SpringMath

Collection of useful spring methods which can be used for damping, simulating characters etc.

API > API/Runtime > API/Runtime/Core

Collection of useful spring methods which can be used for damping, simulating characters etc.

Reference https://theorangeduck.com/page/spring-roll-callhttps://theorangeduck.com/page/scalar-velocityhttps://theorangeduck.com/page/dead-blendinghttps://theorangeduck.com/page/propagating-velocities-through-animation-systemshttps://theorangeduck.com/page/fitting-code-driven-displacementhttps://theorangeduck.com/page/fitting-code-driven-displacement-revisited

   
Name SpringMath
Type struct
Header File /Engine/Source/Runtime/Core/Public/Math/SpringMath.h
Include Path #include "Math/SpringMath.h"

Syntax

struct SpringMath

Functions

Static

Name Remarks Include Path Unreal Specifiers

static float AngleGetShortestArcWith ( float A,
float B
)

 Gets the version of angle A which is closest to reference angle B Math/SpringMath.h  

static void CriticalDecay ( T& InOutX,
T& InOutV,
float SmoothingTime,
float DeltaTime
)

 Simplified version of CriticalSpringDamper where the target is assumed to be 0. Math/SpringMath.h  

static void CriticalDecayAngle ( float& InOutAngleRadians,
float& InOutAngularVelocityRadians,
float SmoothingTime,
float DeltaTime
)

 Specialized angle version of CriticalDecay that handles angle wrapping. Math/SpringMath.h  

static void CriticalDecayQuat ( FQuat& InOutRotation,
FVector& InOutAngularVelocityRadians,
float SmoothingTime,
float DeltaTime
)

 Specialized quaternion version of CriticalDecay, uses FVector for angular velocity Math/SpringMath.h  

static void CriticalDecayScale ( FVector& InOutScale,
FVector& InOutScalarVelocity,
float SmoothingTime,
float DeltaTime
)

 Specialized scale version of CriticalDecay Math/SpringMath.h  

static void CriticalDoubleSpringDamper ( T& InOutX,
T& InOutV,
T& InOutXi,
T& InOutVi,
T TargetX,
float SmoothingTime,
float DeltaTime
)

 A double spring damper that interpolates the value InOutX towards TargetX via some intermediate state - producing a more S-shaped curve. Math/SpringMath.h  

static void CriticalDoubleSpringDamperAngle ( float& InOutAngleRadians,
float& InOutAngularVelocityRadians,
float& InOutIntermediateAngleRadians,
float& InOutIntermediateAngularVelocityRadians,
float TargetAngleRadians,
float SmoothingTime,
float DeltaTime
)

 Specialized angle version of CriticalDoubleSpringDamper that handles angle wrapping. Math/SpringMath.h  

static void CriticalDoubleSpringDamperQuat ( FQuat& InOutRotation,
FVector& InOutAngularVelocityRadians,
FQuat& InOutIntermediateRotation,
FVector& InOutIntermediateAngularVelocityRadians,
const FQuat& TargetRotation,
float SmoothingTime,
float DeltaTime
)

 Specialized quaternion version of CriticalDoubleSpringDamper, uses FVector for angular velocity Math/SpringMath.h  

static void CriticalDoubleSpringDamperScale ( FVector& InOutScale,
FVector& InOutScalarVelocity,
FVector& InOutIntermediateScale,
FVector& InOutIntermediateScalarVelocity,
const FVector& TargetScale,
float SmoothingTime,
float DeltaTime
)

 Specialized scale version of CriticalDoubleSpringDamper Math/SpringMath.h  

static void CriticalSpringDamper ( T& InOutX,
T& InOutV,
T TargetX,
float SmoothingTime,
float DeltaTime
)

 Simplified version of FMath::CriticallyDampedSmoothing where v_goal is assumed to be 0. Math/SpringMath.h  

static void CriticalSpringDamperAngle ( float& InOutAngleRadians,
float& InOutAngularVelocityRadians,
float TargetAngleRadians,
float SmoothingTime,
float DeltaTime
)

 Specialized angle version of CriticalSpringDamper that handles angle wrapping. Math/SpringMath.h  

static void CriticalSpringDamperQuat ( FQuat& InOutRotation,
FVector& InOutAngularVelocityRadians,
const FQuat& TargetRotation,
float SmoothingTime,
float DeltaTime
)

