tetrees/Plugins/Wwise/ThirdParty/include/AK/Tools/Common/AkVectors.h

/*******************************************************************************
The content of this file includes portions of the AUDIOKINETIC Wwise Technology
released in source code form as part of the SDK installer package.

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Licensees holding valid commercial licenses to the AUDIOKINETIC Wwise Technology
may use this file in accordance with the end user license agreement provided 
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Alternatively, this file may be used under the Apache License, Version 2.0 (the 
"Apache License"); you may not use this file except in compliance with the 
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OR CONDITIONS OF ANY KIND, either express or implied. See the Apache License for
the specific language governing permissions and limitations under the License.

  Copyright (c) 2023 Audiokinetic Inc.
*******************************************************************************/

// AkVectors.h
//

#pragma once

#include <AK/SoundEngine/Common/AkTypes.h>
#include <AK/SoundEngine/Common/AkSimd.h>
#include <AK/SoundEngine/Common/AkSpeakerVolumes.h>
#include <AK/SoundEngine/Common/IAkPluginMemAlloc.h>
#include <AK/Tools/Common/AkArray.h>
#include <AK/Tools/Common/AkObject.h>

#include <math.h>
#include <stdio.h>
#include <float.h>

//#define AKVBAP_DEBUG 1
//#define AKPORTALS_DEBUG

#define AKVECTORS_PI				(3.1415926535897932384626433832795f)
#define AKVECTORS_TWOPI				(6.283185307179586476925286766559f)
#define AKVECTORS_PIOVERTWO			(1.5707963267948966192313216916398f)
#define	AKVECTORS_EPSILON			(1.0e-38f)									// epsilon value for fast log(0)

class Ak4DVector
{
public:
	//-----------------------------------------------------------
	// Constructor/Destructor functions
	Ak4DVector()
	{
		v[0] = 0.0f;
		v[1] = 0.0f;
		v[2] = 0.0f;
		v[3] = 0.0f;
	}

	Ak4DVector(const AkVector& b)
	{
		v[0] = b.X;
		v[1] = b.Y;
		v[2] = b.Z;
		v[3] = 1;
	}

	//-----------------------------------------------------------
	// Basic vector operators
	Ak4DVector& operator=(const Ak4DVector& b)
	{
		v[0] = b.v[0];
		v[1] = b.v[1];
		v[2] = b.v[2];
		v[3] = b.v[3];

		return *this;
	}

	Ak4DVector& operator/=(const AkReal32 f)
	{
		v[0] = v[0] / f;
		v[1] = v[1] / f;
		v[2] = v[2] / f;
		v[3] = v[3] / f;

		return *this;
	}

	Ak4DVector operator-(const Ak4DVector& b) const
	{
		Ak4DVector p;

		p.v[0] = v[0] - b.v[0];
		p.v[1] = v[1] - b.v[1];
		p.v[2] = v[2] - b.v[2];
		p.v[3] = v[3] - b.v[3];

		return p;
	}

	AkReal32 v[4];
};

struct Ak3DIntVector
{
public:
	Ak3DIntVector() = default;

	Ak3DIntVector(AkInt32 x, AkInt32 y, AkInt32 z) :
		X(x),
		Y(y),
		Z(z)
	{
	}

	AkInt32 X;	///< X Position
	AkInt32 Y;	///< Y Position
	AkInt32 Z;	///< Z Position
};

///
/// Specialization must provide these methods. Could enforce that through static_assert...
/// static TDataType Cos(TDataType in_value) const;
/// static TDataType Sin(TDataType in_value) const;
/// static TDataType Sqrt(TDataType in_value) const;
/// static constexpr TDataType POSITIVE_EPSILON;
/// static constexpr TDataType VECTOR_EPSILON;
///
template<typename TDataType> class RealPrecision;

template<>
class RealPrecision<AkReal32>
{
public:
	static AkReal32 Cos(AkReal32 in_value) { return cosf(in_value); }
	static AkReal32 Sin(AkReal32 in_value) { return sinf(in_value); }
	static AkReal32 Sqrt(AkReal32 in_value) { return sqrtf(in_value); }
	static AkReal32 ACos(AkReal32 in_value) { return acosf(in_value); }
	static bool IsFinite(AkReal32 in_val) 
	{ 
		// Purposely not using std::isnan() or isfinite because fastmath on clang & gcc may optimize them to be false always.
		return !(((*(AkUInt32*)&in_val) & 0x7fffffff) >= 0x7f800000);
	}

	static constexpr AkReal32 POSITIVE_EPSILON = 0.00001f;
	static constexpr AkReal32 VECTOR_EPSILON = AKVECTORS_EPSILON;

	static constexpr AkReal32 MAX_VALUE = FLT_MAX;
};

template<>
class RealPrecision<AkReal64>
{
public:
	static AkReal64 Cos(AkReal64 in_value) { return cos(in_value); }
	static AkReal64 Sin(AkReal64 in_value) { return sin(in_value); }
	static AkReal64 Sqrt(AkReal64 in_value) { return sqrt(in_value); }
	static AkReal64 ACos(AkReal64 in_value) { return acos(in_value); }
	static bool IsFinite(AkReal64 in_val)
	{
		// Purposely not using std::isnan() or isfinite because fastmath on clang & gcc may optimize them to be false always.
		return !(((*(AkUInt64*)&in_val) & 0x7fffffffffffffff) >= 0x7ff0000000000000);
	}

	static constexpr AkReal64 POSITIVE_EPSILON = 0.000000000001f;
	static constexpr AkReal64 VECTOR_EPSILON = AKVECTORS_EPSILON;

	static constexpr AkReal64 MAX_VALUE = DBL_MAX;
};

// AkImplicitConversion
// Permits automatic conversion from any real type to any other real type.
// May result in loss of precision.
class AkImplicitConversion
{
public:
	template<typename TFromReal, typename TToReal>
	AkForceInline void Convert(TToReal& out_to, TFromReal in_from)
	{
		out_to = static_cast<TToReal>(in_from);
	}
};

// AkSafeConversion
// Permits automatic conversion only from 32-bit to 64-bit types.
// Conversion from 64-bit to 32-bit is not permitted and will generate and error.
class AkSafeConversion
{
public:
	AkForceInline void Convert(AkReal64& out_to, AkReal32 in_from)
	{
		out_to = in_from;
	}
	template<typename TReal>
	AkForceInline void Convert(TReal& out_to, TReal in_from)
	{
		out_to = in_from;
	}
};

// T3DVector<>
// Template 3D vector class, to support both 32 and 64-bit vector types.
// Ak3DVector32 and Ak3DVector64 typedefs are provided below for convenience.
template<typename TDataType>
class T3DVector
{
public:
	/// Expose the data type
	///
	typedef TDataType data_type;

	// Conversion policy for conversions between 32 and 64 bit types.
	typedef AkSafeConversion TTypeConverter;

public:

	//-----------------------------------------------------------
	// Constructor/Destructor functions

	T3DVector() :
		X(static_cast<TDataType>(0.0)),
		Y(static_cast<TDataType>(0.0)),
		Z(static_cast<TDataType>(0.0))
	{}

	T3DVector(TDataType in_x, TDataType in_y, TDataType in_z) :
		X(in_x),
		Y(in_y),
		Z(in_z)
	{}

	// Construct from another T3DVector<> type. 
	// Conversion is (only) permitted in accordance to the conversion policy.
	template<typename TFromDataType>
	T3DVector(const T3DVector<TFromDataType>& in_vector)
	{
		TTypeConverter converter;
		converter.Convert(X, in_vector.X);
		converter.Convert(Y, in_vector.Y);
		converter.Convert(Z, in_vector.Z);
	}

	// Construct from an AkVector type. 
	// Conversion is (only) permitted in accordance to the conversion policy.
	T3DVector(const AkVector& in_vector)
	{
		TTypeConverter converter;
		converter.Convert(X, in_vector.X);
		converter.Convert(Y, in_vector.Y);
		converter.Convert(Z, in_vector.Z);
	}

	// Construct from an AkVector64 type. 
	// Conversion is (only) permitted in accordance to the conversion policy.
	T3DVector(const AkVector64& in_vector)
	{
		TTypeConverter converter;
		converter.Convert(X, in_vector.X);
		converter.Convert(Y, in_vector.Y);
		converter.Convert(Z, in_vector.Z);
	}

	// Implicit conversion to AkVector type, it the conversion policy permits it.
	operator AkVector() const
	{
		AkVector v;
		TTypeConverter converter;
		converter.Convert(v.X, X);
		converter.Convert(v.Y, Y);
		converter.Convert(v.Z, Z);
		return v;
	}

