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b311480ed597aed47b7bfbf01ddcebb41202bd53
occt/src/ElSLib/ElSLib.cxx
bugmaster b311480ed5 0023024: Update headers of OCCT files 
Added appropriate copyright and license information in source files
2012-03-21 19:43:04 +04:00

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// Created on: 1991-09-09
// 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.
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620
#ifndef No_Exception
#define No_Exception
#endif
#include <ElSLib.ixx>
#include <gp.hxx>
#include <gp_XYZ.hxx>
#include <gp_Trsf.hxx>
static Standard_Real PIPI = M_PI + M_PI;
gp_Pnt ElSLib::PlaneValue (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
return gp_Pnt(U * XDir.X() + V * YDir.X() + PLoc.X(),
U * XDir.Y() + V * YDir.Y() + PLoc.Y(),
U * XDir.Z() + V * YDir.Z() + PLoc.Z());
}
gp_Pnt ElSLib::ConeValue (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real R = Radius + V * sin(SAngle);
Standard_Real A3 = V * cos(SAngle);
Standard_Real A1 = R * cos(U);
Standard_Real A2 = R * sin(U);
return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X(),
A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y(),
A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
}
gp_Pnt ElSLib::CylinderValue (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius)
{
// M(u,v) = C + Radius * ( Xdir * Cos(u) + Ydir * Sin(u)) + V * Zdir
// where C is the location point of the Axis2placement
// Xdir, Ydir ,Zdir are the directions of the local coordinates system
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real A1 = Radius * cos(U);
Standard_Real A2 = Radius * sin(U);
return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + V * ZDir.X() + PLoc.X(),
A1 * XDir.Y() + A2 * YDir.Y() + V * ZDir.Y() + PLoc.Y(),
A1 * XDir.Z() + A2 * YDir.Z() + V * ZDir.Z() + PLoc.Z());
}
gp_Pnt ElSLib::SphereValue (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius)
{
//M(U,V) = Location +
// R * CosV (CosU * XDirection + SinU * YDirection) +
// R * SinV * Direction
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real R = Radius * cos(V);
Standard_Real A3 = Radius * sin(V);
Standard_Real A1 = R * cos(U);
Standard_Real A2 = R * sin(U);
return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X(),
A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y(),
A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
}
gp_Pnt ElSLib::TorusValue (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius)
{
//M(U,V) =
// Location +
// (MajRadius+MinRadius*Cos(V)) * (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Sin(V) * Direction
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real R = MajorRadius + MinorRadius * cos(V);
Standard_Real A3 = MinorRadius * sin(V);
Standard_Real A1 = R * cos(U);
Standard_Real A2 = R * sin(U);
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
Standard_Real eps = 10.*(MinorRadius + MajorRadius)*RealEpsilon();
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
if (Abs(A3) <= eps)
A3 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X(),
A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y(),
A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
}
gp_Vec ElSLib::PlaneDN (const Standard_Real,
const Standard_Real,
const gp_Ax3& Pos,
const Standard_Integer Nu,
const Standard_Integer Nv)
{
if (Nu == 0 && Nv == 1) { return gp_Vec (Pos.YDirection()); }
else if (Nu == 1 && Nv == 0) { return gp_Vec (Pos.XDirection()); }
