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-- Created on: 1991-09-10
-- Created by: Michel Chauvat
-- Copyright (c) 1991-1999 Matra Datavision
-- Copyright (c) 1999-2012 OPEN CASCADE SAS
--
-- The content of this file is subject to the Open CASCADE Technology Public
-- License Version 6.5 (the "License"). You may not use the content of this file
-- except in compliance with the License. Please obtain a copy of the License
-- at http://www.opencascade.org and read it completely before using this file.
--
-- The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
-- main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
--
-- The Original Code and all software distributed under the License is
-- distributed on an "AS IS" basis, without warranty of any kind, and the
-- Initial Developer hereby disclaims all such warranties, including without
-- limitation, any warranties of merchantability, fitness for a particular
-- purpose or non-infringement. Please see the License for the specific terms
-- and conditions governing the rights and limitations under the License.
package ElCLib
--- Purpose: Provides functions for basic geometric computations on
-- elementary curves such as conics and lines in 2D and 3D space.
-- This includes:
-- - calculation of a point or derived vector on a 2D or
-- 3D curve where:
-- - the curve is provided by the gp package, or
-- defined in reference form (as in the gp package),
-- and
-- - the point is defined by a parameter,
-- - evaluation of the parameter corresponding to a point
-- on a 2D or 3D curve from gp,
-- - various elementary computations which allow you to
-- position parameterized values within the period of a curve.
-- Notes:
-- - ElCLib stands for Elementary Curves Library.
-- - If the curves provided by the gp package are not
-- explicitly parameterized, they still have an implicit
-- parameterization, analogous to that which they infer
-- for the equivalent Geom or Geom2d curves.
uses gp
is
InPeriod(U, UFirst, ULast : Real) returns Real;
---Purpose: Return a value in the range <UFirst, ULast> by
-- adding or removing the period <ULast - UFirst> to
-- <U>.
AdjustPeriodic(UFirst, ULast, Precision : Real;
U1, U2 : in out Real);
---Purpose: Adjust U1 and U2 in the parametric range UFirst
-- Ulast of a periodic curve, where ULast -
-- UFirst is its period. To do this, this function:
-- - sets U1 in the range [ UFirst, ULast ] by
-- adding/removing the period to/from the value U1, then
-- - sets U2 in the range [ U1, U1 + period ] by
-- adding/removing the period to/from the value U2.
-- Precision is used to test the equalities.
Value (U : Real; L : Lin from gp) returns Pnt from gp;
--- Purpose : For elementary curves (lines, circles and conics) from
-- the gp package, computes the point of parameter U.
-- The result is either:
-- - a gp_Pnt point for a curve in 3D space, or
-- - a gp_Pnt2d point for a curve in 2D space.
Value (U : Real; C : Circ from gp) returns Pnt from gp;
---C++: inline
Value (U : Real; E : Elips from gp) returns Pnt from gp;
---C++: inline
Value (U : Real; H : Hypr from gp) returns Pnt from gp;
---C++: inline
Value (U : Real; Prb : Parab from gp) returns Pnt from gp;
---C++: inline
D1 (U : Real; L : Lin from gp; P : out Pnt from gp; V1 : out Vec from gp);
---Purpose:
-- For elementary curves (lines, circles and conics) from the
-- gp package, computes:
-- - the point P of parameter U, and
-- - the first derivative vector V1 at this point.
-- The results P and V1 are either:
-- - a gp_Pnt point and a gp_Vec vector, for a curve in 3D space, or
-- - a gp_Pnt2d point and a gp_Vec2d vector, for a curve in 2D space.
D1 (U : Real; C : Circ from gp; P : out Pnt from gp; V1 : out Vec from gp);
---C++: inline
D1 (U : Real; E : Elips from gp; P : out Pnt from gp; V1 : out Vec from gp);
---C++: inline
D1 (U : Real; H : Hypr from gp; P : out Pnt from gp; V1 : out Vec from gp);
---C++: inline
D1 (U : Real; Prb : Parab from gp; P : out Pnt from gp;
V1 : out Vec from gp);
---C++: inline
D2 (U : Real; C : Circ from gp; P : out Pnt from gp;
V1, V2 : out Vec from gp);
---Purpose: For elementary curves (circles and conics) from the gp
-- package, computes:
-- - the point P of parameter U, and
-- - the first and second derivative vectors V1 and V2 at this point.