	// Implicit conversion to AkVector64 type, it the conversion policy permits it.
	operator AkVector64() const
	{
		AkVector64 v;
		TTypeConverter converter;
		converter.Convert(v.X, X);
		converter.Convert(v.Y, Y);
		converter.Convert(v.Z, Z);
		return v;
	}

	// Casting method for explicit conversion to another vector type.s
	template<typename TVectorType>
	TVectorType Cast() const;

	// Construct a vector from a scalar.
	explicit T3DVector(TDataType in_scalar)
		: X(in_scalar)
		, Y(in_scalar)
		, Z(in_scalar)
	{}

	// Convert from a vector from a AKSIMD_V4F32. 
	explicit T3DVector(const AKSIMD_V4F32& in_v4f32)
	{
		X = static_cast<TDataType>(AKSIMD_GETELEMENT_V4F32(in_v4f32, 0));
		Y = static_cast<TDataType>(AKSIMD_GETELEMENT_V4F32(in_v4f32, 1));
		Z = static_cast<TDataType>(AKSIMD_GETELEMENT_V4F32(in_v4f32, 2));
	}

	AkForceInline AKSIMD_V4F32 PointV4F32() const
	{
		AKSIMD_V4F32 v4f32;
		AKSIMD_GETELEMENT_V4F32(v4f32, 0) = static_cast<AkReal32>(X);
		AKSIMD_GETELEMENT_V4F32(v4f32, 1) = static_cast<AkReal32>(Y);
		AKSIMD_GETELEMENT_V4F32(v4f32, 2) = static_cast<AkReal32>(Z);
		AKSIMD_GETELEMENT_V4F32(v4f32, 3) = 1.f;
		return v4f32;
	}

	AkForceInline AKSIMD_V4F32 VectorV4F32() const
	{
		AKSIMD_V4F32 v4f32;
		AKSIMD_GETELEMENT_V4F32(v4f32, 0) = static_cast<TDataType>(X);
		AKSIMD_GETELEMENT_V4F32(v4f32, 1) = static_cast<TDataType>(Y);
		AKSIMD_GETELEMENT_V4F32(v4f32, 2) = static_cast<TDataType>(Z);
		AKSIMD_GETELEMENT_V4F32(v4f32, 3) = static_cast<TDataType>(0.0);
		return v4f32;
	}

	void Zero()
	{
		X = static_cast<TDataType>(0.0);
		Y = static_cast<TDataType>(0.0);
		Z = static_cast<TDataType>(0.0);
	}

	//-----------------------------------------------------------
	// Basic vector operators
	AkForceInline bool operator==(const T3DVector& b) const
	{
		return X == b.X && Y == b.Y && Z == b.Z;
	}

	AkForceInline bool operator!=(const T3DVector& b) const
	{
		return X != b.X || Y != b.Y || Z != b.Z;
	}

	AkForceInline bool operator<(const T3DVector& b) const
	{
		return X < b.X && Y < b.Y && Z < b.Z;
	}

	AkForceInline bool operator<=(const T3DVector& b) const
	{
		return X <= b.X && Y <= b.Y && Z <= b.Z;
	}

	AkForceInline bool operator>(const T3DVector b) const
	{
		return X > b.X && Y > b.Y && Z > b.Z;
	}

	AkForceInline bool operator>=(const T3DVector& b) const
	{
		return X >= b.X && Y >= b.Y && Z >= b.Z;
	}

	AkForceInline T3DVector& operator*=(const TDataType f)
	{
		X = X * f;
		Y = Y * f;
		Z = Z * f;

		return *this;
	}

	AkForceInline T3DVector& operator/=(const TDataType f)
	{
		TDataType oneoverf = static_cast<TDataType>(1.0) / f;
		X = X * oneoverf;
		Y = Y * oneoverf;
		Z = Z * oneoverf;

		return *this;
	}

	AkForceInline T3DVector operator*(const T3DVector v2) const
	{
		T3DVector v;

		v.X = X * v2.X;
		v.Y = Y * v2.Y;
		v.Z = Z * v2.Z;

		return v;
	}

	AkForceInline T3DVector operator*(const TDataType f) const
	{
		T3DVector v;

		v.X = X * f;
		v.Y = Y * f;
		v.Z = Z * f;

		return v;
	}

	AkForceInline T3DVector operator/(const T3DVector in_rhs) const
	{
		T3DVector v;

		v.X = X / in_rhs.X;
		v.Y = Y / in_rhs.Y;
		v.Z = Z / in_rhs.Z;

		return v;
	}

	AkForceInline T3DVector operator/(const TDataType f) const
	{
		T3DVector v;

		TDataType oneoverf = static_cast<TDataType>(1.0) / f;

		v.X = X * oneoverf;
		v.Y = Y * oneoverf;
		v.Z = Z * oneoverf;

		return v;
	}

	AkForceInline T3DVector operator+(const TDataType f) const
	{
		T3DVector v;

		v.X = X + f;
		v.Y = Y + f;
		v.Z = Z + f;

		return v;
	}

	AkForceInline T3DVector operator-(const TDataType f) const
	{
		T3DVector v;

		v.X = X - f;
		v.Y = Y - f;
		v.Z = Z - f;

		return v;
	}

	AkForceInline T3DVector operator+(const T3DVector& b) const
	{
		T3DVector v;

		v.X = X + b.X;
		v.Y = Y + b.Y;
		v.Z = Z + b.Z;

		return v;
	}

	AkForceInline T3DVector operator-(const T3DVector& b) const
	{
		T3DVector v;

		v.X = X - b.X;
		v.Y = Y - b.Y;
		v.Z = Z - b.Z;

		return v;
	}

	AkForceInline TDataType HorizontalMin() const
	{
		return AkMin(X, AkMin(Y, Z));
	}

	AkForceInline TDataType HorizontalMax() const
	{
		return AkMax(X, AkMax(Y, Z));
	}

	AkForceInline static T3DVector Min(const T3DVector& A, const T3DVector& B)
	{
		T3DVector min;

		min.X = AkMin(A.X, B.X);
		min.Y = AkMin(A.Y, B.Y);
		min.Z = AkMin(A.Z, B.Z);

		return min;
	}

	AkForceInline static T3DVector Max(const T3DVector& A, const T3DVector& B)
	{
		T3DVector max;

		max.X = AkMax(A.X, B.X);
		max.Y = AkMax(A.Y, B.Y);
		max.Z = AkMax(A.Z, B.Z);

		return max;
	}

	//-----------------------------------------------------------
	// Conversion functions
	AkForceInline T3DVector Rotate180X_90Y() const
	{
		T3DVector v;

		v.X = -X;
		v.Y = Z;
		v.Z = -Y;

		return v;
	}

	AkForceInline T3DVector SphericalToCartesian(
		const TDataType azimuth,
		const TDataType elevation)
	{
		TDataType cosElevation = RealPrecision<TDataType>::Cos(elevation);
		X = RealPrecision<TDataType>::Cos(azimuth) *	cosElevation;
		Y = RealPrecision<TDataType>::Sin(azimuth) *	cosElevation;
		Z = RealPrecision<TDataType>::Sin(elevation);
		
		return *this;
	}

	// Determinant of 3 column vectors.
	static AkForceInline TDataType Determinant(
		const T3DVector& a,
		const T3DVector& b,
		const T3DVector& c)
	{
		return	(a.X*b.Y*c.Z + a.Y*b.Z*c.X + a.Z*b.X*c.Y) -
			(a.Z*b.Y*c.X + a.Y*b.X*c.Z + a.X*b.Z*c.Y);
	}

	// Convert a vector to a different base
	AkForceInline T3DVector LinearCombination(
		const T3DVector& A,
		const T3DVector& B,
		const T3DVector& C) const
	{
		T3DVector v;

		TDataType d = Determinant(A, B, C);

		if (d < RealPrecision<TDataType>::VECTOR_EPSILON && d > -RealPrecision<TDataType>::VECTOR_EPSILON)
		{
			v.X = static_cast<TDataType>(0.0); v.Y = static_cast<TDataType>(0.0); v.Z = static_cast<TDataType>(0.0);
			return v;
		}

		// http://mathworld.wolfram.com/MatrixInverse.html
		T3DVector invA = T3DVector(B.Y*C.Z - B.Z*C.Y, A.Z*C.Y - A.Y*C.Z, A.Y*B.Z - A.Z*B.Y);
		T3DVector invB = T3DVector(B.Z*C.X - B.X*C.Z, A.X*C.Z - A.Z*C.X, A.Z*B.X - A.X*B.Z);
		T3DVector invC = T3DVector(B.X*C.Y - B.Y*C.X, A.Y*C.X - A.X*C.Y, A.X*B.Y - A.Y*B.X);

