/// offset-ellipse Brent solver
/// offfset-ellipse solver using Brent's method
/// find the EllipsePosition that makes the offset-ellipse point be at p
/// this is a zero of Ellipse::error()
/// returns number of iterations
///
/// called (only?) by BullCutter::singleEdgeDropCanonical()
public int solver_brent()
{
int iters = 1;
EllipsePosition apos = new EllipsePosition(); // Brent's method requires bracketing the root in [apos.diangle, bpos.diangle]
EllipsePosition bpos = new EllipsePosition();
apos.setDiangle(0.0);
Debug.Assert(apos.isValid());
bpos.setDiangle(3.0);
Debug.Assert(bpos.isValid());
if (Math.Abs(error(apos)) < DefineConstants.OE_ERROR_TOLERANCE)
{ // if we are lucky apos is the solution
EllipsePosition1.CopyFrom(apos); // and we do not need to search further.
find_EllipsePosition2();
return(iters);
}
else if (Math.Abs(error(bpos)) < DefineConstants.OE_ERROR_TOLERANCE)
{ // or bpos might be the solution?
EllipsePosition1.CopyFrom(bpos);
find_EllipsePosition2();
return(iters);
}
// neither apos nor bpos is the solution
// but root is now bracketed, so we can use brent_zero
Debug.Assert(error(apos) * error(bpos) < 0.0);
// this looks for the diangle that makes the offset-ellipse point y-coordinate zero
double dia_sln = ocl.GlobalMembers.brent_zero(apos.diangle, bpos.diangle, 3E-16, DefineConstants.OE_ERROR_TOLERANCE, this); // brent_zero.hpp
EllipsePosition1.setDiangle(dia_sln);
Debug.Assert(EllipsePosition1.isValid());
// because we only work with the y-coordinate of the offset-ellipse-point, there are two symmetric solutions
find_EllipsePosition2();
return(iters);
}
/// aligned offset-ellipse solver. callsn Numeric::brent_solver()
// used by BullCutter pushcutter edge-test
public bool aligned_solver(Fiber f)
{
error_dir.CopyFrom(f.dir.xyPerp()); // now calls to error(diangle) will give the right error
Debug.Assert(error_dir.xyNorm() > 0.0);
target.CopyFrom(f.p1); // target is either x or y-coord of f.p1
// find position(s) where ellipse tangent is parallel to fiber. Here error() will be minimized/maximized.
// tangent at point is: -a t + b s = -a*major_dir*t + b*minor_dir*s
// -at ma.y + bs mi.y = 0 for X-fiber
// s = sqrt(1-t^2)
// -a*ma.y * t + b*mi.y* sqrt(1-t^2) = 0
// => t^2 = b^2 / (a^2 + b^2)
double t1 = 0.0;
if (f.p1.y == f.p2.y)
{
t1 = Math.Sqrt(ocl.GlobalMembers.square(b * minor_dir.y) / (ocl.GlobalMembers.square(a * major_dir.y) + ocl.GlobalMembers.square(b * minor_dir.y)));
}
else if (f.p1.x == f.p2.x)
{
t1 = Math.Sqrt(ocl.GlobalMembers.square(b * minor_dir.x) / (ocl.GlobalMembers.square(a * major_dir.x) + ocl.GlobalMembers.square(b * minor_dir.x)));
}
else
{
Debug.Assert(false);
}
// bracket root
EllipsePosition tmp = new EllipsePosition();
EllipsePosition apos = new EllipsePosition();
EllipsePosition bpos = new EllipsePosition();
double s1 = Math.Sqrt(1.0 - ocl.GlobalMembers.square(t1));
bool found_positive = false;
bool found_negative = false;
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(s1, t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(s1, -t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(-s1, t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(-s1, -t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
if (found_positive)
{
if (found_negative)
{
Debug.Assert(this.error(apos.diangle) * this.error(bpos.diangle) < 0.0); // root is now bracketed.
double lolim = 0.0;
double hilim = 0.0;
if (apos.diangle > bpos.diangle)
{
lolim = bpos.diangle;
hilim = apos.diangle;
}
else if (bpos.diangle > apos.diangle)
{
hilim = bpos.diangle;
lolim = apos.diangle;
}
double dia_sln = ocl.GlobalMembers.brent_zero(lolim, hilim, 3E-16, DefineConstants.OE_ERROR_TOLERANCE, this);
double dia_sln2 = ocl.GlobalMembers.brent_zero(hilim - 4.0, lolim, 3E-16, DefineConstants.OE_ERROR_TOLERANCE, this);
EllipsePosition1.setDiangle(dia_sln);
EllipsePosition2.setDiangle(dia_sln2);
Debug.Assert(EllipsePosition1.isValid());
Debug.Assert(EllipsePosition2.isValid());
/*
* // FIXME. This assert fails in some cases (30sphere.stl z=0, for example)
* // FIXME. The allowed error should probably be in proportion to the difficulty of the case.
