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Data Structures
Extrema_FuncExtPS.hxx File Reference
#include <Standard.hxx>
#include <Standard_DefineAlloc.hxx>
#include <Standard_Macro.hxx>
#include <gp_Pnt.hxx>
#include <Adaptor3d_SurfacePtr.hxx>
#include <Standard_Real.hxx>
#include <TColStd_SequenceOfReal.hxx>
#include <Extrema_SequenceOfPOnSurf.hxx>
#include <Standard_Boolean.hxx>
#include <math_FunctionSetWithDerivatives.hxx>
#include <Standard_Integer.hxx>

Data Structures

class  Extrema_FuncExtPS
 
Functional for search of extremum of the distance between point P and
surface S, starting from approximate solution (u0, v0).

The class inherits math_FunctionSetWithDerivatives and thus is intended
for use in math_FunctionSetRoot algorithm .

Denoting derivatives of the surface S(u,v) by u and v, respectively, as
Su and Sv, the two functions to be nullified are:

F1(u,v) = (S - P) * Su
F2(u,v) = (S - P) * Sv

The derivatives of the functional are:

Duf1(u,v) = Su^2 + (S-P) * Suu;
Dvf1(u,v) = Su * Sv + (S-P) * Suv
Duf2(u,v) = Sv * Su + (S-P) * Suv = Dvf1
Dvf2(u,v) = Sv^2 + (S-P) * Svv

Here * denotes scalar product, and ^2 is square power.
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