		TDataType oneover_d = static_cast<TDataType>(1.0) / d;
		invA *= oneover_d;
		invB *= oneover_d;
		invC *= oneover_d;

		// Project coordinates using a vector to matrix multiplication
		v.X = X * invA.X + Y * invB.X + Z * invC.X;
		v.Y = X * invA.Y + Y * invB.Y + Z * invC.Y;
		v.Z = X * invA.Z + Y * invB.Z + Z * invC.Z;

		// v /= v.Length();

		return v;
	}

	AkForceInline T3DVector& Normalize()
	{
		TDataType l = Length();
		if (l != static_cast<TDataType>(0.0))
		{
			X /= l;
			Y /= l;
			Z /= l;
		}
		else
		{
			X = static_cast<TDataType>(0.0);
			Y = static_cast<TDataType>(0.0);
			Z = static_cast<TDataType>(0.0);
		}
		return *this;
	}

	AkForceInline TDataType L2_Norm() const
	{
		return RealPrecision<TDataType>::Sqrt(X*X + Y*Y + Z*Z);
	}

	AkForceInline TDataType DotProduct(const T3DVector& v2) const
	{
		return X*v2.X + Y*v2.Y + Z*v2.Z;
	}

	AkForceInline TDataType Dot(const T3DVector& v2) const
	{
		return DotProduct(v2);
	}

	AkForceInline T3DVector Cross(const T3DVector& v) const
	{
		T3DVector uxv;

		const T3DVector& u = *this;

		uxv.X = u.Y*v.Z - u.Z*v.Y;
		uxv.Y = u.Z*v.X - u.X*v.Z;
		uxv.Z = u.X*v.Y - u.Y*v.X;

		return uxv;
	}
	
	AkForceInline TDataType Length() const
	{
		return RealPrecision<TDataType>::Sqrt(X*X + Y*Y + Z*Z);
	}

	AkForceInline TDataType LengthSquared() const
	{
		return X*X + Y*Y + Z*Z;
	}

	// Usefull in VBAP algorithm, only points that are a positive linear composition matters.
	AkForceInline bool IsAllPositive() const
	{
		return X >= -RealPrecision<TDataType>::POSITIVE_EPSILON &&
			Y >= -RealPrecision<TDataType>::POSITIVE_EPSILON &&
			Z >= -RealPrecision<TDataType>::POSITIVE_EPSILON;
	}

	AkForceInline T3DVector Abs() const
	{
		T3DVector abs = *this;
		abs.X = (TDataType)fabs(abs.X);
		abs.Y = (TDataType)fabs(abs.Y);
		abs.Z = (TDataType)fabs(abs.Z);
		return abs;
	}

	AkForceInline bool IsFinite() const
	{
		return
			RealPrecision<TDataType>::IsFinite(X) &&
			RealPrecision<TDataType>::IsFinite(Y) &&
			RealPrecision<TDataType>::IsFinite(Z);
	}

	TDataType						X;
	TDataType						Y;
	TDataType						Z;
};

template<typename TDataType>
AkForceInline T3DVector<TDataType> operator*(const TDataType f, const T3DVector<TDataType>& v)
{
	return v * f;
}

template<typename TDataType>
AkForceInline T3DVector<TDataType> operator/(const TDataType f, const T3DVector<TDataType>& v)
{
	T3DVector<TDataType> res;
	res.X = f / v.X;
	res.Y = f / v.Y;
	res.Z = f / v.Z;
	return res;
}


// Ak3DVector typedefs

// Ak3DVector32 - Can be implicitly converted to 64 but not the other way around.
typedef T3DVector<AkReal32> Ak3DVector;
typedef T3DVector<AkReal32> Ak3DVector32;

// Ak3DVector64 - It is necessary to call vec.Cast<Ak3DVector64>() to convert to 32 bit vector type.
typedef T3DVector<AkReal64> Ak3DVector64;

// Casting methods.

// Generic cast between two T3DVector<> types.
template<typename TDataType>
template<typename TVectorType>
TVectorType T3DVector<TDataType>::Cast() const
{
	TVectorType v;
	v.X = static_cast<typename TVectorType::data_type>(X);
	v.Y = static_cast<typename TVectorType::data_type>(Y);
	v.Z = static_cast<typename TVectorType::data_type>(Z);
	return v;
}


class Ak2DVector
{
public:
	//-----------------------------------------------------------
	// Constructor/Destructor functions
	Ak2DVector() = default;

	Ak2DVector(AkReal32	x, AkReal32 y) :
		X(x),
		Y(y)
	{
	}

	//-----------------------------------------------------------
	// Basic vector operators
	AkForceInline Ak2DVector operator=(const Ak2DVector& b)
	{
		X = b.X;
		Y = b.Y;

		return *this;
	}

	AkForceInline Ak2DVector operator=(const AkSphericalCoord& b)
	{
		X = b.theta;
		Y = b.phi;

		return *this;
	}

	Ak2DVector operator-(const Ak2DVector& b) const
	{
		Ak2DVector v;

		v.X = X - b.X;
		v.Y = Y - b.Y;

		return v;
	}

	Ak2DVector& operator*=(const AkReal32 f)
	{
		X = X * f;
		Y = Y * f;

		return *this;
	}

	Ak2DVector& operator/=(const AkReal32 f)
	{
		AkReal32 oneoverf = 1.f / f;
		X = X * oneoverf;
		Y = Y * oneoverf;

		return *this;
	}

	AkForceInline bool operator==(const Ak2DVector& b) const
	{
		return b.X == X && b.Y == Y;
	}

	AkForceInline bool operator!=(const Ak2DVector& b) const
	{
		return b.X != X && b.Y != Y;
	}

	AkForceInline AkReal32 Length() const
	{
		return sqrtf(X*X+Y*Y);
	}

	//-----------------------------------------------------------
	// Conversion functions
	AkForceInline Ak2DVector& CartesianToSpherical(const Ak3DVector& in_Cartesian)
	{
		// (radial, azimuth, elevation)
		AkReal32 r = sqrtf( in_Cartesian.X*in_Cartesian.X + in_Cartesian.Y*in_Cartesian.Y + in_Cartesian.Z*in_Cartesian.Z);
		AKASSERT( r != 0);

		X = atan2f(in_Cartesian.Y, in_Cartesian.X);
		Y = asinf(in_Cartesian.Z / r);

		NormalizeSpherical();

		return *this;
	}

	AkForceInline Ak2DVector LinearCombination(
		const Ak2DVector& A,
		const Ak2DVector& B) const
	{
		Ak2DVector v;

		// Project coordinates using a vector to matrix multiplication
		AkReal32 d = (A.X*B.Y - A.Y*B.X);

		if (d < AKVECTORS_EPSILON && d > -AKVECTORS_EPSILON)
		{
			v.X = 0.0f; v.Y = 0.0f;
			return v;
		}

		Ak2DVector invA = Ak2DVector( B.Y, -A.Y );
		Ak2DVector invB = Ak2DVector( -B.X, A.X );

		AkReal32 oneover_d = 1.f / d;
		invA *= oneover_d;
		invB *= oneover_d;

		v.X = X * invA.X + Y * invB.X;
		v.Y = X * invA.Y + Y * invB.Y;
		// v /= v.Length();

		return v;
	}

	AkForceInline Ak2DVector NormalizeSpherical() const
	{
		/*
			Normalise spherical coordinates.
				X (azimuthal)	-> [-PI, PI],		circle lies on xy plan,			0 is on X axix
				Y (elevation)	-> [-PI/2, PI/2],	half circle on Z axis,			0 on XY plan, PI/2 straigt up on Z axis.
		*/

		Ak2DVector v;

		v.X = X;
		v.Y = Y;

		if (X > AKVECTORS_PI)
			v.X = X - AKVECTORS_TWOPI;
		else if (X < -AKVECTORS_PI)
			v.X = X + AKVECTORS_TWOPI;

		if (Y > AKVECTORS_PIOVERTWO)
			v.Y = Y - AKVECTORS_PI;
		else if (Y < -AKVECTORS_PIOVERTWO)
			v.Y = Y + AKVECTORS_PI;

