double ExplicitCurve2d :: NumericalProjectParam (const Point<2> & p, double lb, double ub) const
{
double t(-1);
Vec<2> tan;
Vec<2> curv;
Point<2> cp;
double f, fl, fu;
int cnt;
tan = EvalPrime (lb);
cp = Eval (lb);
fl = tan * (cp - p);
if (fl > 0) // changed by wmf, originally fl >= 0
{
// cerr << "tan = " << tan << " cp - p = " << (cp - p) << endl;
// cerr << "ExplicitCurve2d::NumericalProject: lb wrong" << endl;
return 0;
}
tan = EvalPrime (ub);
cp = Eval (ub);
fu = tan * (cp - p);
if (fu < 0) // changed by wmf, originally fu <= 0
{
// cerr << "tan = " << tan << " cp - p = " << (cp - p) << endl;
// cerr << "ExplicitCurve2d::NumericalProject: ub wrong" << endl;
return 0;
}
cnt = 0;
while (ub - lb > 1e-12 && fu - fl > 1e-12)
{
cnt++;
if (cnt > 50)
{
(*testout) << "Num Proj, cnt = " << cnt << endl;
}
t = (lb * fu - ub * fl) / (fu - fl);
if (t > 0.9 * ub + 0.1 * lb) t = 0.9 * ub + 0.1 * lb;
if (t < 0.1 * ub + 0.9 * lb) t = 0.1 * ub + 0.9 * lb;
tan = EvalPrime (t);
cp = Eval (t);
f = tan * (cp - p);
if (f >= 0)
{
ub = t;
fu = f;
}
else
{
lb = t;
fl = f;
}
}
return t;
}
bool BSplineCurve2d :: Inside (const Point<2> & p, double & dist) const
{
Point<2> hp = p;
double t = ProjectParam (p);
hp = Eval(t);
Vec<2> v = EvalPrime (t);
Vec<2> n (v(0), -v(1));
cout << "p = " << p << ", hp = " << hp << endl;
dist = Dist (p, hp);
double scal = (hp-p) * n;
cout << "scal = " << scal << endl;
return scal >= 0;
}
Point<2> ExplicitCurve2d :: CurvCircle (double t) const
{
Point<2> cp;
Vec<2> tan, n, curv;
double den;
cp = Eval (t);
tan = EvalPrime (t);
n = Normal (t);
curv = EvalPrimePrime (t);
den = n * curv;
if (fabs (den) < 1e-12)
return cp + 1e12 * n;
return cp + (tan.Length2() / den) * n;
}
double ExplicitCurve2d :: MaxCurvature () const
{
double t, tmin, tmax, dt;
double curv;
Vec<2> tan;
double maxcurv;
maxcurv = 0;
tmin = MinParam ();
tmax = MaxParam ();
dt = (tmax - tmin) / 1000;
for (t = tmin; t <= tmax+dt; t += dt)
if (SectionUsed (t))
{
tan = EvalPrime (t);
curv = fabs ( (Normal(t) * EvalPrimePrime(t)) / tan.Length2());
if (curv > maxcurv) maxcurv = curv;
}
return maxcurv;
}
double ExplicitCurve2d :: MaxCurvatureLoc (const Point<2> & p, double rad) const
{
double t, tmin, tmax, dt;
double curv;
Vec<2> tan;
double maxcurv;
maxcurv = 0;
tmin = MinParam ();
tmax = MaxParam ();
dt = (tmax - tmin) / 1000;
for (t = tmin; t <= tmax+dt; t += dt)
if (Dist (Eval(t), p) < rad)
{
tan = EvalPrime (t);
curv = fabs ( (Normal(t) * EvalPrimePrime(t)) / tan.Length2());
if (curv > maxcurv) maxcurv = curv;
}
return maxcurv;
}
Vec<2> ExplicitCurve2d :: Normal (double t) const
{
Vec<2> tan = EvalPrime (t);
tan.Normalize();
return Vec<2> (tan(1), -tan(0));
}
