_ak_vectors_8h

Wwise SDK 2024.1.1

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 released in source code form as part of the SDK installer package.
  
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 // 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 <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;
     }
  
     AkForceInline bool Equals(const T3DVector& b, const TDataType tolerance = static_cast<TDataType>(0.0)) const
     {
         return fabs(X - b.X) <= tolerance && fabs(Y - b.Y) <= tolerance && fabs(Z - b.Z) <= tolerance;
     }
  
     //-----------------------------------------------------------
     // 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;
 };

AkMatrix3x3::operator/=

AkMatrix3x3 & operator/=(const AkReal32 f)

Definition: AkVectors.h:952

T3DVector::operator*=

AkForceInline T3DVector & operator*=(const TDataType f)

Definition: AkVectors.h:367

TBoundingBox::TBoundingBox

TBoundingBox()

Definition: AkVectors.h:1769

AkQuaternion::Normalize

AkForceInline AkQuaternion & Normalize()

Definition: AkVectors.h:1153

AkMin

#define AkMin(x1, x2)

Definition: AkPlatformFuncs.h:90

Ak3DVector

T3DVector< AkReal32 > Ak3DVector

Definition: AkVectors.h:690

AkSpeakerVolumes.h

T3DVector::X

TDataType X

Definition: AkVectors.h:665

AkPlane::FindIntersectionPoints

bool FindIntersectionPoints(const AkPlane &in_PlaneB, AkIntersectionPoints &out_Intrs) const

Definition: AkVectors.h:1563

T3DVector::T3DVector

T3DVector(const AkVector &in_vector)

Definition: AkVectors.h:249

AkPlane::DistPoint_to_Plane

AkReal32 DistPoint_to_Plane(Ak3DVector in_P, Ak3DVector &out_B) const

Definition: AkVectors.h:1521

AKVECTORS_TWOPI

#define AKVECTORS_TWOPI

Definition: AkVectors.h:46

AkBox::GetUz

Ak3DVector GetUz() const

Definition: AkVectors.h:1872

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T3DVector(TDataType in_x, TDataType in_y, TDataType in_z)

Definition: AkVectors.h:230

T3DVector::Abs

AkForceInline T3DVector Abs() const

Definition: AkVectors.h:648

Ak3DIntVector::Y

AkInt32 Y

Y Position

Definition: AkVectors.h:121

RealPrecision< AkReal64 >::ACos

static AkReal64 ACos(AkReal64 in_value)

Definition: AkVectors.h:162

AkIntersectionPoints::points

Ak3DVector points[2]

Definition: AkVectors.h:1278

Ak3DIntVector

Definition: AkVectors.h:109

T3DVector::operator==

AkForceInline bool operator==(const T3DVector &b) const

Definition: AkVectors.h:337

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AkForceInline bool IsWithin(const TBoundingBox &in_BB) const

Definition: AkVectors.h:1800

AkPlane::AkPlane

AkPlane()=default

Ak2DVector::operator=

AkForceInline Ak2DVector operator=(const Ak2DVector &b)

Definition: AkVectors.h:726

AkBoundingBox

TBoundingBox< AkReal32 > AkBoundingBox

Definition: AkVectors.h:1836

RealPrecision

Definition: AkVectors.h:133

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T3DVector< AkReal64 > Ak3DVector64

Definition: AkVectors.h:694

AKVECTORS_PI

#define AKVECTORS_PI

Definition: AkVectors.h:45

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#define AkMax(x1, x2)

Definition: AkPlatformFuncs.h:89

AkPlane::GetN

Ak3DVector GetN() const

Definition: AkVectors.h:1560

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Ak3DVector PointAt(AkReal32 t) const

Definition: AkVectors.h:1299

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bool Intersect(Ak3DVector A, Ak3DVector B)

Definition: AkVectors.h:1304

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AkReal32 phi

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Definition: AkTypes.h:747

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AkReal32 X

Definition: AkVectors.h:1271

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Ak4DVector operator-(const Ak4DVector &b) const

Definition: AkVectors.h:93

AkBox::SeparatingAxisExists

bool SeparatingAxisExists(const Ak3DVector &L, const AkBox &B) const

Definition: AkVectors.h:1884

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AkSafeConversion TTypeConverter

Definition: AkVectors.h:217

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bool IsPointInBox(const Ak3DVector &in_Point) const

