minetest/irr/include/quaternion.h

// Copyright (C) 2002-2012 Nikolaus Gebhardt
// This file is part of the "Irrlicht Engine".
// For conditions of distribution and use, see copyright notice in irrlicht.h

#pragma once

#include "irrTypes.h"
#include "irrMath.h"
#include "matrix4.h"
#include "vector3d.h"

// NOTE: You *only* need this when updating an application from Irrlicht before 1.8 to Irrlicht 1.8 or later.
// Between Irrlicht 1.7 and Irrlicht 1.8 the quaternion-matrix conversions changed.
// Before the fix they had mixed left- and right-handed rotations.
// To test if your code was affected by the change enable IRR_TEST_BROKEN_QUATERNION_USE and try to compile your application.
// This defines removes those functions so you get compile errors anywhere you use them in your code.
// For every line with a compile-errors you have to change the corresponding lines like that:
// - When you pass the matrix to the quaternion constructor then replace the matrix by the transposed matrix.
// - For uses of getMatrix() you have to use quaternion::getMatrix_transposed instead.
// #define IRR_TEST_BROKEN_QUATERNION_USE

namespace irr
{
namespace core
{

//! Quaternion class for representing rotations.
/** It provides cheap combinations and avoids gimbal locks.
Also useful for interpolations. */
class quaternion
{
public:
	//! Default Constructor
	constexpr quaternion() :
			X(0.0f), Y(0.0f), Z(0.0f), W(1.0f) {}

	//! Constructor
	constexpr quaternion(f32 x, f32 y, f32 z, f32 w) :
			X(x), Y(y), Z(z), W(w) {}

	//! Constructor which converts Euler angles (radians) to a quaternion
	quaternion(f32 x, f32 y, f32 z);

	//! Constructor which converts Euler angles (radians) to a quaternion
	quaternion(const vector3df &vec);

#ifndef IRR_TEST_BROKEN_QUATERNION_USE
	//! Constructor which converts a matrix to a quaternion
	quaternion(const matrix4 &mat);
#endif

	//! Equality operator
	constexpr bool operator==(const quaternion &other) const
	{
		return ((X == other.X) &&
				(Y == other.Y) &&
				(Z == other.Z) &&
				(W == other.W));
	}

	//! inequality operator
	constexpr bool operator!=(const quaternion &other) const
	{
		return !(*this == other);
	}

#ifndef IRR_TEST_BROKEN_QUATERNION_USE
	//! Matrix assignment operator
	inline quaternion &operator=(const matrix4 &other);
#endif

	//! Add operator
	quaternion operator+(const quaternion &other) const;

	//! Multiplication operator
	//! Be careful, unfortunately the operator order here is opposite of that in CMatrix4::operator*
	quaternion operator*(const quaternion &other) const;

	//! Multiplication operator with scalar
	quaternion operator*(f32 s) const;

	//! Multiplication operator with scalar
	quaternion &operator*=(f32 s);

	//! Multiplication operator
	vector3df operator*(const vector3df &v) const;

	//! Multiplication operator
	quaternion &operator*=(const quaternion &other);

	//! Calculates the dot product
	inline f32 dotProduct(const quaternion &other) const;

	//! Sets new quaternion
	inline quaternion &set(f32 x, f32 y, f32 z, f32 w);

	//! Sets new quaternion based on Euler angles (radians)
	inline quaternion &set(f32 x, f32 y, f32 z);

	//! Sets new quaternion based on Euler angles (radians)
	inline quaternion &set(const core::vector3df &vec);

	//! Sets new quaternion from other quaternion
	inline quaternion &set(const core::quaternion &quat);

	//! returns if this quaternion equals the other one, taking floating point rounding errors into account
	inline bool equals(const quaternion &other,
			const f32 tolerance = ROUNDING_ERROR_f32) const;

	//! Normalizes the quaternion
	inline quaternion &normalize();

#ifndef IRR_TEST_BROKEN_QUATERNION_USE
	//! Creates a matrix from this quaternion
	matrix4 getMatrix() const;
#endif
	//! Faster method to create a rotation matrix, you should normalize the quaternion before!
	void getMatrixFast(matrix4 &dest) const;