		AKASSERT(X<AKVECTORS_PI);
		AKASSERT(Y<AKVECTORS_PIOVERTWO);

		return v;
	}

	AkForceInline void NormalizeSpherical()
	{
		/*
			Normalise spherical coordinates.
				X (azimuthal)	-> [-PI, PI],		circle lies on xy plan,		0 is on X axix
				Y (elevation)	-> [-PI/2, PI/2],	half circle on Z axis,		0 on XY plan, PI/2 straigt up on Z axis.
		*/
		
		if (X > AKVECTORS_PI)
			X = X - AKVECTORS_TWOPI;
		else if (X < -AKVECTORS_PI)
			X = X + AKVECTORS_TWOPI;

		if (Y > AKVECTORS_PIOVERTWO)
			Y = Y - AKVECTORS_PI;
		else if (Y < -AKVECTORS_PIOVERTWO)
			Y = Y + AKVECTORS_PI;
	}

	// Useful in VBAP algorithm, only points that are a positive linear composition matters.
	AkForceInline bool IsAllPositive() const
	{
		const AkReal32 POSITIVE_TEST_EPSILON = 0.00001f; //0.005f;
		return X >= -POSITIVE_TEST_EPSILON &&
			Y >= -POSITIVE_TEST_EPSILON;
	}

    AkReal32 X;
    AkReal32 Y;
};



class AkMatrix4x4
{
	static const int MAX_SIZE = 16;

public:
	//-----------------------------------------------------------
	// Constructor/Destructor functions
	AkMatrix4x4() = default;

	//-----------------------------------------------------------
	// Basic vector operators
	AkMatrix4x4& operator/=(const AkReal32 f)
	{
		for (int i = 0; i < MAX_SIZE; i++)
			m_Data[i] /= f;

		return *this;
	}

	AkMatrix4x4& operator=(AkReal32 * in_Data)
	{
		for (int i = 0; i < MAX_SIZE; i++)
		{
			m_Data[i] = in_Data[i];
		}

		return *this;
	}

	AkReal32 m_Data[MAX_SIZE];
};

class AkMatrix3x3
{

public:
	//-----------------------------------------------------------
	// Constructor/Destructor functions
	AkMatrix3x3() = default;

	static AkMatrix3x3 FromColumnVectors(const Ak3DVector& in_col0, const Ak3DVector& in_col1, const Ak3DVector& in_col2)
	{
		AkMatrix3x3 m;

		m(0, 0) = in_col0.X;
		m(1, 0) = in_col0.Y;
		m(2, 0) = in_col0.Z;

		m(0, 1) = in_col1.X;
		m(1, 1) = in_col1.Y;
		m(2, 1) = in_col1.Z;

		m(0, 2) = in_col2.X;
		m(1, 2) = in_col2.Y;
		m(2, 2) = in_col2.Z;

		return m;
	}

	//-----------------------------------------------------------
	// Basic vector operators
	AkMatrix3x3& operator/=(const AkReal32 f)
	{
		for (int i = 0; i < 3; i++)
		{
			for (int j = 0; j < 3; j++)
			{
				m_Data[i][j] /= f;
			}
		}
		return *this;
	}

	AkForceInline AkReal32& operator()(const AkUInt32 row, const AkUInt32 column)
	{
		return m_Data[column][row];
	}

	AkForceInline const AkReal32& operator()(const AkUInt32 row, const AkUInt32 column) const
	{
		return m_Data[column][row];
	}

	AkForceInline Ak3DVector operator*(const Ak3DVector& in_rhs) const
	{
		Ak3DVector res;
		res.X = in_rhs.X * m_Data[0][0] + in_rhs.Y * m_Data[1][0] + in_rhs.Z * m_Data[2][0];
		res.Y = in_rhs.X * m_Data[0][1] + in_rhs.Y * m_Data[1][1] + in_rhs.Z * m_Data[2][1];
		res.Z = in_rhs.X * m_Data[0][2] + in_rhs.Y * m_Data[1][2] + in_rhs.Z * m_Data[2][2];
		return res;
	}

	AkForceInline AkMatrix3x3& operator+=(const AkMatrix3x3& in_rhs)
	{
		Add(*this, *this, in_rhs);
		return *this;
	}

	static AkForceInline void Add(AkMatrix3x3& out_res, const AkMatrix3x3& in_m0, const AkMatrix3x3& in_m1)
	{
#define ADD(i,j) out_res(i,j) = in_m0(i,j) + in_m1(i,j)
		ADD(0, 0); ADD(0, 1); ADD(0, 2);
		ADD(1, 0); ADD(1, 1); ADD(1, 2);
		ADD(2, 0); ADD(2, 1); ADD(2, 2);
#undef ADD
	}

	AkForceInline AkMatrix3x3& operator*=(const AkReal32& in_f)
	{
		m_Data[0][0] *= in_f; m_Data[0][1] *= in_f; m_Data[0][2] *= in_f;
		m_Data[1][0] *= in_f; m_Data[1][1] *= in_f; m_Data[1][2] *= in_f;
		m_Data[2][0] *= in_f; m_Data[2][1] *= in_f; m_Data[2][2] *= in_f;
		return *this;
	}

	static AkForceInline void Diagonal(AkMatrix3x3& out_mat, AkReal32 in_f)
	{
		out_mat(0, 0) = in_f;		out_mat(0, 1) = 0.f;		out_mat(0, 2) = 0.f;
		out_mat(1, 0) = 0.f;		out_mat(1, 1) = in_f;		out_mat(1, 2) = 0.f;
		out_mat(2, 0) = 0.f;		out_mat(2, 1) = 0.f;		out_mat(2, 2) = in_f;
	}

	// Creates the matrix Mu such that Mu*v = u X v
	static AkForceInline  void CrossProductMatrix(AkMatrix3x3& out_mat, const Ak3DVector& in_u)
	{
		out_mat(0, 0) = 0.f;		out_mat(0, 1) = -in_u.Z;		out_mat(0, 2) = in_u.Y;
		out_mat(1, 0) = in_u.Z;		out_mat(1, 1) = 0.f;			out_mat(1, 2) = -in_u.X;
		out_mat(2, 0) = -in_u.Y;	out_mat(2, 1) = in_u.X;			out_mat(2, 2) = 0.f;
	}

	static AkForceInline void OuterProduct(AkMatrix3x3& out_mat, const Ak3DVector& in_v0, const Ak3DVector& in_v1)
	{
		out_mat(0, 0) = in_v0.X*in_v1.X;	out_mat(0, 1) = in_v0.X*in_v1.Y;		out_mat(0, 2) = in_v0.X*in_v1.Z;
		out_mat(1, 0) = in_v0.Y*in_v1.X;	out_mat(1, 1) = in_v0.Y*in_v1.Y;		out_mat(1, 2) = in_v0.Y*in_v1.Z;
		out_mat(2, 0) = in_v0.Z*in_v1.X;	out_mat(2, 1) = in_v0.Z*in_v1.Y;		out_mat(2, 2) = in_v0.Z*in_v1.Z;
	}

	static AkForceInline void Rotation(AkMatrix3x3& out_mat, AkReal32 in_angle, const Ak3DVector& in_axis)
	{
		Rotation(out_mat, sinf(in_angle), cosf(in_angle), in_axis);
	}

	static void Rotation(AkMatrix3x3& out_mat, AkReal32 in_sin, AkReal32 in_cos, const Ak3DVector& in_axis)
	{
		Diagonal(out_mat, in_cos);

		AkMatrix3x3 outer;
		OuterProduct(outer, in_axis, in_axis);
		outer *= (1.f - in_cos);
		out_mat += outer;

		AkMatrix3x3 cross;
		CrossProductMatrix(cross, in_axis*in_sin);
		out_mat += cross;
	}

	// [column][row]
	AkReal32 m_Data[3][3];
};

class AkQuaternion
{
public:
	// Identity quaternion
	AkQuaternion(): W(1.f), X(0.f), Y(0.f), Z(0.f) {}

	AkQuaternion(AkReal32 in_W, AkReal32 in_X, AkReal32 in_Y, AkReal32 in_Z) : 
		W(in_W), 
		X(in_X), 
		Y(in_Y), 
		Z(in_Z) 
	{}

	// Create a quaternion from a 3x3 rotation matrix
	static AkQuaternion FromRotationMatrix(const AkMatrix3x3& in_mat)
	{
		AkQuaternion q;
		
		AkReal32 trace = in_mat(0,0) + in_mat(1, 1) + in_mat(2, 2);
		if (trace > 0.0f)
		{
			AkReal32 srt = sqrtf(trace + 1.f);
			AkReal32 s = 0.5f / srt;
			
			q.W = 0.5f * srt;
 			q.X = (in_mat(2, 1) - in_mat(1, 2)) * s;
 			q.Y = (in_mat(0, 2) - in_mat(2, 0)) * s;
 			q.Z = (in_mat(1, 0) - in_mat(0, 1)) * s;

