crown-engine/src/core/math/Mat4.cpp

/*
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.
*/

#include "Assert.h"
#include "Mat3.h"
#include "Types.h"
#include "Mat4.h"
#include "MathUtils.h"
#include "Quat.h"
#include "Vec3.h"
#include "Vec4.h"

namespace crown
{

const Mat4 Mat4::IDENTITY = Mat4(1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0);

//-----------------------------------------------------------------------------
Mat4::Mat4()
{
}

//-----------------------------------------------------------------------------
Mat4::Mat4(real r1c1, real r2c1, real r3c1, real r4c1, real r1c2, real r2c2, real r3c2, real r4c2,
	real r1c3, real r2c3, real r3c3, real r4c3, real r1c4, real r2c4, real r3c4, real r4c4)
{
	m[0] = r1c1;
	m[1] = r2c1;
	m[2] = r3c1;
	m[3] = r4c1;
	m[4] = r1c2;
	m[5] = r2c2;
	m[6] = r3c2;
	m[7] = r4c2;
	m[8] = r1c3;
	m[9] = r2c3;
	m[10] = r3c3;
	m[11] = r4c3;
	m[12] = r1c4;
	m[13] = r2c4;
	m[14] = r3c4;
	m[15] = r4c4;
}

//-----------------------------------------------------------------------------
Mat4::Mat4(const real v[16])
{
	m[0] = v[0];
	m[1] = v[1];
	m[2] = v[2];
	m[3] = v[3];
	m[4] = v[4];
	m[5] = v[5];
	m[6] = v[6];
	m[7] = v[7];
	m[8] = v[8];
	m[9] = v[9];
	m[10] = v[10];
	m[11] = v[11];
	m[12] = v[12];
	m[13] = v[13];
	m[14] = v[14];
	m[15] = v[15];
}

//-----------------------------------------------------------------------------
Mat4::Mat4(const Mat4& a)
{
	m[0] = a.m[0];
	m[1] = a.m[1];
	m[2] = a.m[2];
	m[3] = a.m[3];
	m[4] = a.m[4];
	m[5] = a.m[5];
	m[6] = a.m[6];
	m[7] = a.m[7];
	m[8] = a.m[8];
	m[9] = a.m[9];
	m[10] = a.m[10];
	m[11] = a.m[11];
	m[12] = a.m[12];
	m[13] = a.m[13];
	m[14] = a.m[14];
	m[15] = a.m[15];
}

//-----------------------------------------------------------------------------
Mat4& Mat4::operator=(const Mat4& a)
{
	m[0] = a.m[0];
	m[1] = a.m[1];
	m[2] = a.m[2];
	m[3] = a.m[3];
	m[4] = a.m[4];
	m[5] = a.m[5];
	m[6] = a.m[6];
	m[7] = a.m[7];
	m[8] = a.m[8];
	m[9] = a.m[9];
	m[10] = a.m[10];
	m[11] = a.m[11];
	m[12] = a.m[12];
	m[13] = a.m[13];
	m[14] = a.m[14];
	m[15] = a.m[15];

	return *this;
}

//-----------------------------------------------------------------------------
real Mat4::operator[](uint32_t i) const
{
	ce_assert(i < 16, "Index must be < 16");

	return m[i];
}

//-----------------------------------------------------------------------------
real& Mat4::operator[](uint32_t i)
{
	ce_assert(i < 16, "Index must be < 16");

	return m[i];
}

//-----------------------------------------------------------------------------
real Mat4::operator()(uint32_t row, uint32_t column) const
{
	ce_assert(row < 4 && column < 4, "Row and column must be < 4");

	return m[row + column * 4];
}

//-----------------------------------------------------------------------------
Mat4 Mat4::operator+(const Mat4& a) const
{
	Mat4 tmp;

	tmp.m[0] = m[0] + a.m[0];
	tmp.m[1] = m[1] + a.m[1];
	tmp.m[2] = m[2] + a.m[2];
	tmp.m[3] = m[3] + a.m[3];
	tmp.m[4] = m[4] + a.m[4];
	tmp.m[5] = m[5] + a.m[5];
	tmp.m[6] = m[6] + a.m[6];
	tmp.m[7] = m[7] + a.m[7];
	tmp.m[8] = m[8] + a.m[8];
	tmp.m[9] = m[9] + a.m[9];
	tmp.m[10] = m[10] + a.m[10];
	tmp.m[11] = m[11] + a.m[11];
	tmp.m[12] = m[12] + a.m[12];
	tmp.m[13] = m[13] + a.m[13];
	tmp.m[14] = m[14] + a.m[14];
	tmp.m[14] = m[15] + a.m[15];