	//! Creates a matrix from this quaternion
	void getMatrix(matrix4 &dest, const core::vector3df &translation = core::vector3df()) const;

	/*!
		Creates a matrix from this quaternion
		Rotate about a center point
		shortcut for
		core::quaternion q;
		q.rotationFromTo ( vin[i].Normal, forward );
		q.getMatrixCenter ( lookat, center, newPos );

		core::matrix4 m2;
		m2.setInverseTranslation ( center );
		lookat *= m2;

		core::matrix4 m3;
		m2.setTranslation ( newPos );
		lookat *= m3;

	*/
	void getMatrixCenter(matrix4 &dest, const core::vector3df &center, const core::vector3df &translation) const;

	//! Creates a matrix from this quaternion
	inline void getMatrix_transposed(matrix4 &dest) const;

	//! Inverts this quaternion
	quaternion &makeInverse();

	//! Set this quaternion to the linear interpolation between two quaternions
	/** NOTE: lerp result is *not* a normalized quaternion. In most cases
	you will want to use lerpN instead as most other quaternion functions expect
	to work with a normalized quaternion.
	\param q1 First quaternion to be interpolated.
	\param q2 Second quaternion to be interpolated.
	\param time Progress of interpolation. For time=0 the result is
	q1, for time=1 the result is q2. Otherwise interpolation
	between q1 and q2. Result is not normalized.
	*/
	quaternion &lerp(quaternion q1, quaternion q2, f32 time);

	//! Set this quaternion to the linear interpolation between two quaternions and normalize the result
	/**
	\param q1 First quaternion to be interpolated.
	\param q2 Second quaternion to be interpolated.
	\param time Progress of interpolation. For time=0 the result is
	q1, for time=1 the result is q2. Otherwise interpolation
	between q1 and q2. Result is normalized.
	*/
	quaternion &lerpN(quaternion q1, quaternion q2, f32 time);

	//! Set this quaternion to the result of the spherical interpolation between two quaternions
	/** \param q1 First quaternion to be interpolated.
	\param q2 Second quaternion to be interpolated.
	\param time Progress of interpolation. For time=0 the result is
	q1, for time=1 the result is q2. Otherwise interpolation
	between q1 and q2.
	\param threshold To avoid inaccuracies at the end (time=1) the
	interpolation switches to linear interpolation at some point.
	This value defines how much of the remaining interpolation will
	be calculated with lerp. Everything from 1-threshold up will be
	linear interpolation.
	*/
	quaternion &slerp(quaternion q1, quaternion q2,
			f32 time, f32 threshold = .05f);

	//! Set this quaternion to represent a rotation from angle and axis.
	/** Axis must be unit length.
	The quaternion representing the rotation is
	q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k).
	\param angle Rotation Angle in radians.
	\param axis Rotation axis. */
	quaternion &fromAngleAxis(f32 angle, const vector3df &axis);

	//! Fills an angle (radians) around an axis (unit vector)
	void toAngleAxis(f32 &angle, core::vector3df &axis) const;

	//! Output this quaternion to an Euler angle (radians)
	void toEuler(vector3df &euler) const;

	//! Set quaternion to identity
	quaternion &makeIdentity();

	//! Set quaternion to represent a rotation from one vector to another.
	quaternion &rotationFromTo(const vector3df &from, const vector3df &to);

	//! Quaternion elements.
	f32 X; // vectorial (imaginary) part
	f32 Y;
	f32 Z;
	f32 W; // real part
};

// Constructor which converts Euler angles to a quaternion
inline quaternion::quaternion(f32 x, f32 y, f32 z)
{
	set(x, y, z);
}

// Constructor which converts Euler angles to a quaternion
inline quaternion::quaternion(const vector3df &vec)
{
	set(vec.X, vec.Y, vec.Z);
}

#ifndef IRR_TEST_BROKEN_QUATERNION_USE
// Constructor which converts a matrix to a quaternion
inline quaternion::quaternion(const matrix4 &mat)
{
	(*this) = mat;
}
#endif

#ifndef IRR_TEST_BROKEN_QUATERNION_USE
// matrix assignment operator
inline quaternion &quaternion::operator=(const matrix4 &m)
{
	const f32 diag = m[0] + m[5] + m[10] + 1;

	if (diag > 0.0f) {
		const f32 scale = sqrtf(diag) * 2.0f; // get scale from diagonal

