自学教程：C++ GetSquared函数代码示例

Real Distance<Real,TVector>::GetSquared (Real tmin, Real tmax,    const TVector& velocity0, const TVector& velocity1){    // The assumption is that distance f(t) is a convex function.  If    // f'(tmin) >= 0, then the minimum occurs at tmin.  If f'(tmax) <= 0,    // then the minimum occurs at tmax.  Otherwise, f'(0) < 0 and    // f'(tmax) > 0 and the minimum occurs at some t in (tmin,tmax).    Real t0 = tmin;    Real f0 = GetSquared(t0, velocity0, velocity1);    if (f0 <= ZeroThreshold)    {        // The distance is effectively zero.  The objects are initially in        // contact.        mContactTime = t0;        return (Real)0;    }    Real df0 = GetDerivativeSquared(t0, velocity0, velocity1);    if (df0 >= (Real)0)    {        // The distance is increasing on [0,tmax].        mContactTime = t0;        return f0;    }    Real t1 = tmax;    Real f1 = GetSquared(t1, velocity0, velocity1);    if (f1 <= ZeroThreshold)    {        // The distance is effectively zero.        mContactTime = t1;        return (Real)0;    }    Real df1 = GetDerivativeSquared(t1, velocity0, velocity1);    if (df1 <= (Real)0)    {        // The distance is decreasing on [0,tmax].        mContactTime = t1;        return f1;    }    // Start the process with Newton's method for computing a time when the    // distance is zero.  During this process we will switch to a numerical    // minimizer if we decide that the distance cannot be zero.    int i;    for (i = 0; i < MaximumIterations; ++i)    {        // Compute the next Newton's iterate.        Real t = t0 - f0/df0;        if (t >= tmax)        {            // The convexity of the graph guarantees that when this condition            // happens, the distance is always positive.  Switch to a            // numerical minimizer.            break;        }        Real f = GetSquared(t, velocity0, velocity1);        if (f <= ZeroThreshold)        {            // The distance is effectively zero.            mContactTime = t;            return (Real)0;        }        Real df = GetDerivativeSquared(t, velocity0, velocity1);        if (df >= (Real)0)        {            // The convexity of the graph guarantees that when this condition            // happens, the distance is always positive.  Switch to a            // numerical minimizer.            break;        }        t0 = t;        f0 = f;        df0 = df;    }    if (i == MaximumIterations)    {        // Failed to converge within desired number of iterations.  To        // reach here, the derivative values were always negative, so report        // the distance at the last time.        mContactTime = t0;        return f0;    }    // The distance is always positive.  Use bisection to find the root of    // the derivative function.    Real tm = t0;    for (i = 0; i < MaximumIterations; ++i)    {        tm = ((Real)0.5)*(t0 + t1);        Real dfm = GetDerivativeSquared(tm, velocity0, velocity1);        Real product = dfm*df0;        if (product < -ZeroThreshold)        {            t1 = tm;            df1 = dfm;//.........这里部分代码省略.........

Real DistVector3Segment3<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real DistLine2Segment2<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistSegment3Rectangle3<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real DistPoint3Segment3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistLine2Ray2<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistVector3Box3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistRay3Triangle3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistLine2Line2<Real>::Get (){	Real sqrDist = GetSquared();	return Math<Real>::Sqrt(sqrDist);}

Real DistLine3Circle3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistVector3Tetrahedron3<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real DistVector3Frustum3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistPoint3Ellipsoid3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistPoint3Tetrahedron3<Real>::Get (){    return Math<Real>::Sqrt( GetSquared() );}

Real DistLine3Triangle3<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real DistPoint2Line2<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistRay2Segment2<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real DistPoint3Rectangle3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistPoint3Frustum3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real SEDistance<Real, TVector>::GetSquared(Real fTMin, Real fTMax,     const TVector& rVelocity0, const TVector& rVelocity1){    // 假设基于函数f(t)是convex function的前提下.    // 如果f'(tmin) >= 0,则最小值在tmin处.    // 如果f'(tmax) <= 0,则最小值在tmax处.    // 否则,f'(tmin) < 0且f'(tmax) > 0,最小值在(tmin,tmax)区间内.    Real fT0 = fTMin;    Real fF0 = GetSquared(fT0, rVelocity0, rVelocity1);    if( fF0 <= ZeroThreshold )    {        // 距离几乎为零.        // 对象初始时刻接触.        m_fContactTime = fT0;        return (Real)0.0;    }    Real fDF0 = GetDerivativeSquared(fT0, rVelocity0, rVelocity1);    if( fDF0 >= (Real)0.0 )    {        // 距离在[tmin, tmax]上持续增大.        m_fContactTime = fT0;        return fF0;    }    Real fT1 = fTMax;    Real fF1 = GetSquared(fT1, rVelocity0, rVelocity1);    if( fF1 <= ZeroThreshold )    {        // 距离几乎为零.        m_fContactTime = fT1;        return (Real)0.0;    }    Real fDF1 = GetDerivativeSquared(fT1, rVelocity0, rVelocity1);    if( fDF1 <= (Real)0.0 )    {        // 距离在[tmin, tmax]上持续减小.        m_fContactTime = fT1;        return fF1;    }    // 用牛顿法计算函数值为0时的自变量t值.    // 在该过程中,如果距离不能达到0值,则切换到一个numerical minimizer.    int i;    for( i = 0; i < MaximumIterations; i++ )    {        // 计算下一次牛顿迭代位置.        Real fT = fT0 - fF0/fDF0;        if( fT >= fTMax )        {            // 函数图形的凸性确保当这种情况发生时,距离总是正值.            // 切换到一个numerical minimizer.            break;        }        Real fF = GetSquared(fT, rVelocity0, rVelocity1);        if( fF <= ZeroThreshold )        {            // 距离几乎为零.            m_fContactTime = fT;            return (Real)0.0;        }        Real fDF = GetDerivativeSquared(fT, rVelocity0, rVelocity1);        if( fDF >= (Real)0.0 )        {            // 函数图形的凸性确保当这种情况发生时,距离总是正值.            // 切换到一个numerical minimizer.            break;        }        fT0 = fT;        fF0 = fF;        fDF0 = fDF;    }    if( i == MaximumIterations )    {        // 在指定迭代次数内函数没能收敛到0值附近.        // 到达这里时,函数的导数必定都为负值,        // 因此把最后一次迭代时刻t的函数值作为距离值返回.        m_fContactTime = fT0;        return fF0;    }    // 距离总是正值.    // 用二分法查找导函数的根.    Real fTm = fT0;    for( i = 0; i < MaximumIterations; i++ )    {        fTm = ((Real)0.5)*(fT0 + fT1);        Real fDFm = GetDerivativeSquared(fTm, rVelocity0, rVelocity1);        Real fProduct = fDFm*fDF0;        if( fProduct < -ZeroThreshold )//.........这里部分代码省略.........

