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-- File: LeastSquare.cdl
-- Created: Thu Jul 25 17:24:41 1991
-- Author: Laurent PAINNOT
-- <lpa@topsn3>
---Copyright: Matra Datavision 1991, 1992
generic class LeastSquare from AppParCurves
(MultiLine as any;
ToolLine as any) -- as ToolLine(MultiLine)
---Purpose: This class describes the least square fitting of a
-- MultiLine using the Householder method from the
-- mathematical package.
-- The problem to solve is the following one:
-- minimizing the sum(|C(ui)- Qi|)2 where Qi are the points of
-- the MultiLine and C(ui) the points of the approximating
-- curves.
uses Matrix from math,
Vector from math,
IntegerVector from math,
Constraint from AppParCurves,
MultiCurve from AppParCurves,
MultiBSpCurve from AppParCurves,
Array1OfInteger from TColStd,
Array1OfReal from TColStd,
HArray1OfInteger from TColStd,
HArray1OfReal from TColStd
raises NotDone from StdFail,
OutOfRange from Standard,
DimensionError from Standard,
NoSuchObject from Standard
is
Create(SSP: MultiLine; FirstPoint, LastPoint: Integer;
FirstCons, LastCons: Constraint;
Parameters: Vector from math; NbPol: Integer)
---Purpose: given a MultiLine, this algorithm computes the least
-- square resolution using the Householder-QR method.
-- If the first and/or the last point is a constraint
-- point, the value of the tangency or curvature is
-- computed in the resolution.
-- NbPol is the number of control points wanted
-- for the approximating curves.
-- The system to solve is the following:
-- A X = B.
-- Where A is the Bernstein matrix computed with the
-- parameters, B the points coordinates and X the poles
-- solutions.
-- The matrix A is the same for each coordinate x, y and z
-- and is also the same for each MultiLine point because
-- they are approximated in parallel(so with the same
-- parameter, only the vector B changes).
returns LeastSquare from AppParCurves
raises DimensionError from Standard;
Create(SSP: MultiLine; FirstPoint, LastPoint: Integer;
FirstCons, LastCons: Constraint; NbPol: Integer)
---Purpose: Initializes the fields of the object.
returns LeastSquare;
Create(SSP: MultiLine; Knots: Array1OfReal; Mults: Array1OfInteger;
FirstPoint, LastPoint: Integer;
FirstCons, LastCons: Constraint;
Parameters: Vector from math; NbPol: Integer)
---Purpose: given a MultiLine, this algorithm computes the least
-- square resolution using the Householder-QR method.
-- If the first and/or the last point is a constraint
-- point, the value of the tangency or curvature is
-- computed in the resolution.
-- Deg is the degree wanted for the approximating curves.
-- The system to solve is the following:
-- A X = B.
-- Where A is the BSpline functions matrix computed with
-- <parameters>, B the points coordinates and X the poles
-- solutions.
-- The matrix A is the same for each coordinate x, y and z
-- and is also the same for each MultiLine point because
-- they are approximated in parallel(so with the same
-- parameter, only the vector B changes).
returns LeastSquare from AppParCurves
raises DimensionError from Standard;
Create(SSP: MultiLine; Knots: Array1OfReal; Mults: Array1OfInteger;
FirstPoint, LastPoint: Integer;
FirstCons, LastCons: Constraint; NbPol: Integer)
---Purpose: Initializes the fields of the object.
returns LeastSquare;
Init(me: in out; SSP: MultiLine; FirstPoint, LastPoint: Integer)
---Purpose: is used by the constuctors above.
is static protected;
Perform(me: in out; Parameters: Vector)
---Purpose: Is used after having initialized the fields.
-- The case "CurvaturePoint" is not treated in this method.
is static;
Perform(me: in out; Parameters: Vector;
l1, l2: Real)
---Purpose: Is used after having initialized the fields.
is static;
----------------------------------------------------------------------
-- for the two following methods, vectors <V> must be constructed
-- as follow:
-- V(v1x, v1y, v1z, ....., vnx, vny, vnz, v1x, v1y, ....., vmx, vmy)
-- 3d curve 3d curve 2d curve 2d curve
--
-- the length of V must be Nb3dpoints*3 + Nb2dpoints*2
Perform(me: in out; Parameters: Vector;
V1t, V2t: Vector;
l1, l2: Real)
---Purpose: Is used after having initialized the fields.
--- <V1t> is the tangent vector at the first point.
--- <V2t> is the tangent vector at the last point.
is static;
Perform(me: in out; Parameters: Vector;
V1t, V2t, V1c, V2c: Vector;
l1, l2: Real)
---Purpose: Is used after having initialized the fields.
--- <V1t> is the tangent vector at the first point.
--- <V2t> is the tangent vector at the last point.
--- <V1c> is the tangent vector at the first point.