return gp_Vec (0., 0., 0.);
}
gp_Vec ElSLib::ConeDN (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
const Standard_Integer Nu,
const Standard_Integer Nv)
{
gp_XYZ Xdir = Pos.XDirection().XYZ();
gp_XYZ Ydir = Pos.YDirection().XYZ();
Standard_Real Um = U + Nu * M_PI_2; // M_PI * 0.5
Xdir.Multiply(cos(Um));
Ydir.Multiply(sin(Um));
Xdir.Add(Ydir);
if(Nv == 0) {
Xdir.Multiply(Radius + V * sin(SAngle));
if(Nu == 0) Xdir.Add(Pos.Location().XYZ());
return gp_Vec(Xdir);
}
else if(Nv == 1) {
Xdir.Multiply(sin(SAngle));
return gp_Vec(Xdir);
}
return gp_Vec(0.0,0.0,0.0);
}
gp_Vec ElSLib::CylinderDN (const Standard_Real U,
const Standard_Real,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Integer Nu,
const Standard_Integer Nv)
{
if (Nu + Nv < 1 || Nu < 0 || Nv < 0) { return gp_Vec(); }
if (Nv == 0) {
Standard_Real RCosU = Radius * cos(U);
Standard_Real RSinU = Radius * sin(U);
gp_XYZ Xdir = Pos.XDirection().XYZ();
gp_XYZ Ydir = Pos.YDirection().XYZ();
if ((Nu + 6) % 4 == 0) {
Xdir.Multiply (-RCosU);
Ydir.Multiply (-RSinU);
}
else if ((Nu + 5) % 4 == 0) {
Xdir.Multiply ( RSinU);
Ydir.Multiply (-RCosU);
}
else if ((Nu + 3) % 4 == 0) {
Xdir.Multiply (-RSinU);
Ydir.Multiply ( RCosU);
}
else if (Nu % 4 == 0) {
Xdir.Multiply ( RCosU);
Ydir.Multiply ( RSinU);
}
Xdir.Add (Ydir);
return gp_Vec (Xdir);
}
else if (Nv == 1 && Nu == 0) { return gp_Vec (Pos.Direction()); }
else { return gp_Vec (0.0, 0.0, 0.0); }
}
gp_Vec ElSLib::SphereDN (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Integer Nu,
const Standard_Integer Nv)
{
if (Nu + Nv < 1 || Nu < 0 || Nv < 0) { return gp_Vec(); }
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real RCosV = Radius * cos(V);
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
Standard_Real A1,A2,A3,X,Y,Z;
if (Nu == 0) {
Standard_Real RSinV = Radius * sin(V);
if (IsOdd (Nv)) { A1 = - RSinV * CosU; A2 = - RSinV * SinU; A3 = RCosV; }
else { A1 = - RCosV * CosU; A2 = - RCosV * SinU; A3 = - RSinV; }
X = A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z();
if (!( (Nv + 2) % 4 == 0 || (Nv + 3) % 4 == 0 ))
{ X = - X; Y = - Y; Z = - Z; }
}
else if (Nv == 0) {
if (IsOdd (Nu)) { A1 = - RCosV * SinU; A2 = RCosV * CosU; }
else { A1 = RCosV * CosU; A2 = RCosV * SinU; }
X = A1 * XDir.X() + A2 * YDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z();
if ( (Nu + 2) % 4 == 0 || (Nu + 1) % 4 == 0 )
{ X = - X; Y = - Y; Z = - Z; }
}
else {
Standard_Real RSinV = Radius * sin(V);
if (IsOdd (Nu)) { A1 = - SinU; A2 = CosU; }
else { A1 = - CosU; A2 = - SinU; }
if (IsOdd (Nv)) A3 = - RSinV;
else A3 = - RCosV;
X = (A1 * XDir.X() + A2 * YDir.X()) * A3;
Y = (A1 * XDir.Y() + A2 * YDir.Y()) * A3;
Z = (A1 * XDir.Z() + A2 * YDir.Z()) * A3;
if ((!((Nu + 2) % 4 == 0 || (Nu + 3) % 4 == 0) &&
((Nv + 2) % 4 == 0 || (Nv + 3) % 4 == 0)) ||
(((Nu + 2) % 4 == 0 || (Nu + 3) % 4 == 0) &&
!((Nv + 2) % 4 == 0 || (Nv + 3) % 4 == 0)))
{ X = - X; Y = - Y; Z = - Z; }
}
return gp_Vec(X,Y,Z);
}
gp_Vec ElSLib::TorusDN (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
const Standard_Integer Nu,
const Standard_Integer Nv)
{
if (Nu + Nv < 1 || Nu < 0 || Nv < 0) { return gp_Vec(); }
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
Standard_Real A1,A2,A3,X=0,Y=0,Z=0;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
Standard_Real eps = 10.*(MinorRadius + MajorRadius)*RealEpsilon();
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 End
if (Nv == 0) {
Standard_Real R = MajorRadius + MinorRadius * cos(V);