	return tmp;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::operator+=(const Mat4& a)
{
	m[0] = m[0] + a.m[0];
	m[1] = m[1] + a.m[1];
	m[2] = m[2] + a.m[2];
	m[3] = m[3] + a.m[3];
	m[4] = m[4] + a.m[4];
	m[5] = m[5] + a.m[5];
	m[6] = m[6] + a.m[6];
	m[7] = m[7] + a.m[7];
	m[8] = m[8] + a.m[8];
	m[9] = m[9] + a.m[9];
	m[10] = m[10] + a.m[10];
	m[11] = m[11] + a.m[11];
	m[12] = m[12] + a.m[12];
	m[13] = m[13] + a.m[13];
	m[14] = m[14] + a.m[14];
	m[14] = m[15] + a.m[15];

	return *this;
}

//-----------------------------------------------------------------------------
Mat4 Mat4::operator-(const Mat4& a) const
{
	Mat4 tmp;

	tmp.m[0] = m[0] - a.m[0];
	tmp.m[1] = m[1] - a.m[1];
	tmp.m[2] = m[2] - a.m[2];
	tmp.m[3] = m[3] - a.m[3];
	tmp.m[4] = m[4] - a.m[4];
	tmp.m[5] = m[5] - a.m[5];
	tmp.m[6] = m[6] - a.m[6];
	tmp.m[7] = m[7] - a.m[7];
	tmp.m[8] = m[8] - a.m[8];
	tmp.m[9] = m[9] - a.m[9];
	tmp.m[10] = m[10] - a.m[10];
	tmp.m[11] = m[11] - a.m[11];
	tmp.m[12] = m[12] - a.m[12];
	tmp.m[13] = m[13] - a.m[13];
	tmp.m[14] = m[14] - a.m[14];
	tmp.m[14] = m[15] - a.m[15];

	return tmp;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::operator-=(const Mat4& a)
{
	m[0] = m[0] - a.m[0];
	m[1] = m[1] - a.m[1];
	m[2] = m[2] - a.m[2];
	m[3] = m[3] - a.m[3];
	m[4] = m[4] - a.m[4];
	m[5] = m[5] - a.m[5];
	m[6] = m[6] - a.m[6];
	m[7] = m[7] - a.m[7];
	m[8] = m[8] - a.m[8];
	m[9] = m[9] - a.m[9];
	m[10] = m[10] - a.m[10];
	m[11] = m[11] - a.m[11];
	m[12] = m[12] - a.m[12];
	m[13] = m[13] - a.m[13];
	m[14] = m[14] - a.m[14];
	m[14] = m[15] - a.m[15];

	return *this;
}

//-----------------------------------------------------------------------------
Mat4 Mat4::operator*(real k) const
{
	Mat4 tmp;

	tmp.m[0] = m[0] * k;
	tmp.m[1] = m[1] * k;
	tmp.m[2] = m[2] * k;
	tmp.m[3] = m[3] * k;
	tmp.m[4] = m[4] * k;
	tmp.m[5] = m[5] * k;
	tmp.m[6] = m[6] * k;
	tmp.m[7] = m[7] * k;
	tmp.m[8] = m[8] * k;
	tmp.m[9] = m[9] * k;
	tmp.m[10] = m[10] * k;
	tmp.m[11] = m[11] * k;
	tmp.m[12] = m[12] * k;
	tmp.m[13] = m[13] * k;
	tmp.m[14] = m[14] * k;
	tmp.m[15] = m[15] * k;

	return tmp;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::operator*=(real k)
{
	m[0] *= k;
	m[1] *= k;
	m[2] *= k;
	m[3] *= k;
	m[4] *= k;
	m[5] *= k;
	m[6] *= k;
	m[7] *= k;
	m[8] *= k;
	m[9] *= k;
	m[10] *= k;
	m[11] *= k;
	m[12] *= k;
	m[13] *= k;
	m[14] *= k;
	m[15] *= k;

	return *this;
}

//-----------------------------------------------------------------------------
Mat4 Mat4::operator/(real k) const
{
	Mat4 tmp;

	k = (real)1.0 / k;

