//---------------------------------------------------------------------------------
// Torque Slip Angle to Lateral Force Example
//---------------------------------------------------------------------------------

#include "TA/Common/Maths.h"
#include "TA/Common/Geometry.h"

//---------------------------------------------------------------------------------
// An implementation of TA::CarTemplate::FnSlipAngleToLateralForce
//--------------------------------------------------------------------------------- 
float TAC_CALL SlipAngleToLateralForce(
    float fSlipAngle, 
    float fLongitudalSlipRatio, 
    const SurfaceAttribute& surfaceAttribute)
{
    const float fInitialGradient = 14.0f;
    const float fEndGradient = -0.1f;
    const float fEndOffset = 2.0f;

    const float fSegmentEndA = 0.08f;
    const float fSegmentEndB = 0.27f;

    const float fSegmentEndAOut = fInitialGradient * fSegmentEndA;
    const float fSegmentEndBOut = fEndGradient * fSegmentEndB + fEndOffset;

    const float fInvSegBLength = 1.0f / (fSegmentEndB - fSegmentEndA);
    const float fCubicGradA = fInitialGradient * (fSegmentEndB - fSegmentEndA);
    const float fCubicGradB = fEndGradient * (fSegmentEndB - fSegmentEndA);

    float fSign = TA::Sign(fSlipAngle);
    fSlipAngle *= fSign;

    float fResult;
    if (fSlipAngle < fSegmentEndA)
    {
        // As the slip angle increases from zero 
        // the lateral force increases linearly.
        fResult = fSign * fInitialGradient * fSlipAngle;
    }
    else if (fSlipAngle < fSegmentEndB)
    {       
        // As the slip angle approaches its optimal level
        // the increase lateral force slows so a stop
        // then begins to fall away.
        // This meens that if the steering wheel
        // is turned too far at high speed,
        // the car will understeer.
        fResult = fSign * TA::Geometry::CubicInterpolate(
            fSegmentEndAOut, 
            fSegmentEndBOut,
            fCubicGradA, 
            fCubicGradB, 
            (fSlipAngle - fSegmentEndA) * fInvSegBLength);
    }
    else
    {
        // As slip angle moves well past its optimal level
        // lateral force linearily decreases to zero.
        float fValue = fEndGradient * fSlipAngle + fEndOffset;
        if (fValue < 0.0f)
            fValue = 0.0f;
        fResult = fSign * fValue;
    }

    // The amount of turning grip can be easily increased
    // and degceased by multipliing here with out altering
    // the position of the peak with respect to fSlipAngles.
    fResult *= 2.5f; 

    // Reduce lateral force based on how much longitudal force has already been applied.
    // For hand brake turns and the like.
    fResult /= (TA::Fabs(fLongitudalSlipRatio) * 8.5f + 1.0f);
    return fResult;
}
SlipAngleToLateralForceExample.cpp