Definition: AkVectors.h:1861

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TDataType Y

Definition: AkVectors.h:666

RealPrecision< AkReal64 >::Cos

static AkReal64 Cos(AkReal64 in_value)

Definition: AkVectors.h:159

RealPrecision< AkReal64 >::IsFinite

static bool IsFinite(AkReal64 in_val)

Definition: AkVectors.h:163

AkQuaternion::Inverse

AkForceInline AkQuaternion Inverse() const

Definition: AkVectors.h:1163

AkQuaternion::operator*

AkForceInline AkQuaternion operator*(const AkQuaternion &Q) const

Quaternion multiplication.

Definition: AkVectors.h:1225

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Ak4DVector & operator/=(const AkReal32 f)

Definition: AkVectors.h:83

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Definition: AkVectors.h:113

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static AkQuaternion FromRotationMatrix(const AkMatrix3x3 &in_mat)

Definition: AkVectors.h:1065

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void SetPlane(Ak3DVector in_p1, Ak3DVector in_p2, Ak3DVector in_p4)

Definition: AkVectors.h:1394

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void OutputDebugMsg(const char *in_pszMsg)

Output a debug message on the console (Ansi string)

Definition: AkPlatformFuncs.h:73

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AkMatrix4x4()=default

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static AkForceInline void Diagonal(AkMatrix3x3 &out_mat, AkReal32 in_f)

Definition: AkVectors.h:1006

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Definition: AkVectors.h:179

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Definition: AkVectors.h:1761

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Definition: AkVectors.h:51

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T3DVector(TDataType in_scalar)

Definition: AkVectors.h:294

TBoundingBox::IsEmpty

AkForceInline bool IsEmpty() const

Definition: AkVectors.h:1822

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Definition: AkVectors.h:210

Ak3DVector32

T3DVector< AkReal32 > Ak3DVector32

Definition: AkVectors.h:691

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

Definition: AkVectors.h:1033

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float32x4_t AKSIMD_V4F32

Vector of 4 32-bit floats

Definition: AkSimdTypes.h:62

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AkForceInline bool operator==(const Ak2DVector &b) const

Definition: AkVectors.h:769

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Ak3DVector GetUx() const

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uint8_t AkUInt8

Unsigned 8-bit integer

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static AkReal64 Sqrt(AkReal64 in_value)

Definition: AkVectors.h:161

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Ak3DVector GetCenter() const

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static AkForceInline TDataType Determinant(const T3DVector &a, const T3DVector &b, const T3DVector &c)

Definition: AkVectors.h:539

AkReal32

float AkReal32

32-bit floating point

Definition: AkNumeralTypes.h:46

Ak2DVector::operator/=

Ak2DVector & operator/=(const AkReal32 f)

Definition: AkVectors.h:760

T3DVector::LinearCombination

AkForceInline T3DVector LinearCombination(const T3DVector &A, const T3DVector &B, const T3DVector &C) const

Definition: AkVectors.h:549

RealPrecision< AkReal32 >::Sqrt

static AkReal32 Sqrt(AkReal32 in_value)

Definition: AkVectors.h:141

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Definition: AkVectors.h:885

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int32_t AkInt32

Signed 32-bit integer

Definition: AkNumeralTypes.h:43

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

Definition: AkVectors.h:931

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TBoundingBox Intersect(const TBoundingBox &in_BB) const

Definition: AkVectors.h:1807

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Ak2DVector()=default

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AkForceInline TDataType DotProduct(const T3DVector &v2) const

Definition: AkVectors.h:607

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AkForceInline T3DVector operator-(const T3DVector &b) const

Definition: AkVectors.h:465

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AkForceInline T3DVector & operator/=(const TDataType f)

Definition: AkVectors.h:376

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Definition: AkVectors.h:1379

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Definition: AkVectors.h:1052

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AkForceInline T3DVector operator*(const T3DVector v2) const

Definition: AkVectors.h:386

AKVECTORS_PIOVERTWO

#define AKVECTORS_PIOVERTWO

Definition: AkVectors.h:47

T3DVector::IsFinite

AkForceInline bool IsFinite() const

Definition: AkVectors.h:657

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Ak4DVector & operator=(const Ak4DVector &b)