		}
		else
		{
			// diagonal is negative
			AkUInt32 i = 0;
			if (in_mat(1, 1) > in_mat(0, 0))
				i = 1;
			if (in_mat(2, 2) > in_mat(i, i))
				i = 2;

			AkUInt32 j = (i + 1) % 3;
			AkUInt32 k = (i + 2) % 3;

			AkReal32 s = sqrtf( in_mat(i, i) - in_mat(j, j) - in_mat(k, k) + 1.0f );
			AkReal32 t = (s == 0.f) ? 0.f : (0.5f / s);

			AkReal32 qt[4];

			qt[i] = 0.5f * s;
			qt[j] = (in_mat(j, i) + in_mat(i, j)) * t;
			qt[k] = (in_mat(k, i) + in_mat(i, k)) * t;
			qt[3] = (in_mat(k, j) - in_mat(j, k)) * t;

			q.X = qt[0];
			q.Y = qt[1];
			q.Z = qt[2];
			q.W = qt[3];
		}

		return q;
	}

	// Create a rotation quaternion from euler angles. 
	static AkQuaternion FromEulers( 
		AkReal32 in_x,	// Rotation around the X axis, in radians.
		AkReal32 in_y,	// Rotation around the Y axis, in radians.
		AkReal32 in_z	// Rotation around the Z axis, in radians.
	)
	{
		AkReal32 sy = sinf(in_z / 2.f);
		AkReal32 cy = cosf(in_z / 2.f);
		AkReal32 sp = sinf(in_y / 2.f);
		AkReal32 cp = cosf(in_y / 2.f);
		AkReal32 sr = sinf(in_x / 2.f);
		AkReal32 cr = cosf(in_x / 2.f);

		AkQuaternion q;
		q.W = cr * cp * cy + sr * sp * sy;
		q.X = sr * cp * cy - cr * sp * sy;
		q.Y = cr * sp * cy + sr * cp * sy;
		q.Z = cr * cp * sy - sr * sp * cy;

		return q;
	}

	static AkQuaternion FromAngleAndAxis(AkReal32 in_angle, const Ak3DVector& in_axis)
	{
		AkQuaternion q;

		AkReal32 sa = sinf(in_angle / 2.f);
		q.W = cosf(in_angle / 2.f);
		q.X = in_axis.X * sa;
		q.Y = in_axis.Y * sa;
		q.Z = in_axis.Z * sa;
		
		return q;
	}

	AkForceInline AkReal32 Length() const
	{
		return sqrtf( W*W + X*X + Y*Y + Z*Z );
	}

	AkForceInline AkQuaternion& Normalize()
	{
		AkReal32 f = 1.0f / Length();
		W *= f;
		X *= f;
		Y *= f;
		Z *= f;
		return *this;
	}

	AkForceInline AkQuaternion Inverse() const
	{
		AkReal32 norm = W*W + X*X + Y*Y + Z*Z;
		if (norm > 0.0)
		{
			AkReal32 invNorm = 1.0f / norm;
			return AkQuaternion(W*invNorm, -X*invNorm, -Y*invNorm, -Z*invNorm);
		}
		else
		{
			return AkQuaternion();
		}
	}

	// Create a quaternion representing the shortest arc rotation between (normalized) vectors v0, v1
	AkQuaternion(const Ak3DVector& in_v0, const Ak3DVector& in_v1)
	{
		AkReal32 dot = in_v0.Dot(in_v1);
		if (dot >= 1.0f - AKVECTORS_EPSILON)
		{
			// No rotation - return unity quaternion.
			AkQuaternion();
		}
		if (dot <= -1.f - AKVECTORS_EPSILON)
		{
			// 180 degree rotation - can use any non-zero length axis.
			Ak3DVector axis = Ak3DVector(0.f, 0.f, 1.f).Cross(in_v0);
			AkReal32 len = axis.Length();
			if (len < AKVECTORS_EPSILON)
			{
				axis = Ak3DVector(0.f, 1.f, 0.f).Cross(in_v0);
				len = axis.Length();
			}
			axis.Normalize();
			AkQuaternion(AKVECTORS_PI, axis);
		}
		else
		{
			AkReal32 sqrt = sqrtf((1.f + dot) * 2.f);
			AkReal32 invs = 1.f / sqrt;

			Ak3DVector cross = in_v0.Cross(in_v1);

			X = cross.X * invs;
			Y = cross.Y * invs;
			Z = cross.Z * invs;
			W = sqrt * 0.5f;
			Normalize();
		}
	}
	
	// Build quaternion from an axis and angle representation.
	AkQuaternion(AkReal32 in_angle, const Ak3DVector& in_axis)
	{
		AkReal32 cosHalfAngle = cosf(in_angle / 2.f);
		W = cosHalfAngle;
		X = cosHalfAngle*in_axis.X;
		Y = cosHalfAngle*in_axis.Y;
		Z = cosHalfAngle*in_axis.Z;
	}
	
	/// Quaternion multiplication.
	AkForceInline AkQuaternion operator*(const AkQuaternion& Q) const
	{
		return AkQuaternion(
			W*Q.W - X*Q.X - Y*Q.Y - Z*Q.Z,
            W*Q.X + X*Q.W + Y*Q.Z - Z*Q.Y,
            W*Q.Y - X*Q.Z + Y*Q.W + Z*Q.X,
            W*Q.Z + X*Q.Y - Y*Q.X + Z*Q.W);
	}
	
	AkForceInline Ak3DVector32 operator*(const Ak3DVector32& in_v) const
	{
		return RotateVector(in_v);
	}

	AkForceInline Ak3DVector RotateVector(const Ak3DVector32& in_v) const
	{
		/*
		// impl 1
		Ak3DVector uv, uuv;
		Ak3DVector qvec(X, Y, Z);
		uv = qvec.Cross(in_v);
		uuv = qvec.Cross(uv);
		uv *= (2.0f * W);
		uuv *= 2.0f;
		return in_v + uv + uuv;
		*/

		// impl 2
		Ak3DVector32 u(X, Y, Z);
		Ak3DVector32 res =
			u * u.Dot(in_v) * 2.f
			+ in_v * (W * W - u.Dot(u))
			+ u.Cross(in_v) * W * 2.0f;

		return res;
	}

	AkForceInline Ak3DVector UnrotateVector(const Ak3DVector32& in_v) const
	{
		Ak3DVector32 u(-X, -Y, -Z);
		Ak3DVector32 t = 2.f * u.Cross(in_v);
		Ak3DVector32 res = in_v + (W * t) + u.Cross(t);
		return res;
	}

	AkReal32 W;
	AkReal32 X;
	AkReal32 Y;
	AkReal32 Z;
};

struct AkIntersectionPoints
{
	Ak3DVector points[2];
	AkUInt32 count;
};

class AkLine
{
public:
	AkLine() :
		mint(1.175494351e-38F),
		maxt(3.402823466e+38F)
	{
	}

	AkLine(Ak3DVector in_L, Ak3DVector in_P) :
		L(in_L),
		P(in_P),
		mint(1.175494351e-38F),
		maxt(3.402823466e+38F)
	{
	}

	Ak3DVector PointAt(AkReal32 t) const
	{
		return P + L*t;
	}

	bool Intersect(Ak3DVector A, Ak3DVector B)
	{
		/*
		a (V1 X V2) = (P2 - P1) X V2
		If the lines intersect at a single point, then the resultant vectors
		on each side of this equation must be parallel, and the left side must
		not be the zero vector. We should check to make sure that this is
		true. Once we have checked this, we can solve for 'a' by taking the
		magnitude of each side and dividing. If the resultant vectors are
		parallel, but in opposite directions, then 'a' is the negative of the
		ratio of magnitudes. Once we have 'a' we can go back to the equation
		for L1 to find the intersection point.
		*/
		Ak3DVector V1 = L;
		Ak3DVector V2 = B - A;
		Ak3DVector P1 = P;
		Ak3DVector P2 = A;

		// k(V1 X V2) = (A - P) X V2

		Ak3DVector v1CrossV2 = V1.Cross(V2);
		AkReal32 det = Ak3DVector::Determinant(
			P2 - P1,
			V2,
			v1CrossV2
			);
		AkReal32 t = det / v1CrossV2.LengthSquared();

		det = Ak3DVector::Determinant(
			P2 - P1,
			V1,
			v1CrossV2
			);
		AkReal32 s = det / v1CrossV2.LengthSquared();