if (IsOdd (Nu)) { A1 = - R * SinU; A2 = R * CosU; }
else { A1 = - R * CosU; A2 = - R * SinU; }
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
X = A1 * XDir.X() + A2 * YDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z();
if (!((Nu + 2) % 4 == 0 || (Nu + 3) % 4 == 0))
{ X = - X; Y = - Y; Z = - Z; }
}
else if (Nu == 0) {
Standard_Real RCosV = MinorRadius * cos(V);
Standard_Real RSinV = MinorRadius * sin(V);
if (IsOdd (Nv)) { A1 = - RSinV * CosU; A2 = - RSinV * SinU; A3 = RCosV; }
else { A1 = - RCosV * CosU; A2 = - RCosV * SinU; A3 = - RSinV; }
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
if (Abs(A3) <= eps)
A3 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
X = A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z();
if (!((Nv + 2) % 4 == 0 || (Nv + 3) % 4 == 0))
{ X = - X; Y = - Y; Z = - Z; }
}
else {
if (IsOdd (Nu) &&
IsOdd (Nv)) {
Standard_Real RSinV = MinorRadius * sin(V);
A1 = RSinV * SinU; A2 = - RSinV * CosU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
X = A1 * XDir.X() + A2 * YDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z();
}
else if (IsEven (Nu) && IsEven (Nv)) {
Standard_Real RCosV = MinorRadius * cos(V);
A1 = RCosV * CosU; A2 = RCosV * SinU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
X = A1 * XDir.X() + A2 * YDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z();
}
else if (IsEven (Nv) && IsOdd (Nu)) {
Standard_Real RCosV = MinorRadius * cos(V);
A1 = RCosV * SinU; A2 = - RCosV * CosU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
X = A1 * XDir.X() + A2 * YDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z();
if (((Nv + Nu + 3) % 4) == 0)
{ X = - X; Y = - Y; Z = - Z; }
}
else if (IsOdd (Nv) && IsEven (Nu)) {
Standard_Real RSinV = MinorRadius * sin(V);
A1 = RSinV * CosU; A2 = RSinV * SinU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
X = A1 * XDir.X() + A2 * YDir.X();
Y = A1 * XDir.Y() + A2 * YDir.Y();
Z = A1 * XDir.Z() + A2 * YDir.Z();
if (((Nu + Nv + 3) % 4) == 0)
{ X = - X; Y = - Y; Z = - Z; }
}
}
return gp_Vec (X,Y,Z);
}
void ElSLib::PlaneD0 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
gp_Pnt& P)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
P.SetX(U * XDir.X() + V * YDir.X() + PLoc.X());
P.SetY(U * XDir.Y() + V * YDir.Y() + PLoc.Y());
P.SetZ(U * XDir.Z() + V * YDir.Z() + PLoc.Z());
}
void ElSLib::ConeD0 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
gp_Pnt& P)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real R = Radius + V * sin(SAngle);
Standard_Real A3 = V * cos(SAngle);
Standard_Real A1 = R * cos(U);
Standard_Real A2 = R * sin(U);
P.SetX(A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X());
P.SetY(A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y());
P.SetZ(A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
}
void ElSLib::CylinderD0 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real A1 = Radius * cos(U);
Standard_Real A2 = Radius * sin(U);
P.SetX(A1 * XDir.X() + A2 * YDir.X() + V * ZDir.X() + PLoc.X());
P.SetY(A1 * XDir.Y() + A2 * YDir.Y() + V * ZDir.Y() + PLoc.Y());
P.SetZ(A1 * XDir.Z() + A2 * YDir.Z() + V * ZDir.Z() + PLoc.Z());
}
void ElSLib::SphereD0 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius, gp_Pnt& P)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real R = Radius * cos(V);
Standard_Real A3 = Radius * sin(V);
Standard_Real A1 = R * cos(U);
Standard_Real A2 = R * sin(U);
P.SetX(A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X());
