp32_quaternion_get_both_matrices(rotation, reverse, &turn->_versor);
}

inline void bgc_fp64_turn3_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Turn3* turn)
{
    bgc_fp64_quaternion_get_both_matrices(rotation, reverse, &turn->_versor);
}

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

inline void bgc_fp32_turn3_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* versor, const BGC_FP32_Vector3* vector)
{
    const float tx1 = 2.0f * (versor->_versor.x2 * vector->x3 - versor->_versor.x3 * vector->x2);
    const float tx2 = 2.0f * (versor->_versor.x3 * vector->x1 - versor->_versor.x1 * vector->x3);
    const float tx3 = 2.0f * (versor->_versor.x1 * vector->x2 - versor->_versor.x2 * vector->x1);

    const float x1 = (vector->x1 + tx1 * versor->_versor.s0) + (versor->_versor.x2 * tx3 - versor->_versor.x3 * tx2);
    const float x2 = (vector->x2 + tx2 * versor->_versor.s0) + (versor->_versor.x3 * tx1 - versor->_versor.x1 * tx3);
    const float x3 = (vector->x3 + tx3 * versor->_versor.s0) + (versor->_versor.x1 * tx2 - versor->_versor.x2 * tx1);

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

inline void bgc_fp64_turn3_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* vector)
{
    const double tx1 = 2.0 * (turn->_versor.x2 * vector->x3 - turn->_versor.x3 * vector->x2);
    const double tx2 = 2.0 * (turn->_versor.x3 * vector->x1 - turn->_versor.x1 * vector->x3);
    const double tx3 = 2.0 * (turn->_versor.x1 * vector->x2 - turn->_versor.x2 * vector->x1);

    const double x1 = (vector->x1 + tx1 * turn->_versor.s0) + (turn->_versor.x2 * tx3 - turn->_versor.x3 * tx2);
    const double x2 = (vector->x2 + tx2 * turn->_versor.s0) + (turn->_versor.x3 * tx1 - turn->_versor.x1 * tx3);
    const double x3 = (vector->x3 + tx3 * turn->_versor.s0) + (turn->_versor.x1 * tx2 - turn->_versor.x2 * tx1);

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

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

inline void bgc_fp32_turn3_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* vector)
{
    const float tx1 = 2.0f * (turn->_versor.x2 * vector->x3 - turn->_versor.x3 * vector->x2);
    const float tx2 = 2.0f * (turn->_versor.x3 * vector->x1 - turn->_versor.x1 * vector->x3);
    const float tx3 = 2.0f * (turn->_versor.x1 * vector->x2 - turn->_versor.x2 * vector->x1);

    const float x1 = (vector->x1 - tx1 * turn->_versor.s0) + (turn->_versor.x2 * tx3 - turn->_versor.x3 * tx2);
    const float x2 = (vector->x2 - tx2 * turn->_versor.s0) + (turn->_versor.x3 * tx1 - turn->_versor.x1 * tx3);
    const float x3 = (vector->x3 - tx3 * turn->_versor.s0) + (turn->_versor.x1 * tx2 - turn->_versor.x2 * tx1);

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

inline void bgc_fp64_turn3_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* vector)
{
    const double tx1 = 2.0 * (turn->_versor.x2 * vector->x3 - turn->_versor.x3 * vector->x2);
    const double tx2 = 2.0 * (turn->_versor.x3 * vector->x1 - turn->_versor.x1 * vector->x3);
    const double tx3 = 2.0 * (turn->_versor.x1 * vector->x2 - turn->_versor.x2 * vector->x1);

    const double x1 = (vector->x1 - tx1 * turn->_versor.s0) + (turn->_versor.x2 * tx3 - turn->_versor.x3 * tx2);
    const double x2 = (vector->x2 - tx2 * turn->_versor.s0) + (turn->_versor.x3 * tx1 - turn->_versor.x1 * tx3);
    const double x3 = (vector->x3 - tx3 * turn->_versor.s0) + (turn->_versor.x1 * tx2 - turn->_versor.x2 * tx1);

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

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

inline int bgc_fp32_turn3_are_close(const BGC_FP32_Turn3* turn1, const BGC_FP32_Turn3* turn2)
{
    BGC_FP32_Quaternion difference;
    bgc_fp32_quaternion_subtract(&difference, &turn1->_versor, &turn2->_versor);
    return bgc_fp32_quaternion_get_square_modulus(&difference) <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_turn3_are_close(const BGC_FP64_Turn3* turn1, const BGC_FP64_Turn3* turn2)
{
    BGC_FP64_Quaternion difference;
    bgc_fp64_quaternion_subtract(&difference, &turn1->_versor, &turn2->_versor);
    return bgc_fp64_quaternion_get_square_modulus(&difference) <= BGC_FP64_SQUARE_EPSILON;
}

#endif