		AkReal32 distsqrd = ((P2 + V2*s) - (P1 + V1*t)).LengthSquared();

		if ((AkReal32)fabs(v1CrossV2.L2_Norm()) >= AKVECTORS_EPSILON
			&& distsqrd < 0.001
			&& s <= 1.0f )
		{
#ifdef AKPORTALS_DEBUG
			Ak3DVector minPoint = PointAt(t);

			char msg[256];
			sprintf(msg, "L1a=[%0.2f,%0.2f,%0.2f];\n", P.X, P.Y, P.Z); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "L1b=[%0.2f,%0.2f,%0.2f];\n", V1.X + P.X, V1.Y + P.Y, V1.Z + P.Z); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "L2a=[%0.2f,%0.2f,%0.2f];\n", A.X, A.Y, A.Z); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "L2b=[%0.2f,%0.2f,%0.2f];\n", B.X, B.Y, B.Z); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "%% t=%0.2f Min t=%0.2f, Max t=%0.2f\n", t, mint, maxt); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "intrPoint=[%0.2f,%0.2f,%0.2f];\n", minPoint.X, minPoint.Y, minPoint.Z); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "\n"); AKPLATFORM::OutputDebugMsg(msg);
#endif

			mint = AkMin(mint, t);
			maxt = AkMax(maxt, t);
			
			return true;
		}

#ifdef AKPORTALS_DEBUG
	//	char msg[256];
	//	sprintf(msg, "%% DISCARTED t=%0.2f Min t=%0.2f, Max t=%0.2f\n", t, mint, maxt); AKPLATFORM::OutputDebugMsg(msg);
#endif
		return false;
	}

	Ak3DVector L;
	Ak3DVector P;

	AkReal32 mint;
	AkReal32 maxt;
};

class AkPlane
{
public:
	AkPlane() = default;

	AkPlane(
		Ak3DVector in_p1,
		Ak3DVector in_p2,
		Ak3DVector in_p4)
	{
		SetPlane(
			in_p1,
			in_p2,
			in_p4);
	}

	void SetPlane(
		Ak3DVector in_p1,
		Ak3DVector in_p2,
		Ak3DVector in_p4)
	{
		// Reorder A-B-C to clockwwise if necessary
		AKASSERT(in_p1.X < 100000 && in_p1.X > -100000);
		AKASSERT(in_p1.Y < 100000 && in_p1.Y > -100000);
		AKASSERT(in_p1.Z < 100000 && in_p1.Z > -100000);

		AKASSERT(in_p2.X < 100000 && in_p2.X > -100000);
		AKASSERT(in_p2.Y < 100000 && in_p2.Y > -100000);
		AKASSERT(in_p2.Z < 100000 && in_p2.Z > -100000);

		AKASSERT(in_p4.X < 100000 && in_p4.X > -100000);
		AKASSERT(in_p4.Y < 100000 && in_p4.Y > -100000);
		AKASSERT(in_p4.Z < 100000 && in_p4.Z > -100000);

		p1 = in_p1;
		p2 = in_p2;
		p4 = in_p4;

		SetNormal();

		// Ax + By + Cz + D = 0
		// Find D using the normal and a point
		D = -(N.X*p1.X) - (N.Y*p1.Y) - (N.Z*p1.Z);
	}

#define EPSILON 0.01f
	bool DoesRayIntersect(
		const Ak3DVector& in_Origin,
		const Ak3DVector& in_Destination,
		Ak3DVector& out_Intersection
		) const
	{
		AkReal32 A = N.X;
		AkReal32 B = N.Y;
		AkReal32 C = N.Z;

		Ak3DVector ray = in_Destination - in_Origin;
		AkReal32 rayLength = ray.Length();

		Ak3DVector intersect;

		// If ray is < EPSILON, use on of the point directly for the test and skip the linear projection
		if (rayLength <= EPSILON)
		{
			Ak3DVector temp = in_Origin - p1;
			AkReal32 dot = temp.DotProduct(N);
			if (dot < EPSILON && dot > -EPSILON)
			{
				intersect = in_Origin;
			}
			else
			{
				// For debug only, to remove
				out_Intersection = p1;
				return false;
			}

		}
		else
		{
			// Normalize ray
			ray.Normalize();

			// 1) if ray len ~= 0, only check if one of the point is on target, ie: assign the intersect point

			// Is ray parallel to the plane?
			if ((A*ray.X + B*ray.Y + C*ray.Z) == 0.0f)
			{
				// For debug only, to remove
				AkReal32 t = -(A*in_Origin.X + B*in_Origin.Y + C*in_Origin.Z + D) / (A*ray.X + B*ray.Y + C*ray.Z);
				intersect = Ak3DVector(in_Origin.X + ray.X*t, in_Origin.Y + ray.Y*t, in_Origin.Z + ray.Z*t);
				out_Intersection = intersect; // For debugging
				return false;
			}


			// Distance along the ray where reflector is hit
			AkReal32 t = -(A*in_Origin.X + B*in_Origin.Y + C*in_Origin.Z + D) / (A*ray.X + B*ray.Y + C*ray.Z);

			// Is the ray going towards the plane? Is it long enough?
			if (t < -EPSILON || t >(rayLength + EPSILON))
			{
				// For debug only, to remove
				intersect = Ak3DVector(in_Origin.X + ray.X*t, in_Origin.Y + ray.Y*t, in_Origin.Z + ray.Z*t);
				out_Intersection = intersect; // For debugging
				return false; // The ray doesn't intersect
			}

			// Find the coordinate of intersection on the plane
			intersect = Ak3DVector(in_Origin.X + ray.X*t, in_Origin.Y + ray.Y*t, in_Origin.Z + ray.Z*t);
		}
		///////////////////////////////////////
		//
		//		p2____v3____p3
		//		|	  .   	|
		//		^	inter  	v4
		//		v1	        v
		//		|	    	|
		//		p1__ v2>___p4

		Ak3DVector v1 = p2 - p1;
		Ak3DVector v2 = p4 - p1;
		Ak3DVector vInter1 = intersect - p1;

		Ak3DVector p3 = p4 + v1;
		Ak3DVector v3 = p2 - p3;
		Ak3DVector v4 = p4 - p3;
		Ak3DVector vInter2 = intersect - p3;

		v1.Normalize(); v2.Normalize(); v3.Normalize(); v4.Normalize(); vInter1.Normalize(); vInter2.Normalize();

		// Since it's a square, the angle between the point of intersection and any segment of the pannel should be < 90 degree,
		// therefore the dot product of the two normalized vectors should be > 0
		AkReal32 dot1 = v1.DotProduct(vInter1);
		AkReal32 dot2 = v2.DotProduct(vInter1);
		AkReal32 dot3 = v3.DotProduct(vInter2);
		AkReal32 dot4 = v4.DotProduct(vInter2);

		out_Intersection = intersect;

		return dot1 >= -EPSILON && dot2 >= -EPSILON && dot3 >= -EPSILON && dot4 >= -EPSILON;
	}

	AkReal32 DistPoint_to_Plane(
		Ak3DVector in_P,
		Ak3DVector& out_B) const
	{
		AkReal32 distance = (AkReal32)(AkReal32)fabs(N.X * in_P.X + N.Y * in_P.Y + N.Z * in_P.Z + D);

		Ak3DVector pointToPlane = N;
		pointToPlane *= distance;

		out_B = in_P + pointToPlane;

		return (AkReal32)fabs(distance);
	}

	void SetReflection(
		AkReal32*			out_mat) const
	{
		// http://ami.ektf.hu/uploads/papers/finalpdf/AMI_40_from175to186.pd
		/* m_pReflectionMatrix
		reflection on z axis

		P0 (x0, y0, z0), P1 (x1, y1, z1) and P2 (x2, y2, z2),
		normal = (cx, cy, cz)
		d = -CxX0 - CyY0 - CzZ0

		Reflect =	1-2Cx^2		-2CxCy		-2CxCz		-2Cxd
		-2CxCy		1-2Cy^2		-2CyCz		-2Cyd
		-2CxCz		-2CyCz		1-2Cz^2		-2Czd
		0			0			0			1
		*/

		AkReal32 d = -(N.X*p1.X) - (N.Y*p1.Y) - (N.Z*p1.Z);

		out_mat[0] = 1 - 2 * N.X*N.X;		out_mat[1] = -2 * N.X*N.Y;				out_mat[2] = -2 * N.X*N.Z;				out_mat[3] = -2 * N.X*d;
		out_mat[0 + 4] = -2 * N.X*N.Y;		out_mat[1 + 4] = 1 - 2 * N.Y*N.Y;		out_mat[2 + 4] = -2 * N.Y*N.Z;			out_mat[3 + 4] = -2 * N.Y*d;
		out_mat[0 + 8] = -2 * N.X*N.Z;		out_mat[1 + 8] = -2 * N.Y*N.Z;			out_mat[2 + 8] = 1 - 2 * N.Z*N.Z;		out_mat[3 + 8] = -2 * N.Z*d;
		out_mat[0 + 12] = 0;				out_mat[1 + 12] = 0;					out_mat[2 + 12] = 0;					out_mat[3 + 12] = 1;
	}