 Specialized quaternion version of CriticalSpringDamper, uses FVector for angular velocity Math/SpringMath.h  

static void CriticalSpringDamperQuatPredict ( TArrayView< FQuat > OutPredictedRotations,
TArrayView< FVector > OutPredictedAngularVelocities,
int32 PredictCount,
const FQuat& CurrentRotation,
const FVector& CurrentAngularVelocity,
const FQuat& TargetRotation,
float SmoothingTime,
float SecondsPerPredictionStep
)

 Prediction of CriticalSpringDamperQuat Math/SpringMath.h  

static void CriticalSpringDamperScale ( FVector& InOutScale,
FVector& InOutScalarVelocity,
const FVector& TargetScale,
float SmoothingTime,
float DeltaTime
)

 Specialized scale version of CriticalSpringDamper, uses FVector for scalar velocity Math/SpringMath.h  

static void CubicDecayWeights ( float& OutW0,
float& OutW1,
float& OutW2,
float& OutW3,
const float Time,
const float BlendTime
)

 Compute the cubic weights required to inertialize out an offset and velocity offset for a given time and blend time Math/SpringMath.h  

static void CubicInertializeApply ( TValue& InOutValue,
TValue& InOutVelocity,
const TValue& InValueOffset,
const TValue& InVelocityOffset,
float TimeSinceTransition,
float BlendTime
)

 Applies a cubic inertialization to the input value (and velocity), updating them in place by adding the appropriate offset given the time since transition. Math/SpringMath.h  

static void CubicInertializeApplyAngle ( float& InOutAngle,
float& InOutAngularVelocity,
float InAngleOffset,
float InAngularVelocityOffset,
float TimeSinceTransition,
float BlendTime
)

 Specialization of CubicInertializeApply for angles. Stores velocities in rad/s. Math/SpringMath.h  

static void CubicInertializeApplyQuat ( FQuat& InOutRotation,
FVector& InOutAngularVelocity,
const FQuat& InRotationOffset,
const FVector& InAngularVelocityOffset,
float TimeSinceTransition,
float BlendTime
)

 Specialization of CubicInertializeApply for quaternions. Stores velocities in rad/s. Math/SpringMath.h  

static void CubicInertializeApplyScale ( FVector& InOutScale,
FVector& InOutScalarVelocity,
const FVector& InScaleOffset,
const FVector& InScalarVelocityOffset,
float TimeSinceTransition,
float BlendTime
)

 Specialization of CubicInertializeApply for scales. Math/SpringMath.h  

static void CubicInertializeTransition ( TValue& InOutValueOffset,
TValue& InOutVelocityOffset,
const TValue& InSrcValue,
const TValue& InSrcVelocity,
const TValue& InDstValue,
const TValue& InDstVelocity,
float TimeSinceTransition,
float BlendTime
)

 Transitions a cubic inertialization, computing a new offset value. Math/SpringMath.h  

static void CubicInertializeTransitionAngle ( float& InOutAngleOffset,
float& InOutAngularVelocityOffset,
float InSrcAngle,
float InSrcAngularVelocity,
float InDstAngle,
float InDstAngularVelocity,
float TimeSinceTransition,
float BlendTime
)

 Specialization of CubicInertializeTransition for angles. Stores velocities in rad/s. Math/SpringMath.h  

static void CubicInertializeTransitionQuat ( FQuat& InOutRotationOffset,
FVector& InOutAngularVelocityOffset,
const FQuat& InSrcRotation,
const FVector& InSrcAngularVelocity,
const FQuat& InDstRotation,
const FVector& InDstAngularVelocity,
float TimeSinceTransition,
float BlendTime
)

 Specialization of CubicInertializeTransition for quaternions. Stores velocities in rad/s. Math/SpringMath.h  

static void CubicInertializeTransitionScale ( FVector& InOutScaleOffset,
FVector& InOutScalarVelocityOffset,
const FVector& InSrcScale,
const FVector& InSrcScalarVelocity,
const FVector& InDstScale,
const FVector& InDstScalarVelocity,
float TimeSinceTransition,
float BlendTime
)