		// TODO: speed this up
		X = (m[6] - m[9]) / scale;
		Y = (m[8] - m[2]) / scale;
		Z = (m[1] - m[4]) / scale;
		W = 0.25f * scale;
	} else {
		if (m[0] > m[5] && m[0] > m[10]) {
			// 1st element of diag is greatest value
			// find scale according to 1st element, and double it
			const f32 scale = sqrtf(1.0f + m[0] - m[5] - m[10]) * 2.0f;

			// TODO: speed this up
			X = 0.25f * scale;
			Y = (m[4] + m[1]) / scale;
			Z = (m[2] + m[8]) / scale;
			W = (m[6] - m[9]) / scale;
		} else if (m[5] > m[10]) {
			// 2nd element of diag is greatest value
			// find scale according to 2nd element, and double it
			const f32 scale = sqrtf(1.0f + m[5] - m[0] - m[10]) * 2.0f;

			// TODO: speed this up
			X = (m[4] + m[1]) / scale;
			Y = 0.25f * scale;
			Z = (m[9] + m[6]) / scale;
			W = (m[8] - m[2]) / scale;
		} else {
			// 3rd element of diag is greatest value
			// find scale according to 3rd element, and double it
			const f32 scale = sqrtf(1.0f + m[10] - m[0] - m[5]) * 2.0f;

			// TODO: speed this up
			X = (m[8] + m[2]) / scale;
			Y = (m[9] + m[6]) / scale;
			Z = 0.25f * scale;
			W = (m[1] - m[4]) / scale;
		}
	}

	normalize();
	return *this;
}
#endif

// multiplication operator
inline quaternion quaternion::operator*(const quaternion &other) const
{
	quaternion tmp;

	tmp.W = (other.W * W) - (other.X * X) - (other.Y * Y) - (other.Z * Z);
	tmp.X = (other.W * X) + (other.X * W) + (other.Y * Z) - (other.Z * Y);
	tmp.Y = (other.W * Y) + (other.Y * W) + (other.Z * X) - (other.X * Z);
	tmp.Z = (other.W * Z) + (other.Z * W) + (other.X * Y) - (other.Y * X);

	return tmp;
}

// multiplication operator
inline quaternion quaternion::operator*(f32 s) const
{
	return quaternion(s * X, s * Y, s * Z, s * W);
}

// multiplication operator
inline quaternion &quaternion::operator*=(f32 s)
{
	X *= s;
	Y *= s;
	Z *= s;
	W *= s;
	return *this;
}

// multiplication operator
inline quaternion &quaternion::operator*=(const quaternion &other)
{
	return (*this = other * (*this));
}

// add operator
inline quaternion quaternion::operator+(const quaternion &b) const
{
	return quaternion(X + b.X, Y + b.Y, Z + b.Z, W + b.W);
}

#ifndef IRR_TEST_BROKEN_QUATERNION_USE
// Creates a matrix from this quaternion
inline matrix4 quaternion::getMatrix() const
{
	core::matrix4 m;
	getMatrix(m);
	return m;
}
#endif

//! Faster method to create a rotation matrix, you should normalize the quaternion before!
inline void quaternion::getMatrixFast(matrix4 &dest) const
{
	// TODO:
	// gpu quaternion skinning => fast Bones transform chain O_O YEAH!
	// http://www.mrelusive.com/publications/papers/SIMD-From-Quaternion-to-Matrix-and-Back.pdf
	dest[0] = 1.0f - 2.0f * Y * Y - 2.0f * Z * Z;
	dest[1] = 2.0f * X * Y + 2.0f * Z * W;
	dest[2] = 2.0f * X * Z - 2.0f * Y * W;
	dest[3] = 0.0f;

	dest[4] = 2.0f * X * Y - 2.0f * Z * W;
	dest[5] = 1.0f - 2.0f * X * X - 2.0f * Z * Z;
	dest[6] = 2.0f * Z * Y + 2.0f * X * W;
	dest[7] = 0.0f;