	tmp.m[0] = m[0] * k;
	tmp.m[1] = m[1] * k;
	tmp.m[2] = m[2] * k;
	tmp.m[3] = m[3] * k;
	tmp.m[4] = m[4] * k;
	tmp.m[5] = m[5] * k;
	tmp.m[6] = m[6] * k;
	tmp.m[7] = m[7] * k;
	tmp.m[8] = m[8] * k;
	tmp.m[9] = m[9] * k;
	tmp.m[10] = m[10] * k;
	tmp.m[11] = m[11] * k;
	tmp.m[12] = m[12] * k;
	tmp.m[13] = m[13] * k;
	tmp.m[14] = m[14] * k;
	tmp.m[15] = m[15] * k;

	return tmp;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::operator/=(real k)
{
	k = (real)1.0 / k;

	m[0] *= k;
	m[1] *= k;
	m[2] *= k;
	m[3] *= k;
	m[4] *= k;
	m[5] *= k;
	m[6] *= k;
	m[7] *= k;
	m[8] *= k;
	m[9] *= k;
	m[10] *= k;
	m[11] *= k;
	m[12] *= k;
	m[13] *= k;
	m[14] *= k;
	m[15] *= k;

	return *this;
}

//-----------------------------------------------------------------------------
Vec3 Mat4::operator*(const Vec3& v) const
{
	Vec3 tmp;

	tmp.x = m[0] * v.x + m[4] * v.y + m[8] * v.z + m[12];
	tmp.y = m[1] * v.x + m[5] * v.y + m[9] * v.z + m[13];
	tmp.z = m[2] * v.x + m[6] * v.y + m[10] * v.z + m[14];

	return tmp;
}

//-----------------------------------------------------------------------------
Vec4 Mat4::operator*(const Vec4& v) const
{
	Vec4 tmp;

	tmp.x = m[0] * v.x + m[4] * v.y + m[8] * v.z + m[12] * v.w;
	tmp.y = m[1] * v.x + m[5] * v.y + m[9] * v.z + m[13] * v.w;
	tmp.z = m[2] * v.x + m[6] * v.y + m[10] * v.z + m[14] * v.w;
	tmp.w = m[3] * v.x + m[7] * v.y + m[11] * v.z + m[15] * v.w;

	return tmp;
}

//-----------------------------------------------------------------------------
Mat4 Mat4::operator*(const Mat4& a) const
{
	Mat4 tmp;

	tmp.m[0] = m[0] * a.m[0] + m[4] * a.m[1] + m[8] * a.m[2] + m[12] * a.m[3];
	tmp.m[1] = m[1] * a.m[0] + m[5] * a.m[1] + m[9] * a.m[2] + m[13] * a.m[3];
	tmp.m[2] = m[2] * a.m[0] + m[6] * a.m[1] + m[10] * a.m[2] + m[14] * a.m[3];
	tmp.m[3] = m[3] * a.m[0] + m[7] * a.m[1] + m[11] * a.m[2] + m[15] * a.m[3];

	tmp.m[4] = m[0] * a.m[4] + m[4] * a.m[5] + m[8] * a.m[6] + m[12] * a.m[7];
	tmp.m[5] = m[1] * a.m[4] + m[5] * a.m[5] + m[9] * a.m[6] + m[13] * a.m[7];
	tmp.m[6] = m[2] * a.m[4] + m[6] * a.m[5] + m[10] * a.m[6] + m[14] * a.m[7];
	tmp.m[7] = m[3] * a.m[4] + m[7] * a.m[5] + m[11] * a.m[6] + m[15] * a.m[7];

	tmp.m[8] = m[0] * a.m[8] + m[4] * a.m[9] + m[8] * a.m[10] + m[12] * a.m[11];
	tmp.m[9] = m[1] * a.m[8] + m[5] * a.m[9] + m[9] * a.m[10] + m[13] * a.m[11];
	tmp.m[10] = m[2] * a.m[8] + m[6] * a.m[9] + m[10] * a.m[10] + m[14] * a.m[11];
	tmp.m[11] = m[3] * a.m[8] + m[7] * a.m[9] + m[11] * a.m[10] + m[15] * a.m[11];

	tmp.m[12] = m[0] * a.m[12] + m[4] * a.m[13] + m[8] * a.m[14] + m[12] * a.m[15];
	tmp.m[13] = m[1] * a.m[12] + m[5] * a.m[13] + m[9] * a.m[14] + m[13] * a.m[15];
	tmp.m[14] = m[2] * a.m[12] + m[6] * a.m[13] + m[10] * a.m[14] + m[14] * a.m[15];
	tmp.m[15] = m[3] * a.m[12] + m[7] * a.m[13] + m[11] * a.m[14] + m[15] * a.m[15];

