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-- File: CSLib.cdl
-- Created: Mon Sep 9 15:44:13 1991
-- Author: Michel Chauvat
-- JCV Decembre 1991
---Copyright: Matra Datavision 1991
package CSLib
---Purpose: This package implements functions for basis geometric
-- computation on curves and surfaces.
-- The tolerance criterions used in this package are
-- Resolution from package gp and RealEpsilon from class
-- Real of package Standard.
uses gp,
TColgp,
TColStd,
math
is
enumeration DerivativeStatus is
Done, D1uIsNull, D1vIsNull, D1IsNull, D1uD1vRatioIsNull,
D1vD1uRatioIsNull, D1uIsParallelD1v;
--- Purpose :
--
-- D1uIsNull : ||D1U|| <= Resolution
--
-- D1vIsNull : ||D1V|| <= Resolution
--
-- D1IsNull : the first derivatives in the U and V parametric
-- directions have null length :
-- ||D1U|| <= Resolution and ||D1V|| <= Resolution
--
-- D1uD1vRatioIsNull : the first derivative in the U direction has
-- null length by comparison with the derivative
-- in the V direction
-- ||D1U|| / ||D1V|| <= RealEpsilon
--
-- D1vD1uRatioIsNull : the first derivative in the V direction has
-- null length by comparison with the derivative
-- in the U direction
-- ||D1V|| / ||D1U|| <= RealEpsilon
--
-- D1uIsParallelD1v : the angle between the derivatives in the U and
-- V direction is null (tolerance criterion given
-- as input data)
enumeration NormalStatus is
Singular,Defined,InfinityOfSolutions, D1NuIsNull, D1NvIsNull, D1NIsNull,
D1NuNvRatioIsNull, D1NvNuRatioIsNull, D1NuIsParallelD1Nv;
--- Purpose :
--
-- if N is the normal
--
-- InfinityOfSolutions : ||DN/du||>Resolution, ||DN/dv||>Resolution
--
-- D1NuIsNull : ||DN/du|| <= Resolution
--
-- D1NvIsNull : ||DN/dv|| <= Resolution
--
-- D1NIsNull : ||DN/du||<=Resolution, ||DN/dv||<=Resolution
--
-- D1NuNvRatioIsNull : ||D1Nu|| / ||D1Nv|| <= RealEpsilon
--
-- D1NvNuRatioIsNull : ||D1Nu|| / ||D1Nv|| <= RealEpsilon
--
-- D1NuIsParallelD1Nv : The angle between D1Nu and D1Nv is Null.
class Class2d;
---Purpose:
--
-- *** Class2d : Low level algorithm for 2d classification
-- this class was moved from package BRepTopAdaptor
--- Purpose :
-- The following functions computes the normal to a surface
private class NormalPolyDef;
--- Purpose :
-- The following functions computes the normal to a surface
-- inherits FunctionWithDerivative from math
--
Normal (D1U, D1V: Vec from gp; SinTol: Real;
Status: out DerivativeStatus;
Normal: out Dir from gp);
--- Purpose :
-- Computes the normal direction of a surface as the cross product
-- between D1U and D1V.
-- If D1U has null length or D1V has null length or D1U and D1V are
-- parallel the normal is undefined.
-- To check that D1U and D1V are colinear the sinus of the angle
-- between D1U and D1V is computed and compared with SinTol.
-- The normal is computed if Status == Done else the Status gives the
-- reason why the computation has failed.
Normal (D1U, D1V, D2U, D2V, D2UV: Vec from gp; SinTol: Real;
Done : out Boolean; Status : out NormalStatus;
Normal: out Dir from gp);
--- Purpose :
-- If there is a singularity on the surface the previous method
-- cannot compute the local normal.
-- This method computes an approched normal direction of a surface.
-- It does a limited development and needs the second derivatives
-- on the surface as input data.
-- It computes the normal as follow :
-- N(u, v) = D1U ^ D1V
-- N(u0+du,v0+dv) = N0 + DN/du(u0,v0) * du + DN/dv(u0,v0) * dv + Eps
-- with Eps->0 so we can have the equivalence N ~ dN/du + dN/dv.
-- DNu = ||DN/du|| and DNv = ||DN/dv||
--
-- . if DNu IsNull (DNu <= Resolution from gp) the answer Done = True
-- the normal direction is given by DN/dv
-- . if DNv IsNull (DNv <= Resolution from gp) the answer Done = True
-- the normal direction is given by DN/du
-- . if the two directions DN/du and DN/dv are parallel Done = True
-- the normal direction is given either by DN/du or DN/dv.
-- To check that the two directions are colinear the sinus of the
-- angle between these directions is computed and compared with
-- SinTol.
-- . if DNu/DNv or DNv/DNu is lower or equal than Real Epsilon
-- Done = False, the normal is undefined
-- . if DNu IsNull and DNv is Null Done = False, there is an
-- indetermination and we should do a limited developpement at
-- order 2 (it means that we cannot omit Eps).
-- . if DNu Is not Null and DNv Is not Null Done = False, there are
-- an infinity of normals at the considered point on the surface.
Normal (D1U, D1V: Vec from gp; MagTol: Real;
Status: out NormalStatus;
Normal: out Dir from gp);
--- Purpose :
-- Computes the normal direction of a surface as the cross product
-- between D1U and D1V.
--
Normal (MaxOrder : Integer ; DerNUV : Array2OfVec from TColgp; MagTol: Real;
U , V , Umin , Umax , Vmin , Vmax : Real; Status: out NormalStatus;
Normal : out Dir from gp; OrderU , OrderV : out Integer);
--- Purpose : find the first order k0 of deriviative of NUV
-- where: foreach order < k0 all the derivatives of NUV are
-- null all the derivatives of NUV corresponding to the order
-- k0 are collinear and have the same sens.
-- In this case, normal at U,V is unique.
DNNUV ( Nu , Nv : Integer; DerSurf : Array2OfVec from TColgp )
returns Vec from gp;
---Purpose : -- Computes the derivative of order Nu in the --
-- direction U and Nv in the direction V of the not --
-- normalized normal vector at the point P(U,V) The
-- array DerSurf contain the derivative (i,j) of the surface
-- for i=0,Nu+1 ; j=0,Nv+1
DNNUV (Nu,Nv : Integer ; DerSurf1 : Array2OfVec from TColgp;
DerSurf2 : Array2OfVec from TColgp )
returns Vec from gp;
---Purpose : Computes the derivatives of order Nu in the direction Nu
-- and Nv in the direction Nv of the not normalized vector
-- N(u,v) = dS1/du * dS2/dv (cases where we use an osculating surface)
-- DerSurf1 are the derivatives of S1
DNNormal( Nu , Nv : Integer; DerNUV : Array2OfVec from TColgp ;
Iduref : Integer = 0; Idvref : Integer = 0 )
returns Vec from gp;
---Purpose : -- Computes the derivative of order Nu in the --
-- direction U and Nv in the direction V of the
-- normalized normal vector at the point P(U,V) array
-- DerNUV contain the derivative (i+Iduref,j+Idvref)
-- of D1U ^ D1V for i=0,Nu ; j=0,Nv Iduref and Idvref
-- correspond to a derivative of D1U ^ D1V which can
-- be used to compute the normalized normal vector.
-- In the regular cases , Iduref=Idvref=0.
end CSLib;
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