P.SetY(A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y());
P.SetZ(A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
}
void ElSLib::TorusD0 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
gp_Pnt& P )
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real R = MajorRadius + MinorRadius * cos(V);
Standard_Real A3 = MinorRadius * sin(V);
Standard_Real A1 = R * cos(U);
Standard_Real A2 = R * sin(U);
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
Standard_Real eps = 10.*(MinorRadius + MajorRadius)*RealEpsilon();
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
if (Abs(A3) <= eps)
A3 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
P.SetX(A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X());
P.SetY(A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y());
P.SetZ(A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
}
void ElSLib::PlaneD1 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
P.SetX(U * XDir.X() + V * YDir.X() + PLoc.X());
P.SetY(U * XDir.Y() + V * YDir.Y() + PLoc.Y());
P.SetZ(U * XDir.Z() + V * YDir.Z() + PLoc.Z());
Vu.SetX(XDir.X());
Vu.SetY(XDir.Y());
Vu.SetZ(XDir.Z());
Vv.SetX(YDir.X());
Vv.SetY(YDir.Y());
Vv.SetZ(YDir.Z());
}
void ElSLib::ConeD1 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv)
{
// Z = V * Cos(SAngle)
// M(U,V) = Location() + V * Cos(SAngle) * ZDirection() +
// (Radius + V*Sin(SAng)) * (Cos(U) * XDirection() + Sin(U) * YDirection())
// D1U =
//(Radius + V*Sin(SAng)) * (-Sin(U) * XDirection() + Cos(U) * YDirection())
// D1V =
// Direction() *Cos(SAngle) + Sin(SAng) * (Cos(U) * XDirection() +
// Sin(U) * YDirection())
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real CosA = cos(SAngle);
Standard_Real SinA = sin(SAngle);
Standard_Real R = Radius + V * SinA;
Standard_Real A3 = V * CosA;
Standard_Real A1 = R * CosU;
Standard_Real A2 = R * SinU;
Standard_Real R1 = SinA * CosU;
Standard_Real R2 = SinA * SinU;
P .SetX( A1 * XDir.X() + A2 * YDir.X() + A3 * ZDir.X() + PLoc.X());
P .SetY( A1 * XDir.Y() + A2 * YDir.Y() + A3 * ZDir.Y() + PLoc.Y());
P .SetZ( A1 * XDir.Z() + A2 * YDir.Z() + A3 * ZDir.Z() + PLoc.Z());
Vu.SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu.SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu.SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv.SetX( R1 * XDir.X() + R2 * YDir.X() + CosA * ZDir.X());
Vv.SetY( R1 * XDir.Y() + R2 * YDir.Y() + CosA * ZDir.Y());
Vv.SetZ( R1 * XDir.Z() + R2 * YDir.Z() + CosA * ZDir.Z());
}
void ElSLib::CylinderD1 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real A1 = Radius * cos(U);
Standard_Real A2 = Radius * sin(U);
P .SetX( A1 * XDir.X() + A2 * YDir.X() + V * ZDir.X() + PLoc.X());
P .SetY( A1 * XDir.Y() + A2 * YDir.Y() + V * ZDir.Y() + PLoc.Y());
P .SetZ( A1 * XDir.Z() + A2 * YDir.Z() + V * ZDir.Z() + PLoc.Z());
Vu.SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu.SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu.SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv.SetX( ZDir.X());
Vv.SetY( ZDir.Y());
Vv.SetZ( ZDir.Z());
}
void ElSLib::SphereD1 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv)
{
// Vxy = CosU * XDirection + SinU * YDirection
// DVxy = -SinU * XDirection + CosU * YDirection
// P(U,V) = Location + R * CosV * Vxy + R * SinV * Direction
// Vu = R * CosV * DVxy
// Vv = -R * SinV * Vxy + R * CosV * Direction
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real R1 = Radius * cos(V);
Standard_Real R2 = Radius * sin(V);
Standard_Real A1 = R1 * CosU;