-- The results, P, V1 and V2, are either:
-- - a gp_Pnt point and two gp_Vec vectors, for a curve in 3D space, or
-- - a gp_Pnt2d point and two gp_Vec2d vectors, for a curve in 2D space.
D2 (U : Real; E : Elips from gp; P : out Pnt from gp;
V1, V2 : out Vec from gp);
---C++: inline
D2 (U : Real; H : Hypr from gp; P : out Pnt from gp;
V1, V2 : out Vec from gp);
---C++: inline
D2 (U : Real; Prb : Parab from gp; P : out Pnt from gp;
V1, V2 : out Vec from gp);
---C++: inline
D3 (U : Real; C : Circ from gp; P : out Pnt from gp;
V1, V2, V3 : out Vec from gp);
---Purpose: For elementary curves (circles, ellipses and hyperbolae)
-- from the gp package, computes:
-- - the point P of parameter U, and
-- - the first, second and third derivative vectors V1, V2
-- and V3 at this point.
-- The results, P, V1, V2 and V3, are either:
-- - a gp_Pnt point and three gp_Vec vectors, for a curve in 3D space, or
-- - a gp_Pnt2d point and three gp_Vec2d vectors, for a curve in 2D space.
D3 (U : Real; E : Elips from gp; P : out Pnt from gp;
V1, V2, V3 : out Vec from gp);
---C++: inline
D3 (U : Real; H : Hypr from gp; P : out Pnt from gp;
V1, V2, V3 : out Vec from gp);
DN (U : Real; L : Lin from gp; N : Integer) returns Vec from gp;
---Purpose:
-- For elementary curves (lines, circles and conics) from
-- the gp package, computes the vector corresponding to
-- the Nth derivative at the point of parameter U. The result is either:
-- - a gp_Vec vector for a curve in 3D space, or
-- - a gp_Vec2d vector for a curve in 2D space.
-- In the following functions N is the order of derivation
-- and should be greater than 0
DN (U : Real; C : Circ from gp; N : Integer) returns Vec from gp;
---C++: inline
DN (U : Real; E : Elips from gp; N : Integer) returns Vec from gp;
---C++: inline
DN (U : Real; H : Hypr from gp; N : Integer) returns Vec from gp;
---C++: inline
DN (U : Real; Prb : Parab from gp; N : Integer) returns Vec from gp;
---C++: inline
Value (U : Real; L : Lin2d from gp) returns Pnt2d from gp;
---C++: inline
Value (U : Real; C : Circ2d from gp) returns Pnt2d from gp;
---C++: inline
Value (U : Real; E : Elips2d from gp) returns Pnt2d from gp;
---C++: inline
Value (U : Real; H : Hypr2d from gp) returns Pnt2d from gp;
---C++: inline
Value (U : Real; Prb : Parab2d from gp) returns Pnt2d from gp;
---C++: inline
D1 (U : Real; L : Lin2d from gp; P : out Pnt2d from gp;
V1 : out Vec2d from gp);
---C++: inline
D1 (U : Real; C : Circ2d from gp; P : out Pnt2d from gp;
V1 : out Vec2d from gp);
---C++: inline
D1 (U : Real; E : Elips2d from gp; P : out Pnt2d from gp;
V1 : out Vec2d from gp);
---C++: inline
D1 (U : Real; H : Hypr2d from gp; P : out Pnt2d from gp;
V1 : out Vec2d from gp);
---C++: inline
D1 (U : Real; Prb : Parab2d from gp; P : out Pnt2d from gp;
V1 : out Vec2d from gp);
---C++: inline
D2 (U : Real; C : Circ2d from gp; P : out Pnt2d from gp;
V1, V2 : out Vec2d from gp);
---C++: inline
D2 (U : Real; E : Elips2d from gp; P : out Pnt2d from gp;
V1, V2 : out Vec2d from gp);
---C++: inline
D2 (U : Real; H : Hypr2d from gp; P : out Pnt2d from gp;
V1, V2 : out Vec2d from gp);
---C++: inline
D2 (U : Real; Prb : Parab2d from gp; P : out Pnt2d from gp;
V1, V2 : out Vec2d from gp);
---C++: inline
D3 (U : Real; C : Circ2d from gp; P : out Pnt2d from gp;
V1, V2, V3 : out Vec2d from gp);
---C++: inline