 Specialization of CubicInertializeTransition for scales. Math/SpringMath.h  

static float DampingToSmoothingTime ( float Damping
)

   Math/SpringMath.h  

static void DeadBlendApply ( TValue& InOutValue,
TValue& InOutVelocity,
const TValue& InValueTransition,
const TValue& InVelocityTransition,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Applies a dead blend to the input value (and velocity), updating them in place by blending them with an extrapolation of the value and velocity at the point of the last transition. Math/SpringMath.h  

static void DeadBlendApplyAngle ( float& InOutValue,
float& InOutVelocity,
const float& InValueTransition,
const float& InVelocityTransition,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Specialization of DeadBlendApply for angles. Stores velocities in rad/s. Math/SpringMath.h  

static void DeadBlendApplyQuat ( FQuat& InOutValue,
FVector& InOutVelocity,
const FQuat& InValueTransition,
const FVector& InVelocityTransition,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Specialization of DeadBlendApply for quaternions. Stores velocities in rad/s. Math/SpringMath.h  

static void DeadBlendApplyScale ( FVector& InOutValue,
FVector& InOutVelocity,
const FVector& InValueTransition,
const FVector& InVelocityTransition,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Specialization of DeadBlendApply for scales. Math/SpringMath.h  

static void DeadBlendExtrapolate ( TValue& InOutValue,
TValue& InOutVelocity,
const float Time,
const float SmoothingTime
)

 Extrapolates a value and velocity in place assuming some decay rate on the velocity. Math/SpringMath.h  

static void DeadBlendExtrapolateQuat ( FQuat& InOutValue,
FVector& InOutVelocity,
const float Time,
const float SmoothingTime
)

 Specialization of DeadBlendExtrapolate for quaternions. Angular velocities are stored in rad/s. Math/SpringMath.h  

static void DeadBlendExtrapolateScale ( FVector& InOutValue,
FVector& InOutVelocity,
const float Time,
const float SmoothingTime
)

 Specialization of DeadBlendExtrapolate for scales. Math/SpringMath.h  

static void DeadBlendTransition ( TValue& InOutValueTransition,
TValue& InOutVelocityTransition,
const TValue& InSrcValue,
const TValue& InSrcVelocity,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Transitions a dead blend, computing the new value and velocity at the point of transition. Math/SpringMath.h  

static void DeadBlendTransitionAngle ( float& InOutValueTransition,
float& InOutVelocityTransition,
const float& InSrcValue,
const float& InSrcVelocity,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Specialization of DeadBlendTransition for angles. Stores velocities in rad/s. Math/SpringMath.h  

static void DeadBlendTransitionQuat ( FQuat& InOutValueTransition,
FVector& InOutVelocityTransition,
const FQuat& InSrcValue,
const FVector& InSrcVelocity,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Specialization of DeadBlendTransition for quaternions. Stores velocities in rad/s. Math/SpringMath.h  

static void DeadBlendTransitionScale ( FVector& InOutValueTransition,
FVector& InOutVelocityTransition,
const FVector& InSrcValue,
const FVector& InSrcVelocity,
float TimeSinceTransition,
float BlendTime,
float SmoothingTime
)

 Specialization of DeadBlendTransition for scales. Math/SpringMath.h  

static void ExponentialSmoothingApproxAngle ( float& InOutAngleRadians,
const float& InTargetAngleRadians,
const float InDeltaTime,
const float SmoothingTime
)

 Specialized angle damper, similar to FMath::ExponentialSmoothingApprox but deals correctly with angle wrap-around. Math/SpringMath.h  

static void ExponentialSmoothingApproxQuat ( FQuat& InOutRotation,
const FQuat& InTargetRotation,
const float InDeltaTime,
const float SmoothingTime
)

 Specialized quaternion damper, similar to FMath::ExponentialSmoothingApprox but for quaternions. Math/SpringMath.h  

static void ExponentialSmoothingApproxScale ( FVector& InOutScale,
const FVector& InTargetScale,
const float InDeltaTime,
const float SmoothingTime
)

 Specialized scale damper, similar to FMath::ExponentialSmoothingApprox but for scales. Math/SpringMath.h  

static float HalfLifeToSmoothingTime ( float HalfLife
)