Standard_Real A2 = R1 * SinU;
Standard_Real A3 = R2 * CosU;
Standard_Real A4 = R2 * SinU;
P .SetX( A1 * XDir.X() + A2 * YDir.X() + R2 * ZDir.X() + PLoc.X());
P .SetY( A1 * XDir.Y() + A2 * YDir.Y() + R2 * ZDir.Y() + PLoc.Y());
P .SetZ( A1 * XDir.Z() + A2 * YDir.Z() + R2 * ZDir.Z() + PLoc.Z());
Vu.SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu.SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu.SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv.SetX(- A3 * XDir.X() - A4 * YDir.X() + R1 * ZDir.X());
Vv.SetY(- A3 * XDir.Y() - A4 * YDir.Y() + R1 * ZDir.Y());
Vv.SetZ(- A3 * XDir.Z() - A4 * YDir.Z() + R1 * ZDir.Z());
}
void ElSLib::TorusD1 ( const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv)
{
//P(U,V) =
// Location +
// (MajorRadius+MinorRadius*Cos(V)) *
// (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Sin(V) * Direction
//Vv = -MinorRadius * Sin(V) * (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Cos(V) * Direction
//Vu =
// (MajorRadius+MinorRadius*Cos(V)) *
// (-Sin(U)*XDirection + Cos(U)*YDirection)
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real R1 = MinorRadius * cos(V);
Standard_Real R2 = MinorRadius * sin(V);
Standard_Real R = MajorRadius + R1;
Standard_Real A1 = R * CosU;
Standard_Real A2 = R * SinU;
Standard_Real A3 = R2 * CosU;
Standard_Real A4 = R2 * SinU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
Standard_Real eps = 10.*(MinorRadius + MajorRadius)*RealEpsilon();
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
if (Abs(A3) <= eps)
A3 = 0.;
if (Abs(A4) <= eps)
A4 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
P .SetX( A1 * XDir.X() + A2 * YDir.X() + R2 * ZDir.X() + PLoc.X());
P .SetY( A1 * XDir.Y() + A2 * YDir.Y() + R2 * ZDir.Y() + PLoc.Y());
P .SetZ( A1 * XDir.Z() + A2 * YDir.Z() + R2 * ZDir.Z() + PLoc.Z());
Vu.SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu.SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu.SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv.SetX(- A3 * XDir.X() - A4 * YDir.X() + R1 * ZDir.X());
Vv.SetY(- A3 * XDir.Y() - A4 * YDir.Y() + R1 * ZDir.Y());
Vv.SetZ(- A3 * XDir.Z() - A4 * YDir.Z() + R1 * ZDir.Z());
}
void ElSLib::ConeD2 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv,
gp_Vec& Vuu,
gp_Vec& Vvv,
gp_Vec& Vuv)
{
// Z = V * Cos(SAngle)
// M(U,V) = Location() + V * Cos(SAngle) * Direction() +
// (Radius + V*Sin(SAng)) * (Cos(U) * XDirection() + Sin(U) * YDirection())
// DU =
//(Radius + V*Sin(SAng)) * (-Sin(U) * XDirection() + Cos(U) * YDirection())
// DV =
// Direction() *Cos(SAngle) + Sin(SAng) * (Cos(U) * XDirection() +
// Sin(U) * YDirection())
// D2U =
//(Radius + V*Sin(SAng)) * (-Cos(U) * XDirection() - Sin(U) * YDirection())
// D2V = 0.0
// DUV =
//Sin(SAng) * (-Sin(U) * XDirection() + Cos(U) * YDirection())
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real CosA = cos(SAngle);
Standard_Real SinA = sin(SAngle);
Standard_Real R = Radius + V * SinA;
Standard_Real A3 = V * CosA;
Standard_Real A1 = R * CosU;
Standard_Real A2 = R * SinU;
Standard_Real R1 = SinA * CosU;
Standard_Real R2 = SinA * SinU;
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
P .SetX( Som1X + A3 * ZDir.X() + PLoc.X());
P .SetY( Som1Y + A3 * ZDir.Y() + PLoc.Y());
P .SetZ( Som1Z + A3 * ZDir.Z() + PLoc.Z());
Vu .SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu .SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu .SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv .SetX( R1 * XDir.X() + R2 * YDir.X() + CosA * ZDir.X());