Definition: AkVectors.h:73

Ak2DVector::operator!=

AkForceInline bool operator!=(const Ak2DVector &b) const

Definition: AkVectors.h:774

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AkForceInline void Convert(AkReal64 &out_to, AkReal32 in_from)

Definition: AkVectors.h:194

Ak2DVector::IsAllPositive

AkForceInline bool IsAllPositive() const

Definition: AkVectors.h:878

AkSafeConversion

Definition: AkVectors.h:192

Ak2DVector::Length

AkForceInline AkReal32 Length() const

Definition: AkVectors.h:779

Ak4DVector::Ak4DVector

Ak4DVector()

Definition: AkVectors.h:55

AkBox::GetSide

Ak3DVector GetSide() const

Definition: AkVectors.h:1876

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AkLine()

Definition: AkVectors.h:1285

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AkReal32 Y

Y Position

Definition: AkTypes.h:423

Ak2DVector::Ak2DVector

Ak2DVector(AkReal32 x, AkReal32 y)

Definition: AkVectors.h:718

RealPrecision< AkReal64 >::Sin

static AkReal64 Sin(AkReal64 in_value)

Definition: AkVectors.h:160

AkMatrix3x3::operator*=

AkForceInline AkMatrix3x3 & operator*=(const AkReal32 &in_f)

Definition: AkVectors.h:998

AkMatrix4x4::operator=

AkMatrix4x4 & operator=(AkReal32 *in_Data)

Definition: AkVectors.h:910

TBoundingBox::Update

void Update(const TVectorType &in_point)

Definition: AkVectors.h:1774

AkQuaternion::FromAngleAndAxis

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

Definition: AkVectors.h:1135

T3DVector::LengthSquared

AkForceInline TDataType LengthSquared() const

Definition: AkVectors.h:635

AkBox::GetVolume

AkReal32 GetVolume() const

Definition: AkVectors.h:1878

AkPlane::GetD

AkReal32 GetD() const

Definition: AkVectors.h:1561

T3DVector::Dot

AkForceInline TDataType Dot(const T3DVector &v2) const

Definition: AkVectors.h:612

AkVector::X

AkReal32 X

X Position

Definition: AkTypes.h:422

T3DVector::data_type

TDataType data_type

Definition: AkVectors.h:214

T3DVector::operator!=

AkForceInline bool operator!=(const T3DVector &b) const

Definition: AkVectors.h:342

Ak2DVector::operator-

Ak2DVector operator-(const Ak2DVector &b) const

Definition: AkVectors.h:742

AKSIMD_GETELEMENT_V4F32

#define AKSIMD_GETELEMENT_V4F32(__vName, __num__)

Get the element at index num in vector __vName

Definition: AkSimd.h:37

AkMatrix4x4::m_Data

AkReal32 m_Data[MAX_SIZE]

Definition: AkVectors.h:920

T3DVector::operator+

AkForceInline T3DVector operator+(const TDataType f) const

Definition: AkVectors.h:432

operator*

AkForceInline T3DVector< TDataType > operator*(const TDataType f, const T3DVector< TDataType > &v)

Definition: AkVectors.h:671

AKASSERT

#define AKASSERT(Condition)

Definition: AkAssert.h:67

T3DVector::operator-

AkForceInline T3DVector operator-(const TDataType f) const

Definition: AkVectors.h:443

Ak4DVector::v

AkReal32 v[4]

Definition: AkVectors.h:105

IAkPluginMemAlloc.h

AkSphericalCoord

Spherical coordinates.

Definition: AkTypes.h:746

T3DVector::Min

static AkForceInline T3DVector Min(const T3DVector &A, const T3DVector &B)

Definition: AkVectors.h:486

T3DVector::SphericalToCartesian

AkForceInline T3DVector SphericalToCartesian(const TDataType azimuth, const TDataType elevation)

Definition: AkVectors.h:526

AkLine::mint

AkReal32 mint

Definition: AkVectors.h:1374

T3DVector::PointV4F32

AkForceInline AKSIMD_V4F32 PointV4F32() const

Definition: AkVectors.h:308

AkIntersectionPoints

Definition: AkVectors.h:1277

AkMatrix3x3::AkMatrix3x3

AkMatrix3x3()=default

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AkReal32 Z

Z Position

Definition: AkTypes.h:424

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AkQuaternion()