	return tmp;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::operator*=(const Mat4& a)
{
	Mat4 tmp;

	tmp.m[0] = m[0] * a.m[0] + m[4] * a.m[1] + m[8] * a.m[2] + m[12] * a.m[3];
	tmp.m[1] = m[1] * a.m[0] + m[5] * a.m[1] + m[9] * a.m[2] + m[13] * a.m[3];
	tmp.m[2] = m[2] * a.m[0] + m[6] * a.m[1] + m[10] * a.m[2] + m[14] * a.m[3];
	tmp.m[3] = m[3] * a.m[0] + m[7] * a.m[1] + m[11] * a.m[2] + m[15] * a.m[3];

	tmp.m[4] = m[0] * a.m[4] + m[4] * a.m[5] + m[8] * a.m[6] + m[12] * a.m[7];
	tmp.m[5] = m[1] * a.m[4] + m[5] * a.m[5] + m[9] * a.m[6] + m[13] * a.m[7];
	tmp.m[6] = m[2] * a.m[4] + m[6] * a.m[5] + m[10] * a.m[6] + m[14] * a.m[7];
	tmp.m[7] = m[3] * a.m[4] + m[7] * a.m[5] + m[11] * a.m[6] + m[15] * a.m[7];

	tmp.m[8] = m[0] * a.m[8] + m[4] * a.m[9] + m[8] * a.m[10] + m[12] * a.m[11];
	tmp.m[9] = m[1] * a.m[8] + m[5] * a.m[9] + m[9] * a.m[10] + m[13] * a.m[11];
	tmp.m[10] = m[2] * a.m[8] + m[6] * a.m[9] + m[10] * a.m[10] + m[14] * a.m[11];
	tmp.m[11] = m[3] * a.m[8] + m[7] * a.m[9] + m[11] * a.m[10] + m[15] * a.m[11];

	tmp.m[12] = m[0] * a.m[12] + m[4] * a.m[13] + m[8] * a.m[14] + m[12] * a.m[15];
	tmp.m[13] = m[1] * a.m[12] + m[5] * a.m[13] + m[9] * a.m[14] + m[13] * a.m[15];
	tmp.m[14] = m[2] * a.m[12] + m[6] * a.m[13] + m[10] * a.m[14] + m[14] * a.m[15];
	tmp.m[15] = m[3] * a.m[12] + m[7] * a.m[13] + m[11] * a.m[14] + m[15] * a.m[15];

	*this = tmp;

	return *this;
}

Mat4 operator*(real k, const Mat4& a)
{
	return a * k;
}

//-----------------------------------------------------------------------------
void Mat4::build_rotation_x(real radians)
{
	m[0] = 1.0;
	m[1] = 0.0;
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = math::cos(radians);
	m[6] = math::sin(radians);
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = -math::sin(radians);
	m[10] = math::cos(radians);
	m[11] = 0.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = 0.0;
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_rotation_y(real radians)
{
	m[0] = math::cos(radians);
	m[1] = 0.0;
	m[2] = -math::sin(radians);
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = 1.0;
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = math::sin(radians);
	m[9] = 0.0;
	m[10] = math::cos(radians);
	m[11] = 0.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = 0.0;
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_rotation_z(real radians)
{
	m[0] = math::cos(radians);
	m[1] = math::sin(radians);
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = -math::sin(radians);
	m[5] = math::cos(radians);
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = 0.0;
	m[10] = 1.0;
	m[11] = 0.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = 0.0;
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_rotation(const Vec3& n, real radians)
{
	real a = (real)1.0 - math::cos(radians);
	real sin_a = math::sin(radians);
	real cos_a = math::cos(radians);

	m[0] = n.x * n.x * a + cos_a;
	m[1] = n.x * n.y * a + n.z * sin_a;
	m[2] = n.x * n.z * a - n.y * sin_a;
	m[3] = 0.0;
	m[4] = n.x * n.y * a - n.z * sin_a;
	m[5] = n.y * n.y * a + cos_a;
	m[6] = n.y * n.z * a + n.x * sin_a;
	m[7] = 0.0;
	m[8] = n.x * n.z * a + n.y * sin_a;
	m[9] = n.y * n.z * a - n.x * sin_a;
	m[10] = n.z * n.z * a + cos_a;
	m[11] = 0.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = 0.0;
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_projection_perspective_rh(real fovy, real aspect, real near, real far)
{
	double top, right;