	dest[8] = 2.0f * X * Z + 2.0f * Y * W;
	dest[9] = 2.0f * Z * Y - 2.0f * X * W;
	dest[10] = 1.0f - 2.0f * X * X - 2.0f * Y * Y;
	dest[11] = 0.0f;

	dest[12] = 0.f;
	dest[13] = 0.f;
	dest[14] = 0.f;
	dest[15] = 1.f;
}

/*!
	Creates a matrix from this quaternion
*/
inline void quaternion::getMatrix(matrix4 &dest,
		const core::vector3df &center) const
{
	// ok creating a copy may be slower, but at least avoid internal
	// state chance (also because otherwise we cannot keep this method "const").

	quaternion q(*this);
	q.normalize();
	f32 X = q.X;
	f32 Y = q.Y;
	f32 Z = q.Z;
	f32 W = q.W;

	dest[0] = 1.0f - 2.0f * Y * Y - 2.0f * Z * Z;
	dest[1] = 2.0f * X * Y + 2.0f * Z * W;
	dest[2] = 2.0f * X * Z - 2.0f * Y * W;
	dest[3] = 0.0f;

	dest[4] = 2.0f * X * Y - 2.0f * Z * W;
	dest[5] = 1.0f - 2.0f * X * X - 2.0f * Z * Z;
	dest[6] = 2.0f * Z * Y + 2.0f * X * W;
	dest[7] = 0.0f;

	dest[8] = 2.0f * X * Z + 2.0f * Y * W;
	dest[9] = 2.0f * Z * Y - 2.0f * X * W;
	dest[10] = 1.0f - 2.0f * X * X - 2.0f * Y * Y;
	dest[11] = 0.0f;

	dest[12] = center.X;
	dest[13] = center.Y;
	dest[14] = center.Z;
	dest[15] = 1.f;
}

/*!
	Creates a matrix from this quaternion
	Rotate about a center point
	shortcut for
	core::quaternion q;
	q.rotationFromTo(vin[i].Normal, forward);
	q.getMatrix(lookat, center);

	core::matrix4 m2;
	m2.setInverseTranslation(center);
	lookat *= m2;
*/
inline void quaternion::getMatrixCenter(matrix4 &dest,
		const core::vector3df &center,
		const core::vector3df &translation) const
{
	quaternion q(*this);
	q.normalize();
	f32 X = q.X;
	f32 Y = q.Y;
	f32 Z = q.Z;
	f32 W = q.W;

	dest[0] = 1.0f - 2.0f * Y * Y - 2.0f * Z * Z;
	dest[1] = 2.0f * X * Y + 2.0f * Z * W;
	dest[2] = 2.0f * X * Z - 2.0f * Y * W;
	dest[3] = 0.0f;

	dest[4] = 2.0f * X * Y - 2.0f * Z * W;
	dest[5] = 1.0f - 2.0f * X * X - 2.0f * Z * Z;
	dest[6] = 2.0f * Z * Y + 2.0f * X * W;
	dest[7] = 0.0f;

	dest[8] = 2.0f * X * Z + 2.0f * Y * W;
	dest[9] = 2.0f * Z * Y - 2.0f * X * W;
	dest[10] = 1.0f - 2.0f * X * X - 2.0f * Y * Y;
	dest[11] = 0.0f;

	dest.setRotationCenter(center, translation);
}

// Creates a matrix from this quaternion
inline void quaternion::getMatrix_transposed(matrix4 &dest) const
{
	quaternion q(*this);
	q.normalize();
	f32 X = q.X;
	f32 Y = q.Y;
	f32 Z = q.Z;
	f32 W = q.W;

	dest[0] = 1.0f - 2.0f * Y * Y - 2.0f * Z * Z;
	dest[4] = 2.0f * X * Y + 2.0f * Z * W;
	dest[8] = 2.0f * X * Z - 2.0f * Y * W;
	dest[12] = 0.0f;

	dest[1] = 2.0f * X * Y - 2.0f * Z * W;
	dest[5] = 1.0f - 2.0f * X * X - 2.0f * Z * Z;
	dest[9] = 2.0f * Z * Y + 2.0f * X * W;
	dest[13] = 0.0f;

	dest[2] = 2.0f * X * Z + 2.0f * Y * W;
	dest[6] = 2.0f * Z * Y - 2.0f * X * W;
	dest[10] = 1.0f - 2.0f * X * X - 2.0f * Y * Y;
	dest[14] = 0.0f;

	dest[3] = 0.f;
	dest[7] = 0.f;
	dest[11] = 0.f;
	dest[15] = 1.f;
}

// Inverts this quaternion
inline quaternion &quaternion::makeInverse()
{
	X = -X;
	Y = -Y;
	Z = -Z;
	return *this;
}

