#ifndef _BGC_TYPES_H_INCLUDED_
#define _BGC_TYPES_H_INCLUDED_

// =================== Vector2 ================== //

typedef struct
{
    float x1, x2;
} BGC_FP32_Vector2;

typedef struct
{
    double x1, x2;
} BGC_FP64_Vector2;

// ================== Vector3 =================== //

typedef struct
{
    float x1, x2, x3;
} BGC_FP32_Vector3;

typedef struct
{
    double x1, x2, x3;
} BGC_FP64_Vector3;

// ================== Matrix2x2 ================= //

typedef struct {
    float r1c1, r1c2;
    float r2c1, r2c2;
} BGC_FP32_Matrix2x2;

typedef struct {
    double r1c1, r1c2;
    double r2c1, r2c2;
} BGC_FP64_Matrix2x2;

// ================== Matrix2x3 ================= //

typedef struct {
    float r1c1, r1c2;
    float r2c1, r2c2;
    float r3c1, r3c2;
} BGC_FP32_Matrix2x3;

typedef struct {
    double r1c1, r1c2;
    double r2c1, r2c2;
    double r3c1, r3c2;
} BGC_FP64_Matrix2x3;

// ================== Matrix3x2 ================= //

typedef struct {
    float r1c1, r1c2, r1c3;
    float r2c1, r2c2, r2c3;
} BGC_FP32_Matrix3x2;

typedef struct {
    double r1c1, r1c2, r1c3;
    double r2c1, r2c2, r2c3;
} BGC_FP64_Matrix3x2;

// ================== Matrix3x3 ================= //

typedef struct {
    float r1c1, r1c2, r1c3;
    float r2c1, r2c2, r2c3;
    float r3c1, r3c2, r3c3;
} BGC_FP32_Matrix3x3;

typedef struct {
    double r1c1, r1c2, r1c3;
    double r2c1, r2c2, r2c3;
    double r3c1, r3c2, r3c3;
} BGC_FP64_Matrix3x3;

// ================ Affine Map 2D ================ //

typedef struct {
    BGC_FP32_Matrix2x2 distortion;
    BGC_FP32_Vector2 shift;
} BGC_FP32_Affine2;

typedef struct {
    BGC_FP64_Matrix2x2 distortion;
    BGC_FP64_Vector2 shift;
} BGC_FP64_Affine2;

// ================ Affine Map 3D ================ //

typedef struct {
    BGC_FP32_Matrix3x3 distortion;
    BGC_FP32_Vector3 shift;
} BGC_FP32_Affine3;

typedef struct {
    BGC_FP64_Matrix3x3 distortion;
    BGC_FP64_Vector3 shift;
} BGC_FP64_Affine3;

// =============== Complex Number =============== //

typedef struct
{
    float real, imaginary;
} BGC_FP32_Complex;

typedef struct
{
    double real, imaginary;
} BGC_FP64_Complex;

// =================== Turn2 ==================== //

typedef struct
{
    float _cos, _sin;
} BGC_FP32_Turn2;

typedef struct
{
    double _cos, _sin;
} BGC_FP64_Turn2;

// ================= Quaternion ================= //

typedef struct {
    float s0, x1, x2, x3;
} BGC_FP32_Quaternion;

typedef struct {
    double s0, x1, x2, x3;
} BGC_FP64_Quaternion;

// =================== Turn3 ==================== //

typedef struct {
    BGC_FP32_Quaternion _versor;
} BGC_FP32_Turn3;

typedef struct {
    BGC_FP64_Quaternion _versor;
} BGC_FP64_Turn3;

// =================== Slerp3 =================== //

typedef struct {
    BGC_FP32_Quaternion _cosine_weight, _sine_weight;
    float radians;
} BGC_FP32_Slerp3;

typedef struct {
    BGC_FP64_Quaternion _cosine_weight, _sine_weight;
    double radians;
} BGC_FP64_Slerp3;

// ================= Position2 ================== //

typedef struct {
    BGC_FP32_Turn2 turn;
    BGC_FP32_Vector2 shift;
} BGC_FP32_Position2;

typedef struct {
    BGC_FP64_Turn2 turn;
    BGC_FP64_Vector2 shift;
} BGC_FP64_Position2;

// ================= Position3 ================== //

typedef struct {
    BGC_FP32_Turn3 turn;
    BGC_FP32_Vector3 shift;
} BGC_FP32_Position3;

typedef struct {
    BGC_FP64_Turn3 turn;
    BGC_FP64_Vector3 shift;
} BGC_FP64_Position3;

// ================ Dual Number ================= //

typedef struct {
    float real_part, dual_part;
} BGC_FP32_DualNumber;

typedef struct {
    double real_part, dual_part;
} BGC_FP64_DualNumber;

// ================ Dual Vector ================= //

typedef struct {
    BGC_FP32_Vector3 real_part, dual_part;
} BGC_FP32_DualVector3;

typedef struct {
    BGC_FP64_Vector3 real_part, dual_part;
} BGC_FP64_DualVector3;

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

typedef struct {
    BGC_FP32_Quaternion real_part, dual_part;
} BGC_FP32_DualQuaternion;

typedef struct {
    BGC_FP64_Quaternion real_part, dual_part;
} BGC_FP64_DualQuaternion;

// ================ Rigid Pose3 ================= //

typedef struct {
    BGC_FP32_DualQuaternion _versor;
} BGC_FP32_RigidPose3;

typedef struct {
    BGC_FP64_DualQuaternion _versor;
} BGC_FP64_RigidPose3;

#endif