Definition: AkVectors.h:1055

AkArray.h

AkMatrix3x3::OuterProduct

static AkForceInline void OuterProduct(AkMatrix3x3 &out_mat, const Ak3DVector &in_v0, const Ak3DVector &in_v1)

Definition: AkVectors.h:1021

AkSafeConversion::Convert

AkForceInline void Convert(TReal &out_to, TReal in_from)

Definition: AkVectors.h:199

AkMatrix3x3

Definition: AkVectors.h:924

AkBox::GetFront

Ak3DVector GetFront() const

Definition: AkVectors.h:1874

AkBox::GetUy

Ak3DVector GetUy() const

Definition: AkVectors.h:1871

T3DVector::operator+

AkForceInline T3DVector operator+(const T3DVector &b) const

Definition: AkVectors.h:454

Ak2DVector::Y

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Definition: AkVectors.h:886

AkMatrix3x3::Add

static AkForceInline void Add(AkMatrix3x3 &out_res, const AkMatrix3x3 &in_m0, const AkMatrix3x3 &in_m1)

Definition: AkVectors.h:989

T3DVector::Cast

TVectorType Cast() const

Definition: AkVectors.h:701

Ak2DVector

Definition: AkVectors.h:712

AkMatrix4x4::operator/=

AkMatrix4x4 & operator/=(const AkReal32 f)

Definition: AkVectors.h:902

AkBoundingBox64

TBoundingBox< AkReal64 > AkBoundingBox64

Definition: AkVectors.h:1837

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Ak3DIntVector()=default

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AkForceInline Ak3DVector UnrotateVector(const Ak3DVector32 &in_v) const

Definition: AkVectors.h:1262

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AkForceInline AkReal32 & operator()(const AkUInt32 row, const AkUInt32 column)

Definition: AkVectors.h:964

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AkReal32 W

Definition: AkVectors.h:1270

AkBox

Definition: AkVectors.h:1840

AkQuaternion::AkQuaternion

AkQuaternion(AkReal32 in_angle, const Ak3DVector &in_axis)

Definition: AkVectors.h:1215

operator/

AkForceInline T3DVector< TDataType > operator/(const TDataType f, const T3DVector< TDataType > &v)

Definition: AkVectors.h:677

AkLine::AkLine

AkLine(Ak3DVector in_L, Ak3DVector in_P)

Definition: AkVectors.h:1291

AkQuaternion::FromEulers

static AkQuaternion FromEulers(AkReal32 in_x, AkReal32 in_y, AkReal32 in_z)

Definition: AkVectors.h:1113

AkReal64

double AkReal64

64-bit floating point

Definition: AkNumeralTypes.h:47

AkMatrix3x3::CrossProductMatrix

static AkForceInline void CrossProductMatrix(AkMatrix3x3 &out_mat, const Ak3DVector &in_u)

Definition: AkVectors.h:1014

AkPlane::DoesRayIntersect

bool DoesRayIntersect(const Ak3DVector &in_Origin, const Ak3DVector &in_Destination, Ak3DVector &out_Intersection) const

Definition: AkVectors.h:1424

AkLine::P

Ak3DVector P

Definition: AkVectors.h:1372

AkQuaternion::Z

AkReal32 Z

Definition: AkVectors.h:1273

AkQuaternion::operator*

AkForceInline Ak3DVector32 operator*(const Ak3DVector32 &in_v) const

Definition: AkVectors.h:1234

AkBox::AkBox

AkBox()=default

T3DVector::operator<

AkForceInline bool operator<(const T3DVector &b) const

Definition: AkVectors.h:347

RealPrecision< AkReal32 >::Cos

static AkReal32 Cos(AkReal32 in_value)

Definition: AkVectors.h:139

Ak2DVector::NormalizeSpherical

AkForceInline Ak2DVector NormalizeSpherical() const

Definition: AkVectors.h:829

TBoundingBox::IsWithin

AkForceInline bool IsWithin(const TVectorType &in_Point) const

Definition: AkVectors.h:1795

AkUInt64

uint64_t AkUInt64

Unsigned 64-bit integer

Definition: AkNumeralTypes.h:39

AkVector64::Y

AkReal64 Y

Y Position

Definition: AkTypes.h:363

ADD

#define ADD(i, j)