	top = math::tan((real)((double)fovy / 360.0 * math::PI)) * (double)near;
	right = top * aspect;

	m[0] = (real)(near / right);
	m[1] = 0.0;
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = (real)(near / top);
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = 0.0;
	m[10] = (real)((far + near) / (near - far));
	m[11] = -1.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = (real)((2.0 * far * near) / (near - far));
	m[15] = 0.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_projection_perspective_lh(real fovy, real aspect, real near, real far)
{
	double top, right;

	top = math::tan((real)((double)fovy / 360.0 * math::PI)) * (double)near;
	right = top * aspect;

	m[0] = (real)(near / right);
	m[1] = 0.0;
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = (real)(near / top);
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = 0.0;
	m[10] = (real)(far / (far - near));
	m[11] = 1.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = (real)((far * near) / (near - far));
	m[15] = 0.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_projection_ortho_rh(real width, real height, real near, real far)
{
	m[0] = (real)2.0 / width;
	m[1] = 0.0;
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = (real)2.0 / height;
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = 0.0;
	m[10] = (real)2 / (near - far);
	m[11] = 0.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = (far + near) / (near - far);
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_projection_ortho_lh(real width, real height, real near, real far)
{
	m[0] = (real)2.0 / width;
	m[1] = 0.0;
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = (real)2.0 / height;
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = 0.0;
	m[10] = (real)2 / (far - near);
	m[11] = 0.0;
	m[12] = 0.0;
	m[13] = 0.0;
	m[14] = near / (near - far);
	m[15] = (real)1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_projection_ortho_2d_rh(real width, real height, real near, real far)
{
	m[0] = (real)2.0 / width;
	m[1] = 0.0;
	m[2] = 0.0;
	m[3] = 0.0;
	m[4] = 0.0;
	m[5] = (real)-2.0 / height;
	m[6] = 0.0;
	m[7] = 0.0;
	m[8] = 0.0;
	m[9] = 0.0;
	m[10] = (real)2.0 / (near - far);
	m[11] = 0.0;
	m[12] = (real)-1.0 + (m[0] * (real)0.375);		// Add 0.375 to acheive
	m[13] =  (real)1.0 + (m[5] * (real)0.375);		// pixel-perfect 2d drawing
	m[14] = near / (near - far);
	m[15] = (real)1.0;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::transpose()
{
	real tmp;

	tmp = m[1];
	m[1] = m[4];
	m[4] = tmp;

	tmp = m[2];
	m[2] = m[8];
	m[8] = tmp;

	tmp = m[3];
	m[3] = m[12];
	m[12] = tmp;

	tmp = m[6];
	m[6] = m[9];
	m[9] = tmp;

	tmp = m[7];
	m[7] = m[13];
	m[13] = tmp;

	tmp = m[11];
	m[11] = m[14];
	m[14] = tmp;

	return *this;
}

//-----------------------------------------------------------------------------
Mat4 Mat4::get_transposed() const
{
	Mat4 tmp;

	tmp.m[0] = m[0];
	tmp.m[1] = m[4];
	tmp.m[2] = m[8];
	tmp.m[3] = m[12];
	tmp.m[4] = m[1];
	tmp.m[5] = m[5];
	tmp.m[6] = m[9];
	tmp.m[7] = m[13];
	tmp.m[8] = m[2];
	tmp.m[9] = m[6];
	tmp.m[10] = m[10];
	tmp.m[11] = m[14];
	tmp.m[12] = m[3];
	tmp.m[13] = m[7];
	tmp.m[14] = m[11];
	tmp.m[15] = m[15];

	return tmp;
}

//-----------------------------------------------------------------------------
void Mat4::build_look_at_rh(const Vec3& pos, const Vec3& target, const Vec3& up)
{
	Vec3 zAxis =  pos - target;
	zAxis.normalize();

