DualQuat.h

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// Copyright Epic Games, Inc. All Rights Reserved.
 
#pragma once
 
#include "CoreTypes.h"
#include "Math/UnrealMathUtility.h"
#include "Math/Vector.h"
#include "Math/Quat.h"
#include "Math/Transform.h"
 
/** Dual quaternion class */
namespace UE
{
namespace Math
{
 
template<typename T>
struct TDualQuat
{
public:
    using FReal = T;
 
    /** rotation or real part */
    TQuat<T> R;
    /** half trans or dual part */
    TQuat<T> D;
 
    // Constructors
    TDualQuat(const TQuat<T> &InR, const TQuat<T> &InD)
        : R(InR)
        , D(InD)
    {}
 
    TDualQuat(const TTransform<T> &Transform)
    {
        TVector<T> V = Transform.GetTranslation()*0.5f;
        *this = TDualQuat<T>(TQuat<T>(0, 0, 0, 1), TQuat<T>(V.X, V.Y, V.Z, 0.f)) * TDualQuat<T>(Transform.GetRotation(), TQuat<T>(0, 0, 0, 0));
    }
 
    // Conversion to other type.
    template<typename FArg, TEMPLATE_REQUIRES(!std::is_same_v<T, FArg>)>
    explicit TDualQuat(const TDualQuat<FArg>& From) : TDualQuat<T>(TQuat<T>(From.R), TQuat<T>(From.D)) {}
 
    /** Dual quat addition */
    TDualQuat<T> operator+(const TDualQuat<T> &B) const
    {
        return{ R + B.R, D + B.D };
    }
 
    /** Dual quat product */
    TDualQuat<T> operator*(const TDualQuat<T> &B) const
    {
        return{ R*B.R, D*B.R + B.D*R };
    }
 
    /** Scale dual quat */
    TDualQuat<T> operator*(const T S) const
    {
        return{ R*S, D*S };
    }
 
    /** Return normalized dual quat */
    TDualQuat<T> Normalized() const
    {
        T MinV = 1.0f / FMath::Sqrt(R | R);
        return{ R*MinV, D*MinV };
    }
 
    /** Convert dual quat to transform */
    TTransform<T> AsFTransform(TVector<T> Scale = TVector<T>(1.0f, 1.0f, 1.0f))
    {
        TQuat<T> TQ = D*TQuat<T>(-R.X, -R.Y, -R.Z, R.W);
        return TTransform<T>(R, TVector<T>(TQ.X, TQ.Y, TQ.Z)*2.0f, Scale);
    }
};
 
}   // namespace UE::Math
}   // namespace UE
 
UE_DECLARE_LWC_TYPE(DualQuat, 4);
 
template<> struct TIsUECoreVariant<FDualQuat4f> { enum { Value = true }; };
template<> struct TIsUECoreVariant<FDualQuat4d> { enum { Value = true }; };