package Rotations is

package Matrices_3D         is new Matrices    (Dimension => 3);

package Matrices_4D         is new Matrices    (Dimension => 4);

subtype Vector              is Vector_3D;

subtype Quaternion_Rotation is Quaternion_Real;

subtype Matrix_3D           is Matrices_3D.Matrix;

subtype Matrix_4D           is Matrices_4D.Matrix;

subtype Radiants            is Real;

subtype Degrees             is Real;

type Rotation_Order is (RPY, RYP, PRY, PYR, YRP, YPR);

Roll_Axis  : constant Vector := (x => 1.0, y => 0.0, z => 0.0);

Pitch_Axis : constant Vector := (x => 0.0, y => 0.0, z => 1.0);

Yaw_Axis   : constant Vector := (x => 0.0, y => 1.0, z => 0.0);

function To_Radiants 
(
A
: Degrees)
return Radiants;

function To_Degrees  
(
A
: Radiants)
return Degrees;

function To_Rotation 
(
Axis
: Vector;
Rotation_Angle
: Radiants)
return Quaternion_Rotation;

function To_Rotation 
(
Roll_Angle, Pitch_Angle, Yaw_Angle
: Radiants)
return Quaternion_Rotation;

function To_Rotation 
(
Matrix
: Matrix_3D)
return Quaternion_Rotation;

function To_Rotation 
(
Matrix
: Matrix_4D)
return Quaternion_Rotation;

function Zero_Rotation return Quaternion_Rotation;

function Inverse 
(
Quad
: Quaternion_Rotation)
return Quaternion_Rotation;

function Rotate 
(
Current_Rotation, Additional_Rotation
: Quaternion_Rotation)
return Quaternion_Rotation;

function Rotate 
(
Current_Rotation
: Quaternion_Rotation;
Rotation_Axis
: Vector;
Rotation_Angle
: Radiants)
return Quaternion_Rotation;

function Rotate 
(
Current_Vector, Rotation_Axis
: Vector;
Rotation_Angle
: Radiants)
return Vector;

function Rotate 
(
Current_Vector
: Vector;
Apply_Rotation
: Quaternion_Rotation)
return Vector;

function Roll  
(
Quad
: Quaternion_Rotation)
return Radiants;

function Pitch 
(
Quad
: Quaternion_Rotation)
return Radiants;

function Yaw   
(
Quad
: Quaternion_Rotation)
return Radiants;

function Roll  
(
Matrix
: Matrix_3D)
return Radiants;

function Pitch 
(
Matrix
: Matrix_3D)
return Radiants;

function Yaw   
(
Matrix
: Matrix_3D)
return Radiants;

function To_Matrix_3D        
(
Quad
: Quaternion_Rotation)
return Matrix_3D;

function To_Matrix_3D_OpenGL 
(
Quad
: Quaternion_Rotation)
return Matrix_3D;

function To_Matrix_4D        
(
Quad
: Quaternion_Rotation)
return Matrix_4D;

function To_Matrix_3D        
(
Roll_Angle, Pitch_Angle, Yaw_Angle
: Radiants)
return Matrix_3D;

function To_Matrix_3D_OpenGL 
(
Roll_Angle, Pitch_Angle, Yaw_Angle
: Radiants;
Order
: Rotation_Order := RPY;
Column_First
: Boolean        := True)
return Matrix_3D;