Real DistSegment3Box3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}

Real DistVector2Ray2<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real Distance<Real,TVector>::GetSquared (Real fTMin, Real fTMax,    const TVector& rkVelocity0, const TVector& rkVelocity1){    // The assumption is that distance f(t) is a convex function.  If    // f'(tmin) >= 0, then the minimum occurs at tmin.  If f'(tmax) <= 0,    // then the minimum occurs at tmax.  Otherwise, f'(0) < 0 and    // f'(tmax) > 0 and the minimum occurs at some t in (tmin,tmax).    Real fT0 = fTMin;    Real fF0 = GetSquared(fT0,rkVelocity0,rkVelocity1);    if (fF0 <= ZeroThreshold)    {        // The distance is effectively zero.  The objects are initially in        // contact.        m_fContactTime = fT0;        return (Real)0.0;    }    Real fDF0 = GetDerivativeSquared(fT0,rkVelocity0,rkVelocity1);    if (fDF0 >= (Real)0.0)    {        // The distance is increasing on [0,tmax].        m_fContactTime = fT0;        return fF0;    }    Real fT1 = fTMax;    Real fF1 = GetSquared(fT1,rkVelocity0,rkVelocity1);    if (fF1 <= ZeroThreshold)    {        // The distance is effectively zero.        m_fContactTime = fT1;        return (Real)0.0;    }    Real fDF1 = GetDerivativeSquared(fT1,rkVelocity0,rkVelocity1);    if (fDF1 <= (Real)0.0)    {        // The distance is decreasing on [0,tmax].        m_fContactTime = fT1;        return fF1;    }    // Start the process with Newton's method for computing a time when the    // distance is zero.  During this process we will switch to a numerical    // minimizer if we decide that the distance cannot be zero.    int i;    for (i = 0; i < MaximumIterations; i++)    {        // compute the next Newton's iterate        Real fT = fT0 - fF0/fDF0;        if (fT >= fTMax)        {            // The convexity of the graph guarantees that when this condition            // happens, the distance is always positive.  Switch to a            // numerical minimizer.            break;        }        Real fF = GetSquared(fT,rkVelocity0,rkVelocity1);        if (fF <= ZeroThreshold)        {            // The distance is effectively zero.            m_fContactTime = fT;            return (Real)0.0;        }        Real fDF = GetDerivativeSquared(fT,rkVelocity0,rkVelocity1);        if (fDF >= (Real)0.0)        {            // The convexity of the graph guarantees that when this condition            // happens, the distance is always positive.  Switch to a            // numerical minimizer.            break;        }        fT0 = fT;        fF0 = fF;        fDF0 = fDF;    }    if (i == MaximumIterations)    {        // Failed to converge within desired number of iterations.  To        // reach here, the derivative values were always negative, so report        // the distance at the last time.        m_fContactTime = fT0;        return fF0;    }    // The distance is always positive.  Use bisection to find the root of    // the derivative function.    Real fTm = fT0;    for (i = 0; i < MaximumIterations; i++)    {        fTm = ((Real)0.5)*(fT0 + fT1);        Real fDFm = GetDerivativeSquared(fTm,rkVelocity0,rkVelocity1);        Real fProduct = fDFm*fDF0;        if (fProduct < -ZeroThreshold)        {            fT1 = fTm;            fDF1 = fDFm;//.........这里部分代码省略.........

Real DistCircle3Circle3<Real>::Get (){    Real fSqrDist = GetSquared();    return Math<Real>::Sqrt(fSqrDist);}

Real DistVector3Ellipsoid3<Real>::Get (){    return Math<Real>::Sqrt(GetSquared());}