crown-engine/engine/core/math/Mat4.h

/*
Copyright (c) 2013 Daniele Bartolini, Michele Rossi
Copyright (c) 2012 Daniele Bartolini, Simone Boscaratto

Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:

The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
*/

#pragma once

#include "Types.h"

namespace crown
{

class Mat3;
class Quat;
class Vec3;
class Vec4;

/// Column-major 4x4 matrix.
/// 
/// The engine uses column vectors for coordinate space transformations
/// so you'll have to specify transformations in reverse order.
/// e.g. (rotation * translation * vector) will produce the result of first translating
/// and then rotating the vector.
/// Also note that a column major matrix needs to be placed to the left of a
/// vector by matrix multiplication, so, to multiply a vector by a matrix you'll have
/// to write something like: matrix * vector. Since we are also using column vectors, inverting
/// the operands would result in an impossible operation.
/// 
/// @a verbatim:
///   X base vector
///     | Y base vector
///     |   | Z base vector
///     |   |   | Translation vector
///     |   |   |   |
/// 1 [ Xx  Yx  Zx  Tx ]
/// 2 | Xy  Yy  Zy  Ty |
/// 3 | Xz  Yz  Zz  Tz |
/// 4 [ 0   0   0   1  ]
///     1   2   3   4
class Mat4
{

public:

	float				m[16];

	/// Does nothing for efficiency.
						Mat4();	

	/// Constructs from a set of float
						Mat4(float r1c1, float r2c1, float r3c1, float r4c1,
								float r1c2, float r2c2, float r3c2, float r4c2,
								float r1c3, float r2c3, float r3c3, float r4c3,
								float r1c4, float r2c4, float r3c4, float r4c4);

	/// Constructs from rotation @a r and position @a p.
						Mat4(const Quat& r, const Vec3& p);
	
	/// Contructs from the @a v array
						Mat4(const float v[16]);						
						Mat4(const Mat4& a);					

	/// Assignment operator (copies the data)
	Mat4&				operator=(const Mat4& a);					

	/// Random access by index
	float				operator[](uint32_t i) const;

	/// Random access by index					
	float&				operator[](uint32_t i);							

	float				operator()(uint32_t row, uint32_t column) const;	//!< Random access by row/column pair

	Mat4				operator+(const Mat4& a) const;
	Mat4&				operator+=(const Mat4& a);					
	Mat4				operator-(const Mat4& a) const;				
	Mat4&				operator-=(const Mat4& a);					
	Mat4				operator*(float k) const;				
	Mat4&				operator*=(float k);							
	Mat4				operator/(float k) const;					
	Mat4&				operator/=(float k);							
	Vec3				operator*(const Vec3& v) const;				
	Vec4				operator*(const Vec4& v) const;				
	Mat4				operator*(const Mat4& a) const;			
	Mat4&				operator*=(const Mat4& a);

	/// For simmetry
	friend Mat4			operator*(float k, const Mat4& a);			

	/// Builds a rotation matrix about the X axis of @a radians radians
	void				build_rotation_x(float radians);

	/// Builds a rotation matrix about the Y axis of "radians" radians	
	void				build_rotation_y(float radians);	

	/// Builds a rotation matrix about the Z axis of @a radians radians			
	void				build_rotation_z(float radians);		

	/// Builds a rotation matrix about an arbitrary axis of "radians" radians		
	void				build_rotation(const Vec3& n, float radians);

	/// Builds a perspetive projection matrix suited to Right-Handed coordinate systems
	void				build_projection_perspective_rh(float fovy, float aspect, float near, float far);

	/// Builds a perspective projection matrix suited to Left-Handed coordinate systems	
	void				build_projection_perspective_lh(float fovy, float aspect, float near, float far);

	/// Builds an orthographic projection matrix suited to Right-Handed coordinate systems	
	void				build_projection_ortho_rh(float width, float height, float near, float far);

	/// Builds an orthographic projection matrix suited to Left-Handed coordinate systems		
	void				build_projection_ortho_lh(float width, float height, float near, float far);	

	/// Builds a 2d orthographic projection matrix suited to Right-Handed coordinate systems	
	void				build_projection_ortho_2d_rh(float width, float height, float near, float far);	

	/// Builds a "Righ-Handed look-at" matrix from a position, a target, and an up vector
	void				build_look_at_rh(const Vec3& pos, const Vec3& target, const Vec3& up);

	/// Builds a "Left-Handed look-at" matrix from a position, a target, and an up vector	
	void				build_look_at_lh(const Vec3& pos, const Vec3& target, const Vec3& up);

	/// Builds a "Viewpoint-Oriented billboard" matrix which can be used to make an object face a specific point in space	
	void				build_viewpoint_billboard(const Vec3& pos, const Vec3& target, const Vec3& up);	

	/// Builds a "Arbitrary-Axis billboard" matrix which can be used to make an object face a specific point in space
	void				build_axis_billboard(const Vec3& pos, const Vec3& target, const Vec3& axis);	

	Mat4&				transpose();								
	Mat4				get_transposed() const;						
	float				get_determinant() const;					
	Mat4&				invert();									
	Mat4				get_inverted() const;						

	/// Builds the identity matrix
	void				load_identity();							

	/// Returns a Vec3 containing the matrix's x base vector.
	Vec3				x() const;

	/// Returns a Vec3 containing the matrix's y base vector.
	Vec3				y() const;

	/// Returns a Vec3 containing the matrix's z base vector.
	Vec3				z() const;

	/// Sets the matrix's x base vector.
	void				set_x(const Vec3& x);

	/// Sets the matrix's y base vector.
	void				set_y(const Vec3& y);

	/// Sets the matrix's z base vector.
	void				set_z(const Vec3& z);

	/// Returns a Vec3 containing the matrix's translation portion
	Vec3				translation() const;	

	/// Fills the matrix's translation portion values contained in @a trans				
	void				set_translation(const Vec3& trans);			

	/// Returns a Vec3 containing the matrix's scale portion
	Vec3				get_scale() const;

	/// Fills the matrix's scale portion with the values contained in @a scale							
	void				set_scale(const Vec3& scale);				

	/// Returns the pointer to the matrix's data
	float*				to_float_ptr();

	/// Returns the pointer to the matrix's data								
	const float*		to_float_ptr() const;

	/// Returns a 3x3 matrix according to the matrix's rotation portion						
	Mat3				to_mat3() const;

	/// Returns a quaternion according to the matrix's rotation portion							
	Quat				to_quat() const;							

	static const Mat4	IDENTITY;
};

} // namespace crown