T3DVector::Zero

void Zero()

Definition: AkVectors.h:328

Ak2DVector::NormalizeSpherical

AkForceInline void NormalizeSpherical()

Definition: AkVectors.h:858

AkMatrix3x3::Rotation

static AkForceInline void Rotation(AkMatrix3x3 &out_mat, AkReal32 in_angle, const Ak3DVector &in_axis)

Definition: AkVectors.h:1028

AkBox::GetUp

Ak3DVector GetUp() const

Definition: AkVectors.h:1875

AKVECTORS_EPSILON

#define AKVECTORS_EPSILON

Definition: AkVectors.h:48

TBoundingBox::m_Max

TVectorType m_Max

Definition: AkVectors.h:1833

T3DVector::Rotate180X_90Y

AkForceInline T3DVector Rotate180X_90Y() const

Definition: AkVectors.h:515

RealPrecision< AkReal32 >::Sin

static AkReal32 Sin(AkReal32 in_value)

Definition: AkVectors.h:140

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void Init(const Ak3DVector &in_center, const Ak3DVector &in_extent, const Ak3DVector &in_Front, const Ak3DVector &in_Up)

Definition: AkVectors.h:1844

AkTypes.h

AkPolarCoord::theta

AkReal32 theta

Azimuth

Definition: AkTypes.h:741

AkMatrix3x3::operator+=

AkForceInline AkMatrix3x3 & operator+=(const AkMatrix3x3 &in_rhs)

Definition: AkVectors.h:983

AkQuaternion::Y

AkReal32 Y

Definition: AkVectors.h:1272

TBoundingBox::IsValid

AkForceInline bool IsValid() const

Definition: AkVectors.h:1827

AkPlane::GetP2

Ak3DVector GetP2() const

Definition: AkVectors.h:1716

AkMatrix3x3::operator()

AkForceInline const AkReal32 & operator()(const AkUInt32 row, const AkUInt32 column) const

Definition: AkVectors.h:969

T3DVector::operator>=

AkForceInline bool operator>=(const T3DVector &b) const

Definition: AkVectors.h:362

T3DVector::operator/

AkForceInline T3DVector operator/(const TDataType f) const

Definition: AkVectors.h:419

AkVector64

3D 64-bit vector. Intended as storage for world positions of sounds and objects, benefiting from 64-b...

Definition: AkTypes.h:334

Ak2DVector::CartesianToSpherical

AkForceInline Ak2DVector & CartesianToSpherical(const Ak3DVector &in_Cartesian)

Definition: AkVectors.h:786

AkMatrix4x4

Definition: AkVectors.h:892

AkPlane::AkPlane

AkPlane(Ak3DVector in_p1, Ak3DVector in_p2, Ak3DVector in_p4)

Definition: AkVectors.h:1383

AkUInt32

uint32_t AkUInt32

Unsigned 32-bit integer

Definition: AkNumeralTypes.h:38

AkQuaternion::AkQuaternion

AkQuaternion(const Ak3DVector &in_v0, const Ak3DVector &in_v1)

Definition: AkVectors.h:1178

RealPrecision< AkReal32 >::ACos

static AkReal32 ACos(AkReal32 in_value)

Definition: AkVectors.h:142

Ak3DIntVector::X

AkInt32 X

X Position

Definition: AkVectors.h:120

T3DVector::operator/

AkForceInline T3DVector operator/(const T3DVector in_rhs) const

Definition: AkVectors.h:408

EPSILON

#define EPSILON

Definition: AkVectors.h:1423

T3DVector::Z

TDataType Z

Definition: AkVectors.h:667

AkVector

3D vector for some operations in 3D space. Typically intended only for localized calculations due to ...

