void generateTaylorModelForLinearFunc(TaylorModel& tm, FCL_REAL p, FCL_REAL v)
{
tm.coeff(0) = p;
tm.coeff(1) = v;
tm.coeff(2) = 0;
tm.coeff(3) = 0;
tm.remainder()[0] = 0;
tm.remainder()[1] = 0;
}
TVector3 operator * (const Vec3f& v, const TaylorModel& a)
{
TVector3 res(a.getTimeInterval());
res[0] = a * v[0];
res[1] = a * v[1];
res[2] = a * v[2];
return res;
}
TMatrix3 operator * (const Matrix3f& m, const TaylorModel& a)
{
TMatrix3 res(a.getTimeInterval());
res(0, 0) = a * m(0, 0);
res(0, 1) = a * m(0, 1);
res(0, 1) = a * m(0, 2);
res(1, 0) = a * m(1, 0);
res(1, 1) = a * m(1, 1);
res(1, 1) = a * m(1, 2);
res(2, 0) = a * m(2, 0);
res(2, 1) = a * m(2, 1);
res(2, 1) = a * m(2, 2);
return res;
}
void generateTaylorModelForSinFunc(TaylorModel& tm, FCL_REAL w, FCL_REAL q0)
{
FCL_REAL a = tm.getTimeInterval()->t_.center();
FCL_REAL t = w * a + q0;
FCL_REAL w2 = w * w;
FCL_REAL fa = sin(t);
FCL_REAL fda = w*cos(t);
FCL_REAL fdda = -w2*fa;
FCL_REAL fddda = -w2*fda;
tm.coeff(0) = fa-a*(fda-0.5*a*(fdda-1.0/3.0*a*fddda));
tm.coeff(1) = fda-a*fdda+0.5*a*a*fddda;
tm.coeff(2) = 0.5*(fdda-a*fddda);
tm.coeff(3) = 1.0/6.0*fddda;
// compute bounds for w^3 sin(wt+q0)/16, t \in [t0, t1]
Interval fddddBounds;
if(w == 0) fddddBounds.setValue(0);
else
{
FCL_REAL sinQL = sin(w * tm.getTimeInterval()->t_[0] + q0);
FCL_REAL sinQR = sin(w * tm.getTimeInterval()->t_[1] + q0);
if(sinQL < sinQR) fddddBounds.setValue(sinQL, sinQR);
else fddddBounds.setValue(sinQR, sinQL);
// enlarge to handle round-off errors
fddddBounds[0] -= 1e-15;
fddddBounds[1] += 1e-15;
// sin reaches maximum if there exists an integer k in [(w*t0+q0-pi/2)/2pi, (w*t1+q0-pi/2)/2pi];
// sin reaches minimum if there exists an integer k in [(w*t0+q0-pi-pi/2)/2pi, (w*t1+q0-pi-pi/2)/2pi]
FCL_REAL k1 = (tm.getTimeInterval()->t_[0] * w + q0) / (2 * boost::math::constants::pi<FCL_REAL>()) - 0.25;
FCL_REAL k2 = (tm.getTimeInterval()->t_[1] * w + q0) / (2 * boost::math::constants::pi<FCL_REAL>()) - 0.25;
if(w > 0)
{
if(ceil(k2) - floor(k1) > 1) fddddBounds[1] = 1;
k1 -= 0.5;
k2 -= 0.5;
if(ceil(k2) - floor(k1) > 1) fddddBounds[0] = -1;
}
else
{
if(ceil(k1) - floor(k2) > 1) fddddBounds[1] = 1;
k1 -= 0.5;
k2 -= 0.5;
if(ceil(k1) - floor(k2) > 1) fddddBounds[0] = -1;
}
FCL_REAL w4 = w2 * w2;
fddddBounds *= w4;
FCL_REAL midSize = 0.5 * (tm.getTimeInterval()->t_[1] - tm.getTimeInterval()->t_[0]);
FCL_REAL midSize2 = midSize * midSize;
FCL_REAL midSize4 = midSize2 * midSize2;
// [0, midSize4] * fdddBounds
if(fddddBounds[0] > 0)
tm.remainder().setValue(0, fddddBounds[1] * midSize4 * (1.0 / 24));
else if(fddddBounds[0] < 0)
tm.remainder().setValue(fddddBounds[0] * midSize4 * (1.0 / 24), 0);
else
tm.remainder().setValue(fddddBounds[0] * midSize4 * (1.0 / 24), fddddBounds[1] * midSize4 * (1.0 / 24));
}
}