*
* if (!isZero_tol( error(EllipsePosition1.diangle) )) {
* std::cout << "AlignedEllipse::aligned_solver() ERROR \n";
* std::cout << "error(EllipsePosition1.diangle)= "<< error(EllipsePosition1.diangle) << " (expected zero)\n";
*
* }
* assert( isZero_tol( error(EllipsePosition1.diangle) ) );
* assert( isZero_tol( error(EllipsePosition2.diangle) ) );
*/
return(true);
}
}
return(false);
}
/// given one EllipsePosition solution, find the other.
// #define DEBUG_SOLVER
//
// given a known EllipsePosition1, look for the other symmetric
// solution EllipsePosition2
public bool find_EllipsePosition2()
{ // a horrible horrible function... :(
Debug.Assert(EllipsePosition1.isValid());
double err1 = Math.Abs(this.error(this.EllipsePosition1));
this.EllipsePosition2.s = this.EllipsePosition1.s; // plus
this.EllipsePosition2.t = -this.EllipsePosition1.t; // minus
if (Math.Abs(this.error(this.EllipsePosition2)) < err1 + DefineConstants.OE_ERROR_TOLERANCE)
{
if ((Math.Abs(this.EllipsePosition2.s - this.EllipsePosition1.s) > 1E-8) || (Math.Abs(this.EllipsePosition2.t - this.EllipsePosition1.t) > 1E-8))
{
#if DEBUG_SOLVER
Console.Write("2nd: (s, t)= ");
Console.Write(this.EllipsePosition2);
Console.Write(" oePoint()= ");
Console.Write(this.oePoint(this.EllipsePosition2));
Console.Write(" e=");
Console.Write(this.error(this.EllipsePosition2));
Console.Write("\n");
#endif
return(true);
}
}
this.EllipsePosition2.s = -this.EllipsePosition1.s;
this.EllipsePosition2.t = this.EllipsePosition1.t;
if (Math.Abs(this.error(this.EllipsePosition2)) < err1 + DefineConstants.OE_ERROR_TOLERANCE)
{
if ((Math.Abs(this.EllipsePosition2.s - this.EllipsePosition1.s) > 1E-8) || (Math.Abs(this.EllipsePosition2.t - this.EllipsePosition1.t) > 1E-8))
{
#if DEBUG_SOLVER
Console.Write("2nd: (s, t)= ");
Console.Write(this.EllipsePosition2);
Console.Write(" oePoint()= ");
Console.Write(this.oePoint(this.EllipsePosition2));
Console.Write(" e=");
Console.Write(this.error(this.EllipsePosition2));
Console.Write("\n");
#endif
return(true);
}
}
this.EllipsePosition2.s = -this.EllipsePosition1.s;
this.EllipsePosition2.t = -this.EllipsePosition1.t;
if (Math.Abs(this.error(this.EllipsePosition2)) < err1 + DefineConstants.OE_ERROR_TOLERANCE)
{
if ((Math.Abs(this.EllipsePosition2.s - this.EllipsePosition1.s) > 1E-8) || (Math.Abs(this.EllipsePosition2.t - this.EllipsePosition1.t) > 1E-8))
{
#if DEBUG_SOLVER
Console.Write("2nd: (s, t)= ");
Console.Write(this.EllipsePosition2);
Console.Write(" oePoint()= ");
Console.Write(this.oePoint(this.EllipsePosition2));
Console.Write(" e=");
Console.Write(this.error(this.EllipsePosition2));
Console.Write("\n");
#endif
return(true);
}
}
// last desperate attempt is identical solutions
this.EllipsePosition2.s = this.EllipsePosition1.s;
this.EllipsePosition2.t = this.EllipsePosition1.t;
if (Math.Abs(this.error(this.EllipsePosition2)) < err1 + DefineConstants.OE_ERROR_TOLERANCE)
{
// DON'T require solutions to differ
// if ( (fabs(this->EllipsePosition2.s - this->EllipsePosition1.s) > 1E-8) || (fabs(this->EllipsePosition2.t - this->EllipsePosition1.t) > 1E-8) ) {
#if DEBUG_SOLVER
Console.Write("2nd: (s, t)= ");
Console.Write(this.EllipsePosition2);
Console.Write(" oePoint()= ");
Console.Write(this.oePoint(this.EllipsePosition2));
Console.Write(" e=");
Console.Write(this.error(this.EllipsePosition2));
Console.Write("\n");
#endif
//std::cout << " find_EllipsePosition2() desperate-mode\n";
return(true);
//}
}
Console.Write("Ellipse::find_EllipsePosition2 cannot find EllipsePosition2! \n");
Console.Write("ellipse= ");
Console.Write(this);
Console.Write("\n");
print_solutions();
Debug.Assert(false); // serious error if we get here!
return(false);
}