D3 (U : Real; E : Elips2d from gp; P : out Pnt2d from gp;
V1, V2, V3 : out Vec2d from gp);
---C++: inline
D3 (U : Real; H : Hypr2d from gp; P : out Pnt2d from gp;
V1, V2, V3 : out Vec2d from gp);
---C++: inline
--- Purpose :
-- In the following functions N is the order of derivation
-- and should be greater than 0
DN (U : Real; L : Lin2d from gp; N : Integer) returns Vec2d from gp;
---C++: inline
DN (U : Real; C : Circ2d from gp; N : Integer) returns Vec2d from gp;
---C++: inline
DN (U : Real; E : Elips2d from gp; N : Integer) returns Vec2d from gp;
---C++: inline
DN (U : Real; H : Hypr2d from gp; N : Integer) returns Vec2d from gp;
---C++: inline
DN (U : Real; Prb : Parab2d from gp; N : Integer) returns Vec2d from gp;
---C++: inline
LineValue (U : Real; Pos : Ax1 from gp)
returns Pnt from gp;
--- Purpose : Curve evaluation
-- The following basis functions compute the derivatives on
-- elementary curves defined by their geometric characteristics.
-- These functions can be called without constructing a conic
-- from package gp. They are called by the previous functions.
-- Example :
-- A circle is defined by its position and its radius.
CircleValue (U : Real; Pos : Ax2 from gp; Radius : Real)
returns Pnt from gp;
EllipseValue (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real)
returns Pnt from gp;
HyperbolaValue (U : Real; Pos : Ax2 from gp;
MajorRadius, MinorRadius : Real)
returns Pnt from gp;
ParabolaValue (U : Real; Pos : Ax2 from gp; Focal : Real)
returns Pnt from gp;
LineD1 (U : Real; Pos : Ax1 from gp; P : out Pnt from gp;
V1 : out Vec from gp);
CircleD1 (U : Real; Pos : Ax2 from gp; Radius : Real; P : out Pnt from gp;
V1 : out Vec from gp);
EllipseD1 (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : out Pnt from gp; V1 : out Vec from gp);
HyperbolaD1 (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : out Pnt from gp; V1 : out Vec from gp);
ParabolaD1 (U : Real; Pos : Ax2 from gp; Focal : Real; P : out Pnt from gp;
V1 : out Vec from gp);
CircleD2 (U : Real; Pos : Ax2 from gp; Radius : Real;
P : out Pnt from gp; V1, V2 : out Vec from gp);
EllipseD2 (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : out Pnt from gp; V1, V2 : out Vec from gp);
HyperbolaD2 (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : out Pnt from gp; V1, V2 : out Vec from gp);
ParabolaD2 (U : Real; Pos : Ax2 from gp; Focal : Real;
P : out Pnt from gp; V1, V2 : out Vec from gp);
CircleD3 (U : Real; Pos : Ax2 from gp; Radius : Real;
P : out Pnt from gp; V1, V2, V3 : out Vec from gp);
EllipseD3 (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : out Pnt from gp; V1, V2, V3 : out Vec from gp);
HyperbolaD3 (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : out Pnt from gp; V1, V2, V3 : out Vec from gp);
LineDN (U : Real; Pos : Ax1 from gp; N : Integer)
returns Vec from gp;
--- Purpose :
-- In the following functions N is the order of derivation
-- and should be greater than 0
CircleDN (U : Real; Pos : Ax2 from gp; Radius : Real; N : Integer)
returns Vec from gp;
EllipseDN (U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
N : Integer)
returns Vec from gp;
HyperbolaDN (
U : Real; Pos : Ax2 from gp; MajorRadius, MinorRadius : Real; N : Integer)
returns Vec from gp;
ParabolaDN (U : Real; Pos : Ax2 from gp; Focal : Real; N : Integer)
returns Vec from gp;
LineValue (U : Real; Pos : Ax2d from gp)