// sets new quaternion
inline quaternion &quaternion::set(f32 x, f32 y, f32 z, f32 w)
{
	X = x;
	Y = y;
	Z = z;
	W = w;
	return *this;
}

// sets new quaternion based on Euler angles
inline quaternion &quaternion::set(f32 x, f32 y, f32 z)
{
	f64 angle;

	angle = x * 0.5;
	const f64 sr = sin(angle);
	const f64 cr = cos(angle);

	angle = y * 0.5;
	const f64 sp = sin(angle);
	const f64 cp = cos(angle);

	angle = z * 0.5;
	const f64 sy = sin(angle);
	const f64 cy = cos(angle);

	const f64 cpcy = cp * cy;
	const f64 spcy = sp * cy;
	const f64 cpsy = cp * sy;
	const f64 spsy = sp * sy;

	X = (f32)(sr * cpcy - cr * spsy);
	Y = (f32)(cr * spcy + sr * cpsy);
	Z = (f32)(cr * cpsy - sr * spcy);
	W = (f32)(cr * cpcy + sr * spsy);

	return normalize();
}

// sets new quaternion based on Euler angles
inline quaternion &quaternion::set(const core::vector3df &vec)
{
	return set(vec.X, vec.Y, vec.Z);
}

// sets new quaternion based on other quaternion
inline quaternion &quaternion::set(const core::quaternion &quat)
{
	return (*this = quat);
}

//! returns if this quaternion equals the other one, taking floating point rounding errors into account
inline bool quaternion::equals(const quaternion &other, const f32 tolerance) const
{
	return core::equals(X, other.X, tolerance) &&
		   core::equals(Y, other.Y, tolerance) &&
		   core::equals(Z, other.Z, tolerance) &&
		   core::equals(W, other.W, tolerance);
}

// normalizes the quaternion
inline quaternion &quaternion::normalize()
{
	// removed conditional branch since it may slow down and anyway the condition was
	// false even after normalization in some cases.
	return (*this *= (f32)reciprocal_squareroot((f64)(X * X + Y * Y + Z * Z + W * W)));
}

// Set this quaternion to the result of the linear interpolation between two quaternions
inline quaternion &quaternion::lerp(quaternion q1, quaternion q2, f32 time)
{
	const f32 scale = 1.0f - time;
	return (*this = (q1 * scale) + (q2 * time));
}

// Set this quaternion to the result of the linear interpolation between two quaternions and normalize the result
inline quaternion &quaternion::lerpN(quaternion q1, quaternion q2, f32 time)
{
	const f32 scale = 1.0f - time;
	return (*this = ((q1 * scale) + (q2 * time)).normalize());
}

// set this quaternion to the result of the interpolation between two quaternions
inline quaternion &quaternion::slerp(quaternion q1, quaternion q2, f32 time, f32 threshold)
{
	f32 angle = q1.dotProduct(q2);

	// make sure we use the short rotation
	if (angle < 0.0f) {
		q1 *= -1.0f;
		angle *= -1.0f;
	}

	if (angle <= (1 - threshold)) { // spherical interpolation
		const f32 theta = acosf(angle);
		const f32 invsintheta = reciprocal(sinf(theta));
		const f32 scale = sinf(theta * (1.0f - time)) * invsintheta;
		const f32 invscale = sinf(theta * time) * invsintheta;
		return (*this = (q1 * scale) + (q2 * invscale));
	} else // linear interpolation
		return lerpN(q1, q2, time);
}

// calculates the dot product
inline f32 quaternion::dotProduct(const quaternion &q2) const
{
	return (X * q2.X) + (Y * q2.Y) + (Z * q2.Z) + (W * q2.W);
}