	Vec3 xAxis = up.cross(zAxis);
	Vec3 yAxis = zAxis.cross(xAxis);

	m[0] = xAxis.x;
	m[1] = yAxis.x;
	m[2] = zAxis.x;
	m[3] = 0.0;
	m[4] = xAxis.y;
	m[5] = yAxis.y;
	m[6] = zAxis.y;
	m[7] = 0.0;
	m[8] = xAxis.z;
	m[9] = yAxis.z;
	m[10] = zAxis.z;
	m[11] = 0.0;
	m[12] = -pos.dot(xAxis);
	m[13] = -pos.dot(yAxis);
	m[14] = -pos.dot(zAxis);
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_look_at_lh(const Vec3& pos, const Vec3& target, const Vec3& up)
{
	Vec3 zAxis =  target - pos;
	zAxis.normalize();

	Vec3 xAxis = up.cross(zAxis);
	Vec3 yAxis = zAxis.cross(xAxis);

	m[0] = xAxis.x;
	m[1] = yAxis.x;
	m[2] = zAxis.x;
	m[3] = 0.0;
	m[4] = xAxis.y;
	m[5] = yAxis.y;
	m[6] = zAxis.y;
	m[7] = 0.0;
	m[8] = xAxis.z;
	m[9] = yAxis.z;
	m[10] = zAxis.z;
	m[11] = 0.0;
	m[12] = -pos.dot(xAxis);
	m[13] = -pos.dot(yAxis);
	m[14] = -pos.dot(zAxis);
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_viewpoint_billboard(const Vec3& pos, const Vec3& target, const Vec3& up)
{
	Vec3 zAxis = target - pos;
	zAxis.normalize();

	Vec3 xAxis = up.cross(zAxis).normalize();
	Vec3 yAxis = zAxis.cross(xAxis).normalize();

	m[0] = xAxis.x;
	m[1] = xAxis.y;
	m[2] = xAxis.z;
	m[3] = 0.0;
	m[4] = yAxis.x;
	m[5] = yAxis.y;
	m[6] = yAxis.z;
	m[7] = 0.0;
	m[8] = zAxis.x;
	m[9] = zAxis.y;
	m[10] = zAxis.z;
	m[11] = 0.0;
	m[12] = pos.x;
	m[13] = pos.y;
	m[14] = pos.z;
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
void Mat4::build_axis_billboard(const Vec3& pos, const Vec3& target, const Vec3& axis)
{
	Vec3 zAxis = target - pos;

	Vec3 xAxis = axis.cross(zAxis).normalize();
	zAxis = axis.cross(xAxis).normalize();
	const Vec3& yAxis = axis;

	m[0] = xAxis.x;
	m[1] = xAxis.y;
	m[2] = xAxis.z;
	m[3] = 0.0;
	m[4] = yAxis.x;
	m[5] = yAxis.y;
	m[6] = yAxis.z;
	m[7] = 0.0;
	m[8] = zAxis.x;
	m[9] = zAxis.y;
	m[10] = zAxis.z;
	m[11] = 0.0;
	m[12] = pos.x;
	m[13] = pos.y;
	m[14] = pos.z;
	m[15] = 1.0;
}

//-----------------------------------------------------------------------------
real Mat4::get_determinant() const
{
	real det;

	real m02m07_m06m03 = m[2] * m[7] - m[6] * m[3];
	real m02m11_m10m03 = m[2] * m[11] - m[10] * m[3];
	real m02m15_m14m03 = m[2] * m[15] - m[14] * m[3];
	real m06m11_m10m07 = m[6] * m[11] - m[10] * m[7];
	real m06m15_m14m07 = m[6] * m[15] - m[14] * m[7];
	real m10m15_m14m11 = m[10] * m[15] - m[14] * m[11];

	det = 	+ m[0] * (m[5] * m10m15_m14m11 - m[9] * m06m15_m14m07 + m[13] * m06m11_m10m07)
			- m[4] * (m[1] * m10m15_m14m11 - m[9] * m02m15_m14m03 + m[13] * m02m11_m10m03)
			+ m[8] * (m[1] * m06m15_m14m07 - m[5] * m02m15_m14m03 + m[13] * m02m07_m06m03)
			- m[12] * (m[1] * m06m11_m10m07 - m[5] * m02m11_m10m03 + m[9] * m02m07_m06m03);

	return det;
}

//-----------------------------------------------------------------------------
Mat4& Mat4::invert()
{
	Mat4 mat;
	real det;