returns Pnt2d from gp;
CircleValue (U : Real; Pos : Ax22d from gp; Radius : Real)
returns Pnt2d from gp;
EllipseValue (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real)
returns Pnt2d from gp;
HyperbolaValue (U : Real; Pos : Ax22d from gp;
MajorRadius, MinorRadius : Real)
returns Pnt2d from gp;
ParabolaValue (U : Real; Pos : Ax22d from gp; Focal : Real)
returns Pnt2d from gp;
LineD1 (U : Real; Pos : Ax2d from gp; P : out Pnt2d from gp;
V1 : out Vec2d from gp);
CircleD1 (U : Real; Pos : Ax22d from gp; Radius : Real;
P : out Pnt2d from gp; V1 : out Vec2d from gp);
EllipseD1 (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : out Pnt2d from gp; V1 : out Vec2d from gp);
HyperbolaD1 (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : out Pnt2d from gp; V1 : out Vec2d from gp);
ParabolaD1 (U : Real; Pos : Ax22d from gp; Focal : Real;
P : out Pnt2d from gp; V1 : out Vec2d from gp);
CircleD2 (U : Real; Pos : Ax22d from gp; Radius : Real;
P : out Pnt2d from gp; V1, V2 : out Vec2d from gp);
EllipseD2 (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : out Pnt2d from gp; V1, V2 : out Vec2d from gp);
HyperbolaD2 (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : out Pnt2d from gp; V1, V2 : out Vec2d from gp);
ParabolaD2 (U : Real; Pos : Ax22d from gp; Focal : Real;
P : out Pnt2d from gp; V1, V2 : out Vec2d from gp);
CircleD3 (U : Real; Pos : Ax22d from gp; Radius : Real;
P : out Pnt2d from gp; V1, V2, V3 : out Vec2d from gp);
EllipseD3 (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : out Pnt2d from gp; V1, V2, V3 : out Vec2d from gp);
HyperbolaD3 (U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : out Pnt2d from gp; V1, V2, V3 : out Vec2d from gp);
--- Purpose :
-- In the following functions N is the order of derivation
-- and should be greater than 0
LineDN (U : Real; Pos : Ax2d from gp; N : Integer)
returns Vec2d from gp;
CircleDN (U : Real; Pos : Ax22d from gp; Radius : Real; N : Integer)
returns Vec2d from gp;
EllipseDN (
U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
N : Integer)
returns Vec2d from gp;
HyperbolaDN (
U : Real; Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
N : Integer)
returns Vec2d from gp;
ParabolaDN (U : Real; Pos : Ax22d from gp; Focal : Real; N : Integer)
returns Vec2d from gp;
--- Purpose :
-- The following functions compute the parametric value corresponding
-- to a given point on a elementary curve. The point should be on the
-- curve.
Parameter (L : Lin from gp; P : Pnt from gp) returns Real;
---Purpose:
-- Computes the parameter value of the point P on the given curve.
-- Note: In its local coordinate system, the parametric
-- equation of the curve is given by the following:
-- - for the line L: P(U) = Po + U*Vo
-- where Po is the origin and Vo the unit vector of its positioning axis.
-- - for the circle C: X(U) = Radius*Cos(U), Y(U) = Radius*Sin(U)
-- - for the ellipse E: X(U) = MajorRadius*Cos(U). Y(U) = MinorRadius*Sin(U)
-- - for the hyperbola H: X(U) = MajorRadius*Ch(U), Y(U) = MinorRadius*Sh(U)
-- - for the parabola Prb:
-- X(U) = U**2 / (2*p)
-- Y(U) = U
-- where p is the distance between the focus and the directrix.
-- Warning
-- The point P must be on the curve. These functions are
-- not protected, however, and if point P is not on the
-- curve, an exception may be raised.