 Convert a halflife to a smoothing time Math/SpringMath.h  

static float LambertWLower ( const float X
)

 Computes the lower (-1) branch of the LambertW function, which is used for solving equations of the form x*e^x - input will be clamped to range [-1/e, 0], output will be in range [-1, -inf] Math/SpringMath.h  

static FVector ScaleDivMax ( FVector Lhs,
FVector Rhs
)

 Divides one scale by another, clamping the Rhs to be greater than some minimum Math/SpringMath.h  

static FVector ScaleEerp ( FVector A,
FVector B,
double Alpha
)

 Performs an Eerp on scales (interpolation in the multiplicative space) Math/SpringMath.h  

static FVector ScaleExp ( FVector V,
double Max
)

 Computes the exponent of a scale, ensuring the value is not too large to prevent it exploding Math/SpringMath.h  

static FVector ScaleLog ( FVector V
)

 Takes the log of a scale, clamping the scale to ensure it is greater than zero Math/SpringMath.h  

static float SmoothingTimeToDamping ( float SmoothingTime
)

   Math/SpringMath.h  

static float SmoothingTimeToHalfLife ( float SmoothingTime
)

 Convert a smoothing time to a half life Math/SpringMath.h  

static float SmoothingTimeToStrength ( float SmoothingTime
)

 Convert from smoothing time to spring strength. Math/SpringMath.h  

static float SpringCharacterMaximumAcceleration ( const float InitialVelocity,
const float InitialAcceleration,
const float TargetVelocity,
const float SmoothingTime
)

 Estimates the maximum acceleration for a character Math/SpringMath.h  

static TOptional< float > SpringCharacterMaximumAccelerationTime ( const float InitialVelocity,
const float InitialAcceleration,
const float TargetVelocity,
const float SmoothingTime
)

 Estimates the time at which the maximum acceleration will occur. Math/SpringMath.h  

static float SpringCharacterMaximumAngularVelocity ( const float InitialAngle,
const float InitialAngularVelocity,
const float TargetAngle,
const float SmoothingTime
)

 Estimates the maximum angular velocity for a character Math/SpringMath.h  

static TOptional< float > SpringCharacterMaximumAngularVelocityTime ( const float InitialAngle,
const float InitialAngularVelocity,
const float TargetAngle,
const float SmoothingTime
)

 Estimates the time in the future at which the maximum angular velocity will occur. Math/SpringMath.h  

static void SpringCharacterPredict ( TArrayView< TVector > OutPredictedPositions,
TArrayView< TVector > OutPredictedVelocities,
TArrayView< TVector > OutPredictedAccelerations,
const TVector& CurrentPosition,
const TVector& CurrentVelocity,
const TVector& CurrentAcceleration,
const TVector& TargetVelocity,
float SmoothingTime,
float SecondsPerPredictionStep,
float VDeadzone,
float ADeadzone
)

 Gives predicted positions, velocities and accelerations for SpringCharacterUpdate. Math/SpringMath.h  

static float SpringCharacterSmoothingTimeFromMaximumAcceleration ( const float InitialVelocity,
const float TargetVelocity,
const float MaximumAcceleration
)

 Estimates an approximate spring smoothing time from the maximum acceleration Math/SpringMath.h  

static float SpringCharacterSmoothingTimeFromMaximumAngularVelocity ( const float InitialAngle,
const float TargetAngle,
const float MaximumAngularVelocity
)

 Estimates an approximate spring smoothing time from the maximum angular velocity Math/SpringMath.h  

static float SpringCharacterSmoothingTimeFromStartingDistance ( const float TargetVelocity,
const float StartingDistance,
const float VelocityThreshold
)

 Estimates an approximate spring smoothing time from a starting distance and target velocity for a character using a simple damped spring. Math/SpringMath.h  

static float SpringCharacterSmoothingTimeFromStartingTime ( const float TargetVelocity,
const float StartingTime,
const float VelocityThreshold
)

 Estimates an approximate spring smoothing time from a starting time and target velocity for a character using a simple damped spring. Math/SpringMath.h  

static float SpringCharacterSmoothingTimeFromStoppingDistance ( const float InitialVelocity,
const float StoppingDistance
)