//! axis must be unit length, angle in radians
inline quaternion &quaternion::fromAngleAxis(f32 angle, const vector3df &axis)
{
	const f32 fHalfAngle = 0.5f * angle;
	const f32 fSin = sinf(fHalfAngle);
	W = cosf(fHalfAngle);
	X = fSin * axis.X;
	Y = fSin * axis.Y;
	Z = fSin * axis.Z;
	return *this;
}

inline void quaternion::toAngleAxis(f32 &angle, core::vector3df &axis) const
{
	const f32 scale = sqrtf(X * X + Y * Y + Z * Z);

	if (core::iszero(scale) || W > 1.0f || W < -1.0f) {
		angle = 0.0f;
		axis.X = 0.0f;
		axis.Y = 1.0f;
		axis.Z = 0.0f;
	} else {
		const f32 invscale = reciprocal(scale);
		angle = 2.0f * acosf(W);
		axis.X = X * invscale;
		axis.Y = Y * invscale;
		axis.Z = Z * invscale;
	}
}

inline void quaternion::toEuler(vector3df &euler) const
{
	const f64 sqw = W * W;
	const f64 sqx = X * X;
	const f64 sqy = Y * Y;
	const f64 sqz = Z * Z;
	const f64 test = 2.0 * (Y * W - X * Z);

	if (core::equals(test, 1.0, 0.000001)) {
		// heading = rotation about z-axis
		euler.Z = (f32)(-2.0 * atan2(X, W));
		// bank = rotation about x-axis
		euler.X = 0;
		// attitude = rotation about y-axis
		euler.Y = (f32)(core::PI64 / 2.0);
	} else if (core::equals(test, -1.0, 0.000001)) {
		// heading = rotation about z-axis
		euler.Z = (f32)(2.0 * atan2(X, W));
		// bank = rotation about x-axis
		euler.X = 0;
		// attitude = rotation about y-axis
		euler.Y = (f32)(core::PI64 / -2.0);
	} else {
		// heading = rotation about z-axis
		euler.Z = (f32)atan2(2.0 * (X * Y + Z * W), (sqx - sqy - sqz + sqw));
		// bank = rotation about x-axis
		euler.X = (f32)atan2(2.0 * (Y * Z + X * W), (-sqx - sqy + sqz + sqw));
		// attitude = rotation about y-axis
		euler.Y = (f32)asin(clamp(test, -1.0, 1.0));
	}
}

inline vector3df quaternion::operator*(const vector3df &v) const
{
	// nVidia SDK implementation

	vector3df uv, uuv;
	const vector3df qvec(X, Y, Z);
	uv = qvec.crossProduct(v);
	uuv = qvec.crossProduct(uv);
	uv *= (2.0f * W);
	uuv *= 2.0f;

	return v + uv + uuv;
}

// set quaternion to identity
inline core::quaternion &quaternion::makeIdentity()
{
	W = 1.f;
	X = 0.f;
	Y = 0.f;
	Z = 0.f;
	return *this;
}

inline core::quaternion &quaternion::rotationFromTo(const vector3df &from, const vector3df &to)
{
	// Based on Stan Melax's article in Game Programming Gems
	// Optimized by Robert Eisele: https://raw.org/proof/quaternion-from-two-vectors

	// Copy, since cannot modify local
	vector3df v0 = from;
	vector3df v1 = to;
	v0.normalize();
	v1.normalize();

	const f32 d = v0.dotProduct(v1);
	if (d >= 1.0f) { // If dot == 1, vectors are the same
		return makeIdentity();
	} else if (d <= -1.0f) { // exactly opposite
		core::vector3df axis(1.0f, 0.f, 0.f);
		axis = axis.crossProduct(v0);
		if (axis.getLength() == 0) {
			axis.set(0.f, 1.f, 0.f);
			axis = axis.crossProduct(v0);
		}
		// same as fromAngleAxis(core::PI, axis).normalize();
		return set(axis.X, axis.Y, axis.Z, 0).normalize();
	}

	const vector3df c = v0.crossProduct(v1);
	return set(c.X, c.Y, c.Z, 1 + d).normalize();
}

} // end namespace core
} // end namespace irr