Parameter (L : Lin2d from gp; P : Pnt2d from gp) returns Real;
---C++: inline
--- Purpose : parametrization
-- P (U) = L.Location() + U * L.Direction()
Parameter (C : Circ from gp; P : Pnt from gp) returns Real;
---C++: inline
Parameter (C : Circ2d from gp; P : Pnt2d from gp) returns Real;
---C++: inline
--- Purpose : parametrization
-- In the local coordinate system of the circle
-- X (U) = Radius * Cos (U)
-- Y (U) = Radius * Sin (U)
Parameter (E : Elips from gp; P : Pnt from gp) returns Real;
---C++: inline
Parameter (E : Elips2d from gp; P : Pnt2d from gp) returns Real;
---C++: inline
--- Purpose : parametrization
-- In the local coordinate system of the Ellipse
-- X (U) = MajorRadius * Cos (U)
-- Y (U) = MinorRadius * Sin (U)
Parameter (H : Hypr from gp; P : Pnt from gp) returns Real;
---C++: inline
Parameter (H : Hypr2d from gp; P : Pnt2d from gp) returns Real;
---C++: inline
--- Purpose : parametrization
-- In the local coordinate system of the Hyperbola
-- X (U) = MajorRadius * Ch (U)
-- Y (U) = MinorRadius * Sh (U)
Parameter (Prb : Parab from gp; P : Pnt from gp) returns Real;
---C++: inline
Parameter (Prb : Parab2d from gp; P : Pnt2d from gp) returns Real;
---C++: inline
--- Purpose : parametrization
-- In the local coordinate system of the parabola
-- Y**2 = (2*P) * X where P is the distance between the focus
-- and the directrix.
LineParameter (Pos : Ax1 from gp; P : Pnt from gp) returns Real;
LineParameter (Pos : Ax2d from gp; P : Pnt2d from gp) returns Real;
--- Purpose : parametrization
-- P (U) = L.Location() + U * L.Direction()
CircleParameter (Pos : Ax2 from gp; P : Pnt from gp) returns Real;
CircleParameter (Pos : Ax22d from gp; P : Pnt2d from gp) returns Real;
--- Purpose : Pos is the Axis of the Circle
--- Purpose : parametrization
-- In the local coordinate system of the circle
-- X (U) = Radius * Cos (U)
-- Y (U) = Radius * Sin (U)
EllipseParameter (Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : Pnt from gp)
returns Real;
EllipseParameter (Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : Pnt2d from gp)
returns Real;
--- Purpose : Pos is the Axis of the Ellipse
--- Purpose : parametrization
-- In the local coordinate system of the Ellipse
-- X (U) = MajorRadius * Cos (U)
-- Y (U) = MinorRadius * Sin (U)
HyperbolaParameter (Pos : Ax2 from gp; MajorRadius, MinorRadius : Real;
P : Pnt from gp)
returns Real;
HyperbolaParameter (Pos : Ax22d from gp; MajorRadius, MinorRadius : Real;
P : Pnt2d from gp)
returns Real;
--- Purpose : Pos is the Axis of the Hyperbola
--- Purpose : parametrization
-- In the local coordinate system of the Hyperbola
-- X (U) = MajorRadius * Ch (U)
-- Y (U) = MinorRadius * Sh (U)
ParabolaParameter (Pos : Ax2 from gp; P : Pnt from gp) returns Real;
ParabolaParameter (Pos : Ax22d from gp; P : Pnt2d from gp) returns Real;
--- Purpose : Pos is the mirror axis of the parabola
--- Purpose : parametrization
-- In the local coordinate system of the parabola
-- Y**2 = (2*P) * X where P is the distance between the focus
-- and the directrix.
--- Purpose: The following functions build a 3d curve from a
-- 2d curve at a given position defined with an Ax2.
To3d (Pos : Ax2 from gp; P : Pnt2d from gp) returns Pnt from gp;
To3d (Pos : Ax2 from gp; V : Vec2d from gp) returns Vec from gp;
To3d (Pos : Ax2 from gp; V : Dir2d from gp) returns Dir from gp;
To3d (Pos : Ax2 from gp; A : Ax2d from gp) returns Ax1 from gp;
To3d (Pos : Ax2 from gp; A : Ax22d from gp) returns Ax2 from gp;
To3d (Pos : Ax2 from gp; L : Lin2d from gp) returns Lin from gp;
To3d (Pos : Ax2 from gp; C : Circ2d from gp) returns Circ from gp;
To3d (Pos : Ax2 from gp; E : Elips2d from gp) returns Elips from gp;
To3d (Pos : Ax2 from gp; H : Hypr2d from gp) returns Hypr from gp;
To3d (Pos : Ax2 from gp; Prb : Parab2d from gp) returns Parab from gp;
--- Purpose:
-- These functions build a 3D geometric entity from a 2D geometric entity.
-- The "X Axis" and the "Y Axis" of the global coordinate
-- system (i.e. 2D space) are lined up respectively with the
-- "X Axis" and "Y Axis" of the 3D coordinate system, Pos.
end ElCLib;
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