Optimized 3D Newton-Raphson solver for systems of 3 equations in 3 unknowns. More...

#include <MathSys_NewtonTypes.hxx>
#include <gp_Pnt.hxx>
#include <gp_Vec.hxx>
#include <algorithm>
#include <array>
#include <cmath>

Namespaces
namespace	MathSys
	Shared types for specialized small-dimension Newton solvers.

namespace	MathSys::detail

Functions
bool	MathSys::detail::IsBoundsValid3D (const NewtonBoundsN< 3 > &theBounds)
	Check that NewtonBoundsN<3> has valid (min <= max) ranges.

bool	MathSys::detail::IsOptionsValid3D (const NewtonOptions &theOptions)
	Check that NewtonOptions fields are positive and valid.

double	MathSys::detail::MaxDomainSize3D (const NewtonBoundsN< 3 > &theBounds)
	Return the largest domain extent across all 3 dimensions (min 1.0).

void	MathSys::detail::Clamp3D (std::array< double, 3 > &theX, const NewtonBoundsN< 3 > &theBounds, bool theUseSoftBounds, double theSoftExtRatio)
	Clamp solution array to bounds, optionally extending by soft-bounds ratio.

bool	MathSys::detail::Solve3x3 (const double theJ[3][3], const double theF[3], double theDelta[3])
	Solve 3x3 linear system J*x = -F using Cramer's rule with cofactor expansion.

template<typename Function >
NewtonResultN< 3 >	MathSys::Solve3D (const Function &theFunc, const std::array< double, 3 > &theX0, const NewtonBoundsN< 3 > &theBounds, const NewtonOptions &theOptions=NewtonOptions())
	Solve a 3x3 nonlinear system by Newton iteration with bounds.

template<typename CurveEvaluator , typename SurfaceEvaluator >
NewtonResultN< 3 >	MathSys::SolveCurveSurfaceExtrema3D (const CurveEvaluator &theCurve, const SurfaceEvaluator &theSurface, const std::array< double, 3 > &theX0, const NewtonBoundsN< 3 > &theBounds, const NewtonOptions &theOptions=NewtonOptions())
	Optimized 3D Newton solver for curve-surface extrema.

Detailed Description

Optimized 3D Newton-Raphson solver for systems of 3 equations in 3 unknowns.

This solver is specifically optimized for 3D problems like:

Optimizations compared to general Newton:

Namespaces