	real m01m06_m05m02 = m[1] * m[6] - m[5] * m[2];
	real m01m07_m05m03 = m[1] * m[7] - m[5] * m[3];
	real m01m10_m09m02 = m[1] * m[10] - m[9] * m[2];
	real m01m11_m09m03 = m[1] * m[11] - m[9] * m[3];
	real m01m14_m13m02 = m[1] * m[14] - m[13] * m[2];
	real m01m15_m13m03 = m[1] * m[15] - m[13] * m[3];
	real m02m07_m06m03 = m[2] * m[7] - m[6] * m[3];
	real m02m11_m10m03 = m[2] * m[11] - m[10] * m[3];
	real m02m15_m14m03 = m[2] * m[15] - m[14] * m[3];
	real m05m10_m09m06 = m[5] * m[10] - m[9] * m[6];
	real m05m11_m09m07 = m[5] * m[11] - m[9] * m[7];
	real m05m14_m13m06 = m[5] * m[14] - m[13] * m[6];
	real m05m15_m13m07 = m[5] * m[15] - m[13] * m[7];
	real m06m11_m10m07 = m[6] * m[11] - m[10] * m[7];
	real m06m15_m14m07 = m[6] * m[15] - m[14] * m[7];
	real m09m14_m13m10 = m[9] * m[14] - m[13] * m[10];
	real m09m15_m13m11 = m[9] * m[15] - m[13] * m[11];
	real m10m15_m14m11 = m[10] * m[15] - m[14] * m[11];

	mat.m[0] = (+ m[5] * m10m15_m14m11 - m[9] * m06m15_m14m07 + m[13] * m06m11_m10m07);
	mat.m[1] = (+ m[1] * m10m15_m14m11 - m[9] * m02m15_m14m03 + m[13] * m02m11_m10m03);
	mat.m[2] = (+ m[1] * m06m15_m14m07 - m[5] * m02m15_m14m03 + m[13] * m02m07_m06m03);
	mat.m[3] = (+ m[1] * m06m11_m10m07 - m[5] * m02m11_m10m03 + m[9] * m02m07_m06m03);

	det = m[0] * mat.m[0] - m[4] * mat.m[1] + m[8] * mat.m[2] - m[12] * mat.m[3];
	det = (real)1.0 / det;

	mat.m[4] = (+ m[4] * m10m15_m14m11 - m[8] * m06m15_m14m07 + m[12] * m06m11_m10m07);
	mat.m[5] = (+ m[0] * m10m15_m14m11 - m[8] * m02m15_m14m03 + m[12] * m02m11_m10m03);
	mat.m[6] = (+ m[0] * m06m15_m14m07 - m[4] * m02m15_m14m03 + m[12] * m02m07_m06m03);
	mat.m[7] = (+ m[0] * m06m11_m10m07 - m[4] * m02m11_m10m03 + m[8] * m02m07_m06m03);
	mat.m[8] = (+ m[4] * m09m15_m13m11 - m[8] * m05m15_m13m07 + m[12] * m05m11_m09m07);
	mat.m[9] = (+ m[0] * m09m15_m13m11 - m[8] * m01m15_m13m03 + m[12] * m01m11_m09m03);
	mat.m[10] = (+ m[0] * m05m15_m13m07 - m[4] * m01m15_m13m03 + m[12] * m01m07_m05m03);
	mat.m[11] = (+ m[0] * m05m11_m09m07 - m[4] * m01m11_m09m03 + m[8] * m01m07_m05m03);
	mat.m[12] = (+ m[4] * m09m14_m13m10 - m[8] * m05m14_m13m06 + m[12] * m05m10_m09m06);
	mat.m[13] = (+ m[0] * m09m14_m13m10 - m[8] * m01m14_m13m02 + m[12] * m01m10_m09m02);
	mat.m[14] = (+ m[0] * m05m14_m13m06 - m[4] * m01m14_m13m02 + m[12] * m01m06_m05m02);
	mat.m[15] = (+ m[0] * m05m10_m09m06 - m[4] * m01m10_m09m02 + m[8] * m01m06_m05m02);

	m[0] = + mat.m[0] * det;
	m[1] = - mat.m[1] * det;
	m[2] = + mat.m[2] * det;
	m[3] = - mat.m[3] * det;
	m[4] = - mat.m[4] * det;
	m[5] = + mat.m[5] * det;
	m[6] = - mat.m[6] * det;
	m[7] = + mat.m[7] * det;
	m[8] = + mat.m[8] * det;
	m[9] = - mat.m[9] * det;
	m[10] = + mat.m[10] * det;
	m[11] = - mat.m[11] * det;
	m[12] = - mat.m[12] * det;
	m[13] = + mat.m[13] * det;
	m[14] = - mat.m[14] * det;
	m[15] = + mat.m[15] * det;

	return *this;
}

//-----------------------------------------------------------------------------
inline Mat4 Mat4::get_inverted() const
{
	Mat4 tmp(*this);

	return tmp.invert();
}

//-----------------------------------------------------------------------------
void Mat4::load_identity()
{
	m[0] = m[5] = m[10] = m[15] = 1.0;
	m[1] = m[2] = m[3] = m[4] = m[6] = m[7] = m[8] = m[9] = m[11] = m[12] = m[13] = m[14] = 0.0;
}