Definition: AkTypes.h:369

T3DVector::T3DVector

T3DVector()

Definition: AkVectors.h:224

AkBox::GetSize

Ak3DVector GetSize() const

Definition: AkVectors.h:1867

AkPlane::GetP1

Ak3DVector GetP1() const

Definition: AkVectors.h:1715

T3DVector::T3DVector

T3DVector(const AKSIMD_V4F32 &in_v4f32)

Definition: AkVectors.h:301

T3DVector::IsAllPositive

AkForceInline bool IsAllPositive() const

Definition: AkVectors.h:641

T3DVector::HorizontalMax

AkForceInline TDataType HorizontalMax() const

Definition: AkVectors.h:481

AkPlane::GetP4

Ak3DVector GetP4() const

Definition: AkVectors.h:1717

AkImplicitConversion::Convert

AkForceInline void Convert(TToReal &out_to, TFromReal in_from)

Definition: AkVectors.h:182

T3DVector::L2_Norm

AkForceInline TDataType L2_Norm() const

Definition: AkVectors.h:602

AkQuaternion::Length

AkForceInline AkReal32 Length() const

Definition: AkVectors.h:1148

T3DVector::Equals

AkForceInline bool Equals(const T3DVector &b, const TDataType tolerance=static_cast< TDataType >(0.0)) const

Definition: AkVectors.h:508

AkVector64::Z

AkReal64 Z

Z Position

Definition: AkTypes.h:364

Ak3DIntVector::Z

AkInt32 Z

Z Position

Definition: AkVectors.h:122

T3DVector::operator*

AkForceInline T3DVector operator*(const TDataType f) const

Definition: AkVectors.h:397

AkForceInline

#define AkForceInline

Definition: AkTypes.h:63

T3DVector::Max

static AkForceInline T3DVector Max(const T3DVector &A, const T3DVector &B)

Definition: AkVectors.h:497

AkPlane::SetReflection

void SetReflection(AkReal32 *out_mat) const

Definition: AkVectors.h:1535

T3DVector::operator<=

AkForceInline bool operator<=(const T3DVector &b) const

Definition: AkVectors.h:352

AkMatrix3x3::operator*

AkForceInline Ak3DVector operator*(const Ak3DVector &in_rhs) const

Definition: AkVectors.h:974

Ak4DVector::Ak4DVector

Ak4DVector(const AkVector &b)

Definition: AkVectors.h:63

T3DVector::Normalize

AkForceInline T3DVector & Normalize()

Definition: AkVectors.h:584

AkLine::L

Ak3DVector L

Definition: AkVectors.h:1371

Ak2DVector::operator*=

Ak2DVector & operator*=(const AkReal32 f)

Definition: AkVectors.h:752

AkQuaternion::RotateVector

AkForceInline Ak3DVector RotateVector(const Ak3DVector32 &in_v) const

Definition: AkVectors.h:1239

T3DVector::T3DVector

T3DVector(const T3DVector< TFromDataType > &in_vector)

Definition: AkVectors.h:239

T3DVector::Cross

AkForceInline T3DVector Cross(const T3DVector &v) const

Definition: AkVectors.h:617

Ak2DVector::operator=

AkForceInline Ak2DVector operator=(const AkSphericalCoord &b)

Definition: AkVectors.h:734

T3DVector::operator>

AkForceInline bool operator>(const T3DVector b) const

Definition: AkVectors.h:357

T3DVector::HorizontalMin

AkForceInline TDataType HorizontalMin() const

Definition: AkVectors.h:476

Ak2DVector::LinearCombination

AkForceInline Ak2DVector LinearCombination(const Ak2DVector &A, const Ak2DVector &B) const

Definition: AkVectors.h:800

RealPrecision< AkReal32 >::IsFinite

static bool IsFinite(AkReal32 in_val)

Definition: AkVectors.h:143

AkSimd.h

AkVector64::X

AkReal64 X

X Position

Definition: AkTypes.h:362

AkQuaternion::AkQuaternion

AkQuaternion(AkReal32 in_W, AkReal32 in_X, AkReal32 in_Y, AkReal32 in_Z)

Definition: AkVectors.h:1057

TBoundingBox::m_Min

TVectorType m_Min

Definition: AkVectors.h:1832

AkMatrix3x3::m_Data

AkReal32 m_Data[3][3]

Definition: AkVectors.h:1048

T3DVector::Length

AkForceInline TDataType Length() const

Definition: AkVectors.h:630

T3DVector::T3DVector

T3DVector(const AkVector64 &in_vector)

Definition: AkVectors.h:259

T3DVector::VectorV4F32

AkForceInline AKSIMD_V4F32 VectorV4F32() const

Definition: AkVectors.h:318

AkLine

Definition: AkVectors.h:1283

TBoundingBox::TBoundingBox

TBoundingBox(const TVectorType &in_min, const TVectorType &in_max)

Definition: AkVectors.h:1764

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