	Ak3DVector GetN() const { return N; }
	AkReal32 GetD() const { return D; }

	bool FindIntersectionPoints(
		const AkPlane& in_PlaneB,
		AkIntersectionPoints& out_Intrs) const
	{
		out_Intrs.count = 0;

		// Use vector to solve A

		Ak3DVector point;

		Ak3DVector N1 = N;
		Ak3DVector N2 = in_PlaneB.GetN();
		AkReal32 D1 = D;
		AkReal32 D2 = in_PlaneB.GetD();

		Ak3DVector L = N1.Cross(N2);
		if (L.Length() < 0.001f)
		{
			return false; // The two planes are parallel
		}

		AkUInt8 pivotAxis = 0;

		if ((AkReal32)fabs(L.Y) > (AkReal32)fabs(L.X))
		{
			pivotAxis = 1;
			if ((AkReal32)fabs(L.Z) > (AkReal32)fabs(L.Y))
			{
				pivotAxis = 2;
			}
		}
		else if ((AkReal32)fabs(L.Z) > (AkReal32)fabs(L.X))
		{
			pivotAxis = 2;
		}

		/*
		Pu = ( N1v*D2 - N2v*D1 ) / Lw
		Pv = ( N2u*D1 - N1u*D2 ) / Lw
		Pz = 0
		*/

		switch (pivotAxis)
		{
		case 0:
			AKASSERT((AkReal32)fabs(L.X) > AKVECTORS_EPSILON);
			point.X = 0.f;
			point.Y = (N1.Z*D2 - N2.Z*D1) / L.X;
			point.Z = (N2.Y*D1 - N1.Y*D2) / L.X;
			break;
		case 1:
			AKASSERT((AkReal32)fabs(L.Y) > AKVECTORS_EPSILON);
			point.X = (N1.Z*D2 - N2.Z*D1) / L.Y;
			point.Y = 0.f;
			point.Z = (N2.X*D1 - N1.X*D2) / L.Y;
			break;
		case 2:
			AKASSERT((AkReal32)fabs(L.Z) > AKVECTORS_EPSILON);
			point.X = (N1.Y*D2 - N2.Y*D1) / L.Z;
			point.Y = (N2.X*D1 - N1.X*D2) / L.Z;
			point.Z = 0.f;
			break;
		};



		L.Normalize();

		AkLine intrLine = AkLine(L, point);
		AkLine intrLine2 = AkLine(L, point);

		//in_PlaneB.GetP1()

		// find min max
		AkUInt32 cpt = 0;
		AkUInt32 cpt2 = 0;
		Ak3DVector p3 = GetP2() + (GetP4() - GetP1());

#ifdef AKPORTALS_DEBUG
		char msg[256];
		sprintf(msg, "P1a=[%0.2f,%0.2f,%0.2f];\n", GetP1().X, GetP1().Y, GetP1().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P2a=[%0.2f,%0.2f,%0.2f];\n", GetP2().X, GetP2().Y, GetP2().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P4a=[%0.2f,%0.2f,%0.2f];\n", GetP4().X, GetP4().Y, GetP4().Z); AKPLATFORM::OutputDebugMsg(msg);

		sprintf(msg, "P1b=[%0.2f,%0.2f,%0.2f];\n", in_PlaneB.GetP1().X, in_PlaneB.GetP1().Y, in_PlaneB.GetP1().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P2b=[%0.2f,%0.2f,%0.2f];\n", in_PlaneB.GetP2().X, in_PlaneB.GetP2().Y, in_PlaneB.GetP2().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P4b=[%0.2f,%0.2f,%0.2f];\n", in_PlaneB.GetP4().X, in_PlaneB.GetP4().Y, in_PlaneB.GetP4().Z); AKPLATFORM::OutputDebugMsg(msg);

		sprintf(msg, "line1=[%0.2f,%0.2f,%0.2f];\n", point.X + L.X*1000.f, point.Y + L.Y*1000.f, point.Z + L.Z*1000.f); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "line2=[%0.2f,%0.2f,%0.2f];\n", point.X - L.X*1000.f, point.Y - L.Y*500.f, point.Z - L.Z*500.f); AKPLATFORM::OutputDebugMsg(msg);


		sprintf(msg, "%% Plane intersec\n"); AKPLATFORM::OutputDebugMsg(msg);
#endif
		// for the four lines in rectangle
		// Find where the line is crossing with plane A
		if (intrLine.Intersect(GetP1(), GetP2())) cpt++;
		if (intrLine.Intersect(GetP1(), GetP4())) cpt++;
		if (intrLine.Intersect(GetP2(), p3)) cpt++;
		if (intrLine.Intersect(p3, GetP4())) cpt++;
		//AKASSERT(cpt == 2);

#ifdef AKPORTALS_DEBUG
		sprintf(msg, "%% Portal intersec\n"); AKPLATFORM::OutputDebugMsg(msg);
#endif

		// Find where the line is crossing with plane B
		p3 = in_PlaneB.GetP2() + (in_PlaneB.GetP4() - in_PlaneB.GetP1());
		if (intrLine2.Intersect(in_PlaneB.GetP1(), in_PlaneB.GetP2())) cpt2++;
		if (intrLine2.Intersect(in_PlaneB.GetP1(), in_PlaneB.GetP4())) cpt2++;
		if (intrLine2.Intersect(in_PlaneB.GetP2(), p3)) cpt2++;
		if (intrLine2.Intersect(p3, in_PlaneB.GetP4())) cpt2++;
		// **AKASSERT(cpt2 == 2 || cpt == 2);

		if (cpt < 2 || cpt2 < 2)
		{
#ifdef AKPORTALS_DEBUG
			sprintf(msg, "%% NON \n"); AKPLATFORM::OutputDebugMsg(msg);
			sprintf(msg, "%% _______________________\n"); AKPLATFORM::OutputDebugMsg(msg);
#endif
			return false;
		}

		AkReal32 start = AkMax(intrLine.mint, intrLine2.mint);
		AkReal32 end = AkMin(intrLine.maxt, intrLine2.maxt);

		Ak3DVector minPoint = intrLine.PointAt(start);
		Ak3DVector maxPoint = intrLine.PointAt(end);
#ifdef AKPORTALS_DEBUG
		sprintf(msg, "P1a=[%0.2f,%0.2f,%0.2f];\n", GetP1().X, GetP1().Y, GetP1().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P2a=[%0.2f,%0.2f,%0.2f];\n", GetP2().X, GetP2().Y, GetP2().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P4a=[%0.2f,%0.2f,%0.2f];\n", GetP4().X, GetP4().Y, GetP4().Z); AKPLATFORM::OutputDebugMsg(msg);

		sprintf(msg, "P1b=[%0.2f,%0.2f,%0.2f];\n", in_PlaneB.GetP1().X, in_PlaneB.GetP1().Y, in_PlaneB.GetP1().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P2b=[%0.2f,%0.2f,%0.2f];\n", in_PlaneB.GetP2().X, in_PlaneB.GetP2().Y, in_PlaneB.GetP2().Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "P4b=[%0.2f,%0.2f,%0.2f];\n", in_PlaneB.GetP4().X, in_PlaneB.GetP4().Y, in_PlaneB.GetP4().Z); AKPLATFORM::OutputDebugMsg(msg);

		sprintf(msg, "line1=[%0.2f,%0.2f,%0.2f];\n", point.X + L.X*1000.f, point.Y + L.Y*1000.f, point.Z + L.Z*1000.f); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "line2=[%0.2f,%0.2f,%0.2f];\n", point.X - L.X*1000.f, point.Y - L.Y*500.f, point.Z - L.Z*500.f); AKPLATFORM::OutputDebugMsg(msg);

		sprintf(msg, "intr1=[%0.2f,%0.2f,%0.2f];\n", minPoint.X, minPoint.Y, minPoint.Z); AKPLATFORM::OutputDebugMsg(msg);
		sprintf(msg, "intr2=[%0.2f,%0.2f,%0.2f];\n", maxPoint.X, maxPoint.Y, maxPoint.Z); AKPLATFORM::OutputDebugMsg(msg);

		sprintf(msg, "%% _______________________\n"); AKPLATFORM::OutputDebugMsg(msg);
#endif
		out_Intrs.points[0] = minPoint;
		out_Intrs.points[1] = maxPoint;
		out_Intrs.count = 2;

		return true;
	}

	Ak3DVector GetP1() const { return p1; }
	Ak3DVector GetP2() const { return p2; }
	Ak3DVector GetP4() const { return p4; }

private:
	bool SetNormal()
	{
		//m_pNormal = (B-A) cross (C-A); normalize
		Ak3DVector a = p2 - p1;
		Ak3DVector b = p4 - p1;

