private bool NewtonSearch(
BsplineCurve curve,
double chord,
ref double param,
ref Point3d result,
double tolerance = 0.0001)
{
//-- Start Point
//--
var start = curve.EvaluatePoint( param );
//-- Initial Guess: Blind Forward
//--
param += 0.1;
while( ( param >= 0.0 ) &&
( param <= 1.0 ) )
{
//-- Evaluate Point
//--
result = curve.EvaluatePoint( param );
var distance = MSApp.Point3dDistance( ref start, ref result ) - chord;
if( Math.Abs( distance ) < tolerance ) return true;
//#debug
{
AddLine( start, result );
}
//#enddebug
//-- Newton Raphson Improved Guess
//-- f'(t) = (f(t+h) - f(t)) / h
var point = curve.EvaluatePoint( param + tolerance );
var delta = ( MSApp.Point3dDistance( ref start, ref point ) - ( distance + chord ) ) / tolerance;
param -= distance / delta;
}
return false;
}
//-- Biforcation/Branching Solver
//--
//--
private bool BranchSearch(
BsplineCurve curve,
double chord,
ref double param,
ref Point3d result,
double tolerance = 0.0001)
{
//-- Evaluate Start Point
//--
var start = curve.EvaluatePoint( param );
//-- Search Between [Curve.start, Curve.Max]
//--
var min = param;
var max = 1.0;
while( ( max - min ) > tolerance )
{
//-- Evaluate Mid-Point
//--
param = 0.5 * ( min + max );
result = curve.EvaluatePoint( param );
//-- Found within Tolerance?
//--
var distance = MSApp.Point3dDistance( ref start, ref result );
if( Math.Abs( distance - chord ) < tolerance ) return true;
//#debug
{
AddLine( start, result );
}
//#enddebug
//-- Select Half-Span
//--
if( distance < chord )
min = param;
else
max = param;
}
//-- End Point Reached
//--
return false;
}
//-- Brute force-ish
//--
private bool MarchSearch(
BsplineCurve curve,
double chord,
ref double param,
ref Point3d result,
double tolerance = 0.0001)
{
//-- Evaluate Start Point
//--
var start = curve.EvaluatePoint( param );
//-- Make step size assumption
//--
var step = 0.1;
while( ( param >= 0.0 ) &&
( param <= 1.0 ) )
{
//-- Next Point
//--
param += step;
result = curve.EvaluatePoint( param );
//-- Found within Tolerance?
//--
var distance = MSApp.Point3dDistance( ref start, ref result );
if( Math.Abs( distance - chord ) < tolerance ) return true;
//#debug
{
AddLine( start, result );
}
//#enddebug
//-- Overshoot -> Switch Direction + Half Step
//--
if( ( ( step > 0 ) && ( distance > chord ) ) ||
( ( step < 0 ) && ( distance < chord ) ) )
step *= -0.5;
}
return false;
}