//-----------------------------------------------------------------------------
Vec3 Mat4::get_translation() const
{
	Vec3 tmp;

	tmp.x = m[12];
	tmp.y = m[13];
	tmp.z = m[14];

	return tmp;
}

//-----------------------------------------------------------------------------
void Mat4::set_translation(const Vec3& trans)
{
	m[12] = trans.x;
	m[13] = trans.y;
	m[14] = trans.z;
}

//-----------------------------------------------------------------------------
Vec3 Mat4::get_scale() const
{
	Vec3 tmp;

	tmp.x = m[0];
	tmp.y = m[5];
	tmp.z = m[10];

	return tmp;
}

//-----------------------------------------------------------------------------
void Mat4::set_scale(const Vec3& scale)
{
	m[0] = scale.x;
	m[5] = scale.y;
	m[10] = scale.z;
}

//-----------------------------------------------------------------------------
real* Mat4::to_float_ptr()
{
	return &m[0];
}

//-----------------------------------------------------------------------------
const real* Mat4::to_float_ptr() const
{
	return &m[0];
}

//-----------------------------------------------------------------------------
Mat3 Mat4::to_mat3() const
{
	Mat3 tmp;

	tmp.m[0] = m[0];
	tmp.m[1] = m[1];
	tmp.m[2] = m[2];
	tmp.m[3] = m[4];
	tmp.m[4] = m[5];
	tmp.m[5] = m[6];
	tmp.m[6] = m[8];
	tmp.m[7] = m[9];
	tmp.m[8] = m[10];

	return tmp;
}

//-----------------------------------------------------------------------------
Quat Mat4::to_quat() const
{
	Quat tmp;
	real fourWSquaredMinusOne = m[0] + m[5] + m[10];
	real fourXSquaredMinusOne = m[0] - m[5] - m[10];
	real fourYSquaredMinusOne = -m[0] + m[5] - m[10];
	real fourZSquaredMinusOne = -m[0] - m[5] + m[10];
	real fourMaxSquaredMinusOne = fourWSquaredMinusOne;
	uint32_t index = 0;

	if (fourXSquaredMinusOne > fourMaxSquaredMinusOne)
	{
		fourMaxSquaredMinusOne = fourXSquaredMinusOne;
		index = 1;
	}

	if (fourYSquaredMinusOne > fourMaxSquaredMinusOne)
	{
		fourMaxSquaredMinusOne = fourYSquaredMinusOne;
		index = 2;
	}

	if (fourZSquaredMinusOne > fourMaxSquaredMinusOne)
	{
		fourMaxSquaredMinusOne = fourZSquaredMinusOne;
		index = 3;
	}

	real biggest = math::sqrt(fourMaxSquaredMinusOne + (real)1.0) * (real)0.5;
	real mult = (real)0.25 / biggest;

	switch (index)
	{
		case 0:
			tmp.w = biggest;
			tmp.v.x = (-m[9] + m[6]) * mult;
			tmp.v.y = (-m[2] + m[8]) * mult;
			tmp.v.z = (-m[4] + m[1]) * mult;
			break;
		case 1:
			tmp.v.x = biggest;
			tmp.w = (-m[9] + m[6]) * mult;
			tmp.v.y = (-m[4] - m[1]) * mult;
			tmp.v.z = (-m[2] - m[8]) * mult;
			break;
		case 2:
			tmp.v.y = biggest;
			tmp.w = (-m[2] + m[8]) * mult;
			tmp.v.x = (-m[4] - m[1]) * mult;
			tmp.v.z = (-m[9] - m[6]) * mult;
			break;
		case 3:
			tmp.v.z = biggest;
			tmp.w = (-m[4] + m[1]) * mult;
			tmp.v.x = (-m[2] - m[8]) * mult;
			tmp.v.y = (-m[9] - m[6]) * mult;
			break;
	}

	return tmp;
}

} // namespace crown