		N = Ak3DVector(a.Y*b.Z - a.Z*b.Y, -(a.X*b.Z - a.Z*b.X), a.X*b.Y - a.Y*b.X);

		AkReal32 len = N.Length();
		AKASSERT(len > 0.f);

		if (len > 0)
		{
			N /= len;
		}
		else
		{
			return false;
		}

		return true;
	};

	/*
	p2__________p3
	|	  .   	|
	^	inter  	v3
	v1	        v
	|	    	|
	p1__ v2>___p4
	*/

	Ak3DVector p1; // Bottom left
	Ak3DVector p2; // Top left
	Ak3DVector p4; // Tottom right
	Ak3DVector N;  // Normal vector
	AkReal32   D;  // Plane equation: Ax + By + Cz = D => N.Xx + N.Yy + N.Zz = D
};

template<typename TReal>
struct TBoundingBox
{
	using TVectorType = T3DVector<TReal>;

	TBoundingBox(const TVectorType& in_min, const TVectorType& in_max) :
		m_Min(in_min),
		m_Max(in_max)
	{}

	TBoundingBox() :
		m_Min(TVectorType(RealPrecision<TReal>::MAX_VALUE, RealPrecision<TReal>::MAX_VALUE, RealPrecision<TReal>::MAX_VALUE)),
		m_Max(TVectorType(-RealPrecision<TReal>::MAX_VALUE, -RealPrecision<TReal>::MAX_VALUE, -RealPrecision<TReal>::MAX_VALUE))
	{}

	void Update(const TVectorType& in_point)
	{
		if (m_Min.X > in_point.X)
			m_Min.X = in_point.X;

		if (m_Min.Y > in_point.Y)
			m_Min.Y = in_point.Y;

		if (m_Min.Z > in_point.Z)
			m_Min.Z = in_point.Z;

		if (m_Max.X < in_point.X)
			m_Max.X = in_point.X;

		if (m_Max.Y < in_point.Y)
			m_Max.Y = in_point.Y;

		if (m_Max.Z < in_point.Z)
			m_Max.Z = in_point.Z;
	}

	AkForceInline bool IsWithin(const TVectorType& in_Point) const
	{
		return in_Point >= m_Min && in_Point <= m_Max;
	}

	AkForceInline bool IsWithin(const TBoundingBox& in_BB) const
	{
		return (m_Min.X <= in_BB.m_Max.X && m_Max.X >= in_BB.m_Min.X) &&
			(m_Min.Y <= in_BB.m_Max.Y && m_Max.Y >= in_BB.m_Min.Y) &&
			(m_Min.Z <= in_BB.m_Max.Z && m_Max.Z >= in_BB.m_Min.Z);
	}

	TBoundingBox Intersect(const TBoundingBox& in_BB) const
	{
		TBoundingBox result;
		
		result.m_Max.X = AkMin(m_Max.X, in_BB.m_Max.X);
		result.m_Max.Y = AkMin(m_Max.Y, in_BB.m_Max.Y);
		result.m_Max.Z = AkMin(m_Max.Z, in_BB.m_Max.Z);

		result.m_Min.X = AkMax(m_Min.X, in_BB.m_Min.X);
		result.m_Min.Y = AkMax(m_Min.Y, in_BB.m_Min.Y);
		result.m_Min.Z = AkMax(m_Min.Z, in_BB.m_Min.Z);
		
		return result;
	}

	AkForceInline bool IsEmpty() const
	{
		return (m_Min.X >= m_Max.X) || (m_Min.Y >= m_Max.Y) || (m_Min.Z >= m_Max.Z);
	}

	AkForceInline bool IsValid() const
	{
		return (m_Min.X <= m_Max.X) && (m_Min.Y <= m_Max.Y) && (m_Min.Z <= m_Max.Z);
	}

	TVectorType m_Min;
	TVectorType m_Max;
};

typedef TBoundingBox<AkReal32> AkBoundingBox;
typedef TBoundingBox<AkReal64> AkBoundingBox64;

class AkBox
{
public:
	AkBox() = default;

	void Init(
		const Ak3DVector& in_center,
		const Ak3DVector& in_extent,
		const Ak3DVector& in_Front,
		const Ak3DVector& in_Up)
	{
		AKASSERT(fabs(in_Front.Length() - 1.f) < 0.001 && fabs(in_Up.Length() - 1.f) < 0.001);//Must be unit vectors.
		AKASSERT(fabs(in_Front.Dot(in_Up) - 0.f) < 0.001); //Must be orthogonal.

		m_Center = in_center;
		m_Extent = in_extent;

		m_Z = in_Front;
		m_Y = in_Up;
		m_X = m_Z.Cross(m_Y);
	}

	bool IsPointInBox(const Ak3DVector& in_Point) const
	{
		Ak3DVector pt = in_Point - m_Center;
		return	fabs(pt.Dot(m_X)) <= m_Extent.X && fabs(pt.Dot(m_Y)) <= m_Extent.Y && fabs(pt.Dot(m_Z)) <= m_Extent.Z;
	}

	Ak3DVector GetSize() const { return m_Extent*2.f; }
	Ak3DVector GetCenter() const { return m_Center; }

	Ak3DVector GetUx() const { return m_X; }
	Ak3DVector GetUy() const { return m_Y; }
	Ak3DVector GetUz() const { return m_Z; }

	Ak3DVector GetFront() const { return m_Z; }
	Ak3DVector GetUp() const { return m_Y; }
	Ak3DVector GetSide() const { return m_X; }

	AkReal32 GetVolume() const
	{
		Ak3DVector size = GetSize();
		return size.X * size.Y * size.Z;
	}

	bool SeparatingAxisExists(
		const Ak3DVector& L,
		const AkBox& B) const
	{
		// Separating Axis Theorem for Oriented Bounding Boxes by Johnny Huynh
		const AkBox& A = *this;
		Ak3DVector T = B.GetCenter() - A.GetCenter();

		AkReal32 WA = A.m_Extent.X;
		AkReal32 HA = A.m_Extent.Y;
		AkReal32 DA = A.m_Extent.Z;

		AkReal32 WB = B.m_Extent.X;
		AkReal32 HB = B.m_Extent.Y;
		AkReal32 DB = B.m_Extent.Z;

		Ak3DVector Ax = A.GetUx();
		Ak3DVector Ay = A.GetUy();
		Ak3DVector Az = A.GetUz();

		Ak3DVector Bx = B.GetUx();
		Ak3DVector By = B.GetUy();
		Ak3DVector Bz = B.GetUz();

		/*
		| T • L | > | (WA*Ax) • L | + | (HA*Ay) • L | + |(DA*Az) • L | +
					| (WB*Bx) • L | +| (HB*By) • L | +| (DB*Bz) • L |*/

		AkReal32 left = (AkReal32)fabs(T.DotProduct(L));
		AkReal32 dpax = (AkReal32)fabs((Ax*WA).DotProduct(L));
		AkReal32 dpay = (AkReal32)fabs((Ay*HA).DotProduct(L));
		AkReal32 dpaz = (AkReal32)fabs((Az*DA).DotProduct(L));
		AkReal32 dpbx = (AkReal32)fabs((Bx*WB).DotProduct(L));
		AkReal32 dpby = (AkReal32)fabs((By*HB).DotProduct(L));
		AkReal32 dpbz = (AkReal32)fabs((Bz*DB).DotProduct(L));

		AkReal32 right = dpax + dpay + dpaz + dpbx + dpby + dpbz;

		return left > right;
	}

	void UpdateBoundingBox(AkBoundingBox& out_aabb) const
	{
		Ak3DVector x = m_X * m_Extent.X;
		out_aabb.Update(m_Center + x);
		out_aabb.Update(m_Center - x);
		Ak3DVector y = m_Y * m_Extent.Y;
		out_aabb.Update(m_Center + y);
		out_aabb.Update(m_Center - y);
		Ak3DVector Z = m_Z * m_Extent.Z;
		out_aabb.Update(m_Center + Z);
		out_aabb.Update(m_Center - Z);
	}

private:

	Ak3DVector m_Center;
	Ak3DVector m_Extent;

	//Orthonormal Axes
	Ak3DVector m_X;
	Ak3DVector m_Y;
	Ak3DVector m_Z;
};