crown-engine/engine/core/math/Quaternion.cpp

/*
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.
*/

#include "Matrix3x3.h"
#include "Matrix4x4.h"
#include "Types.h"
#include "MathUtils.h"
#include "Quaternion.h"
#include "Vector3.h"

namespace crown
{

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

//-----------------------------------------------------------------------------
Quaternion::Quaternion()
{
}

//-----------------------------------------------------------------------------
Quaternion::Quaternion(float nx, float ny, float nz, float nw) :
	v(nx, ny, nz),
	w(nw)
{
}

//-----------------------------------------------------------------------------
Quaternion::Quaternion(const Vector3& axis, float angle) :
	v(axis * math::sin(angle * 0.5)),
	w(math::cos(angle * 0.5))
{
}

//-----------------------------------------------------------------------------
void Quaternion::negate()
{
	w = -w;
	v = -v;
}

//-----------------------------------------------------------------------------
void Quaternion::load_identity()
{
	w = 1.0;
	v.x = 0.0;
	v.y = 0.0;
	v.z = 0.0;
}

//-----------------------------------------------------------------------------
float Quaternion::length() const
{
	return math::sqrt(w * w + v.x * v.x + v.y * v.y + v.z * v.z);
}

//-----------------------------------------------------------------------------
void Quaternion::conjugate()
{
	v = -v;
}

//-----------------------------------------------------------------------------
Quaternion Quaternion::get_conjugate() const
{
	return Quaternion(-v, w);
}

//-----------------------------------------------------------------------------
Quaternion Quaternion::get_inverse() const
{
	return get_conjugate() * (1.0 / length());
}

//-----------------------------------------------------------------------------
Matrix3x3 Quaternion::to_matrix3x3() const
{
	const float x = v.x;
	const float y = v.y;
	const float z = v.z;

	Matrix3x3 tmp;

	tmp.m[0] = (float)(1.0 - 2.0*y*y - 2.0*z*z);
	tmp.m[1] = (float)(2.0*x*y + 2.0*w*z);
	tmp.m[2] = (float)(2.0*x*z - 2.0*w*y);
	tmp.m[3] = (float)(2.0*x*y - 2.0*w*z);
	tmp.m[4] = (float)(1.0 - 2.0*x*x - 2.0*z*z);
	tmp.m[5] = (float)(2.0*y*z + 2.0*w*x);
	tmp.m[6] = (float)(2.0*x*z + 2.0*w*y);
	tmp.m[7] = (float)(2.0*y*z - 2.0*w*x);
	tmp.m[8] = (float)(1.0 - 2.0*x*x - 2.0*y*y);

	return tmp;
}

//-----------------------------------------------------------------------------
Matrix4x4 Quaternion::to_matrix4x4() const
{
	const float x = v.x;
	const float y = v.y;
	const float z = v.z;

	Matrix4x4 tmp;

	tmp.m[0] = (float)(1.0 - 2.0*y*y - 2.0*z*z);
	tmp.m[1] = (float)(2.0*x*y + 2.0*w*z);
	tmp.m[2] = (float)(2.0*x*z - 2.0*w*y);
	tmp.m[3] = 0;
	tmp.m[4] = (float)(2.0*x*y - 2.0*w*z);
	tmp.m[5] = (float)(1.0 - 2.0*x*x - 2.0*z*z);
	tmp.m[6] = (float)(2.0*y*z + 2.0*w*x);
	tmp.m[7] = 0.0;
	tmp.m[8] = (float)(2.0*x*z + 2.0*w*y);
	tmp.m[9] = (float)(2.0*y*z - 2.0*w*x);
	tmp.m[10] = (float)(1.0 - 2.0*x*x - 2.0*y*y);
	tmp.m[11] = 0.0;
	tmp.m[12] = 0.0;
	tmp.m[13] = 0.0;
	tmp.m[14] = 0.0;
	tmp.m[15] = 1.0;

	return tmp;
}

//-----------------------------------------------------------------------------
Quaternion Quaternion::operator*(const Quaternion& b) const
{
	Quaternion tmp;

	tmp.w = w * b.w - vector3::dot(v, b.v);
	tmp.v = w * b.v + b.w * v + vector3::cross(b.v, v);

	return tmp;
}

//-----------------------------------------------------------------------------
Quaternion Quaternion::operator*(const float& k) const
{
	Quaternion tmp;

	tmp.w = w * k;
	tmp.v = v * k;

	return tmp;
}

//-----------------------------------------------------------------------------
Quaternion Quaternion::power(float exp)
{
	Quaternion tmp;

	if (math::abs(w) < 0.9999)
	{
		float alpha = math::acos(w); // alpha = theta/2
		float newAlpha = alpha * exp;
		tmp.w = math::cos(newAlpha);
		float mult = math::sin(newAlpha) / math::sin(alpha);
		tmp.v.x = v.x * mult;
		tmp.v.y = v.y * mult;
		tmp.v.z = v.z * mult;
		return tmp;
	}

	tmp.w = w;
	tmp.v = v;

	return tmp;
}

/*
The geometric interpretation of the Quaternion dot product is similar to the interpretation of
the vector dot product; the larger the absolute value of the Quaternion dot product axb, the more
"similar" the angular displacements represented by a and b.
*/
//-----------------------------------------------------------------------------
float dot(const Quaternion& a, const Quaternion& b)
{
	return a.w * b.w + vector3::dot(a.v, b.v);
}

// Spherical Linear interpolation
//-----------------------------------------------------------------------------
Quaternion slerp(const Quaternion& start, const Quaternion& end, float t)
{
	Quaternion delta = end * start.get_inverse();
	delta = delta.power(t);

	return delta * start;
}

} // namespace crown