 Estimates an approximate spring smoothing time from a stopping distance and velocity for a character using a simple damped spring. Math/SpringMath.h  

static float SpringCharacterSmoothingTimeFromStoppingTime ( const float InitialVelocity,
const float StoppingTime,
const float VelocityThreshold
)

 Estimates an approximate spring smoothing time from a stopping time and velocity for a character using a simple damped spring. Math/SpringMath.h  

static float SpringCharacterStartingDistance ( const float TargetVelocity,
const float SmoothingTime,
const float VelocityThreshold
)

 Estimates an approximate starting distance (the distance traveled until the velocity gets within the VelocityThreshold of the TargetVelocity) from a smoothing time for a character using a simple damped spring Math/SpringMath.h  

static float SpringCharacterStartingTime ( const float TargetVelocity,
const float SmoothingTime,
const float VelocityThreshold
)

 Estimates an approximate starting time (the time at which the velocity gets within the VelocityThreshold of the TargetVelocity) from a smoothing time and target velocity for a character using a simple damped spring Math/SpringMath.h  

static float SpringCharacterStoppingDistance ( const float InitialVelocity,
const float InitialAcceleration,
const float SmoothingTime
)

 Estimates an approximate stopping distance from a smoothing time for a character using a simple damped spring Math/SpringMath.h  

static TOptional< float > SpringCharacterStoppingInflectionTime ( const float InitialVelocity,
const float InitialAcceleration,
const float SmoothingTime
)

 Estimates the time in the future at which a character driven by a critical spring will reach zero acceleration. Math/SpringMath.h  

static float SpringCharacterStoppingTime ( const float InitialVelocity,
const float SmoothingTime,
const float VelocityThreshold
)

 Estimates an approximate stopping time (the time at which the velocity goes below the VelocityThreshold) from a smoothing time and velocity for a character using a simple damped spring Math/SpringMath.h  

static void SpringCharacterUpdate ( TVector& InOutPosition,
TVector& InOutVelocity,
TVector& InOutAcceleration,
const TVector& TargetVelocity,
float SmoothingTime,
float DeltaTime,
float VDeadzone,
float ADeadzone
)

 Update the position of a character given a target velocity using a simple damped spring Math/SpringMath.h  

static void SpringInertializeApply ( TValue& InOutValue,
TValue& InOutVelocity,
const TValue& InValueOffset,
const TValue& InVelocityOffset,
float TimeSinceTransition,
float SmoothingTime
)

 Applies a spring inertialization to the input value (and velocity), updating them in place by adding the appropriate offset given the time since transition. Math/SpringMath.h  

static void SpringInertializeApplyAngle ( float& InOutAngle,
float& InOutAngularVelocity,
float InAngleOffset,
float InAngularVelocityOffset,
float TimeSinceTransition,
float SmoothingTime
)

 Specialization of SpringInertializeApply for angles. Stores velocities in rad/s. Math/SpringMath.h  

static void SpringInertializeApplyQuat ( FQuat& InOutRotation,
FVector& InOutAngularVelocity,
const FQuat& InRotationOffset,
const FVector& InAngularVelocityOffset,
float TimeSinceTransition,
float SmoothingTime
)

 Specialization of SpringInertializeApply for quaternions. Stores velocities in rad/s. Math/SpringMath.h  

static void SpringInertializeApplyScale ( FVector& InOutScale,
FVector& InOutScalarVelocity,
const FVector& InScaleOffset,
const FVector& InScalarVelocityOffset,
float TimeSinceTransition,
float SmoothingTime
)

 Specialization of SpringInertializeApply for scales. Math/SpringMath.h  

static void SpringInertializeTransition ( TValue& InOutValueOffset,
TValue& InOutVelocityOffset,
const TValue& InSrcValue,
const TValue& InSrcVelocity,
const TValue& InDstValue,
const TValue& InDstVelocity,
float TimeSinceTransition,
float SmoothingTime
)

 Transitions a spring inertialization, computing a new offset value. Math/SpringMath.h  

static void SpringInertializeTransitionAngle ( float& InOutAngleOffset,
float& InOutAngularVelocityOffset,
float InSrcAngle,
float InSrcAngularVelocity,
float InDstAngle,
float InDstAngularVelocity,
float TimeSinceTransition,
float SmoothingTime
)