--- <V2c> is the tangent vector at the last point.
is static;
-------------------------------
--- Result methods:
-------------------------------
IsDone(me)
---Purpose: returns True if all has been correctly done.
returns Boolean
is static;
BezierValue(me: in out)
---Purpose: returns the result of the approximation, i.e. all the
-- Curves.
-- An exception is raised if NotDone.
returns MultiCurve from AppParCurves
raises NotDone from StdFail,
NoSuchObject from Standard
is static;
BSplineValue(me: in out)
---Purpose: returns the result of the approximation, i.e. all the
-- Curves.
-- An exception is raised if NotDone.
---C++: return const &
returns MultiBSpCurve from AppParCurves
raises NotDone from StdFail,
NoSuchObject from Standard
is static;
FunctionMatrix(me)
---Purpose: returns the function matrix used to approximate the
-- set.
---C++: return const &
returns Matrix from math
raises NotDone from StdFail
is static;
DerivativeFunctionMatrix(me)
---Purpose: returns the derivative function matrix used
-- to approximate the set.
---C++: return const &
returns Matrix from math
raises NotDone from StdFail
is static;
ErrorGradient(me: in out; Grad: in out Vector;
F: in out Real; MaxE3d, MaxE2d: in out Real)
---Purpose: returns the maximum errors between the MultiLine
-- and the approximation curves. F is the sum of the square
-- distances. Grad is the derivative vector of the
-- function F.
is static;
Distance(me: in out)
---Purpose: returns the distances between the points of the
-- multiline and the approximation curves.
---C++: return const&
returns Matrix from math
is static;
Error(me: in out; F: in out Real;
MaxE3d, MaxE2d: in out Real)
---Purpose: returns the maximum errors between the MultiLine
-- and the approximation curves. F is the sum of the square
-- distances.
is static;
FirstLambda(me)
---Purpose: returns the value (P2 - P1)/ V1 if the first point
-- was a tangency point.
returns Real
is static;
LastLambda(me)
---Purpose: returns the value (PN - PN-1)/ VN if the last point
-- was a tangency point.
returns Real
is static;
Points(me)
---Purpose: returns the matrix of points value.
---C++: return const&
returns Matrix
is static;
Poles(me)
---Purpose: returns the matrix of resulting control points value.
---C++: return const&
returns Matrix
is static;
KIndex(me)
---Purpose: Returns the indexes of the first non null values of
-- A and DA.
-- The values are non null from Index(ieme point) +1
-- to Index(ieme point) + degree +1.
---C++: return const&
returns IntegerVector
is static;
-------------------------------
--- internal methods:
-------------------------------
NbBColumns(me; SSP: MultiLine)
---Purpose: returns the number of second member columns.
-- Is used internally to initialize the fields.
returns Integer
is static protected;
TheFirstPoint(me; FirstCons: Constraint; FirstPoint: Integer)
---Purpose: returns the first point beeing fitted.
returns Integer
is static protected;
TheLastPoint(me; LastCons: Constraint; LastPoint: Integer)
---Purpose: returns the last point beeing fitted.
returns Integer
is static protected;
Affect(me: in out; SSP: MultiLine; Index: Integer;
Cons: in out Constraint; Vt, Vc: in out Vector)
---Purpose: Affects the fields in the case of a constraint point.
is static protected;
ComputeFunction(me: in out; Parameters: Vector)
---Purpose:
is static protected;
SearchIndex(me: in out; Index: in out IntegerVector)
is static protected;
MakeTAA(me: in out; TheA, TheB: in out Vector)
---Purpose: computes internal matrixes for the resolution
is static protected;
MakeTAA(me: in out; TheA: in out Vector)
---Purpose: computes internal matrixes for the resolution
is static protected;
MakeTAA(me: in out; TheA: in out Vector; TheB: in out Matrix)
---Purpose: computes internal matrixes for the resolution
is static protected;
fields
FirstConstraint : Constraint from AppParCurves;
LastConstraint : Constraint from AppParCurves;
SCU: MultiBSpCurve from AppParCurves;
myknots: HArray1OfReal from TColStd;
mymults: HArray1OfInteger from TColStd;
mypoles: Matrix from math;
A: Matrix from math;
DA: Matrix from math;
B2: Matrix from math;
mypoints: Matrix from math;
Vflatknots: Vector from math;
Vec1t: Vector from math;
Vec1c: Vector from math;
Vec2t: Vector from math;
Vec2c: Vector from math;
theError: Matrix from math;
myindex: IntegerVector from math;
ERR3d: Real;
ERR2d: Real;
lambda1: Real;
lambda2: Real;
FirstP: Integer;
LastP: Integer;
Nlignes: Integer;
Ninc: Integer;
NA: Integer;
myfirstp: Integer;
mylastp: Integer;
resinit: Integer;
resfin: Integer;
nbP2d: Integer;
nbP: Integer;
nbpoles: Integer;
deg: Integer;
done: Boolean;
iscalculated : Boolean;
isready : Boolean;
end LeastSquare;
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