 Specialization of SpringInertializeTransition for angles. Stores velocities in rad/s. Math/SpringMath.h  

static void SpringInertializeTransitionQuat ( FQuat& InOutRotationOffset,
FVector& InOutAngularVelocityOffset,
const FQuat& InSrcRotation,
const FVector& InSrcAngularVelocity,
const FQuat& InDstRotation,
const FVector& InDstAngularVelocity,
float TimeSinceTransition,
float SmoothingTime
)

 Specialization of SpringInertializeTransition for quaternions. Stores velocities in rad/s. Math/SpringMath.h  

static void SpringInertializeTransitionScale ( FVector& InOutScaleOffset,
FVector& InOutScalarVelocityOffset,
const FVector& InSrcScale,
const FVector& InSrcScalarVelocity,
const FVector& InDstScale,
const FVector& InDstScalarVelocity,
float TimeSinceTransition,
float SmoothingTime
)

 Specialization of SpringInertializeTransition for Scales Math/SpringMath.h  

static float StrengthToSmoothingTime ( float Strength
)

 Convert from spring strength to smoothing time. Math/SpringMath.h  

static void TrackVelocity ( TValue& InOutValue,
TValue& InOutVelocity,
const TValue& InValue,
float DeltaTime
)

 Tracks the velocity of the input value InValue via finite difference, updating InOutValue and InOutVelocity in place. Math/SpringMath.h  

static void TrackVelocityAngle ( float& InOutValue,
float& InOutVelocity,
float InValue,
float DeltaTime
)

 Tracks the velocity of the input angle InValue via finite difference, updating InOutValue and InOutVelocity in place. Math/SpringMath.h  

static void TrackVelocityQuat ( FQuat& InOutValue,
FVector& InOutVelocity,
FQuat InValue,
float DeltaTime
)

 Tracks the velocity of the input rotation InValue via finite difference, updating InOutValue and InOutVelocity in place. Math/SpringMath.h  

static void TrackVelocityScale ( FVector& InOutValue,
FVector& InOutVelocity,
FVector InValue,
float DeltaTime
)

 Tracks the velocity of the input scale InValue via finite difference, updating InOutValue and InOutVelocity in place. Math/SpringMath.h  

static void VelocitySpringCharacterPredict ( TArrayView< TVector > OutPredictedPositions,
TArrayView< TVector > OutPredictedVelocities,
TArrayView< TVector > OutPredictedIntermediateVelocities,
TArrayView< TVector > OutPredictedAccelerations,
const TVector& CurrentPosition,
const TVector& CurrentVelocity,
const TVector& CurrentIntermediateVelocity,
const TVector& CurrentAcceleration,
const TVector& TargetVelocity,
float SmoothingTime,
float MaxAcceleration,
float SecondsPerPredictionStep,
float VDeadzone,
float ADeadzone
)

 Gives predicted positions, velocities and accelerations for SpringCharacterUpdate. Math/SpringMath.h  

static void VelocitySpringCharacterUpdate ( TVector& InOutPosition,
TVector& InOutVelocity,
TVector& InOutVelocityIntermediate,
TVector& InOutAcceleration,
TVector TargetVelocity,
float SmoothingTime,
float MaxAcceleration,
float DeltaTime,
float VDeadzone,
float ADeadzone
)

 Update a position representing a character given a target velocity using a velocity spring. Math/SpringMath.h  

static void VelocitySpringDamper ( TVector& InOutX,
TVector& InOutV,
TVector& InOutXi,
TVector TargetX,
float MaxSpeed,
float SmoothingTime,
float DeltaTime
)

 A velocity spring will damp towards a target that follows a fixed linear target velocity, allowing control of the interpolation speed while still giving a smoothed behaviour. Math/SpringMath.h  

static void VelocitySpringDamperF ( TFloat& InOutX,
TFloat& InOutV,
TFloat& InOutXi,
TFloat TargetX,
TFloat MaxSpeed,
float SmoothingTime,
float DeltaTime
)

 A velocity spring will damp towards a target that follows a fixed linear target velocity, allowing control of the interpolation speed while still giving a smoothed behavior. Math/SpringMath.h  

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