Vv .SetY( R1 * XDir.Y() + R2 * YDir.Y() + CosA * ZDir.Y());
Vv .SetZ( R1 * XDir.Z() + R2 * YDir.Z() + CosA * ZDir.Z());
Vuu.SetX(- Som1X);
Vuu.SetY(- Som1Y);
Vuu.SetZ(- Som1Z);
Vvv.SetX( 0.0);
Vvv.SetY( 0.0);
Vvv.SetZ( 0.0);
Vuv.SetX(- R2 * XDir.X() + R1 * YDir.X());
Vuv.SetY(- R2 * XDir.Y() + R1 * YDir.Y());
Vuv.SetZ(- R2 * XDir.Z() + R1 * YDir.Z());
}
void ElSLib::CylinderD2 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv,
gp_Vec& Vuu,
gp_Vec& Vvv,
gp_Vec& Vuv)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real A1 = Radius * cos(U);
Standard_Real A2 = Radius * sin(U);
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
P .SetX( Som1X + V * ZDir.X() + PLoc.X());
P .SetY( Som1Y + V * ZDir.Y() + PLoc.Y());
P .SetZ( Som1Z + V * ZDir.Z() + PLoc.Z());
Vu .SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu .SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu .SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv .SetX( ZDir.X());
Vv .SetY( ZDir.Y());
Vv .SetZ( ZDir.Z());
Vuu.SetX(- Som1X);
Vuu.SetY(- Som1Y);
Vuu.SetZ(- Som1Z);
Vvv.SetX( 0.0);
Vvv.SetY( 0.0);
Vvv.SetZ( 0.0);
Vuv.SetX( 0.0);
Vuv.SetY( 0.0);
Vuv.SetZ( 0.0);
}
void ElSLib::SphereD2 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv,
gp_Vec& Vuu,
gp_Vec& Vvv,
gp_Vec& Vuv)
{
// Vxy = CosU * XDirection + SinU * YDirection
// DVxy = -SinU * XDirection + CosU * YDirection
// P(U,V) = Location + R * CosV * Vxy + R * SinV * Direction
// Vu = R * CosV * DVxy
// Vuu = - R * CosV * Vxy
// Vv = -R * SinV * Vxy + R * CosV * Direction
// Vvv = -R * CosV * Vxy - R * SinV * Direction
// Vuv = - R * SinV * DVxy
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real R1 = Radius * cos(V);
Standard_Real R2 = Radius * sin(V);
Standard_Real A1 = R1 * CosU;
Standard_Real A2 = R1 * SinU;
Standard_Real A3 = R2 * CosU;
Standard_Real A4 = R2 * SinU;
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
Standard_Real R2ZX = R2 * ZDir.X();
Standard_Real R2ZY = R2 * ZDir.Y();
Standard_Real R2ZZ = R2 * ZDir.Z();
P .SetX( Som1X + R2ZX + PLoc.X());
P .SetY( Som1Y + R2ZY + PLoc.Y());
P .SetZ( Som1Z + R2ZZ + PLoc.Z());
Vu .SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu .SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu .SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv .SetX(- A3 * XDir.X() - A4 * YDir.X() + R1 * ZDir.X());
Vv .SetY(- A3 * XDir.Y() - A4 * YDir.Y() + R1 * ZDir.Y());
Vv .SetZ(- A3 * XDir.Z() - A4 * YDir.Z() + R1 * ZDir.Z());
Vuu.SetX(- Som1X);
Vuu.SetY(- Som1Y);
Vuu.SetZ(- Som1Z);
Vvv.SetX(- Som1X - R2ZX);
Vvv.SetY(- Som1Y - R2ZY);
Vvv.SetZ(- Som1Z - R2ZZ);
Vuv.SetX( A4 * XDir.X() - A3 * YDir.X());
Vuv.SetY( A4 * XDir.Y() - A3 * YDir.Y());
Vuv.SetZ( A4 * XDir.Z() - A3 * YDir.Z());
}
void ElSLib::TorusD2 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
gp_Pnt& P,
gp_Vec& Vu,
gp_Vec& Vv,
gp_Vec& Vuu,
gp_Vec& Vvv,
gp_Vec& Vuv)
{
//P(U,V) =
// Location +
// (MajorRadius+MinorRadius*Cos(V)) *
// (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Sin(V) * Direction
//Vv = -MinorRadius * Sin(V) * (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Cos(V) * Direction
//Vu =
// (MajorRadius+MinorRadius*Cos(V)) *
// (-Sin(U)*XDirection + Cos(U)*YDirection)
//Vvv = -MinorRadius * Cos(V) * (Cos(U)*XDirection + Sin(U)*YDirection)
// -MinorRadius * Sin(V) * Direction
//Vuu =
// -(MajorRadius+MinorRadius*Cos(V)) *
// (Cos(U)*XDirection + Sin(U)*YDirection)
//Vuv = MinorRadius * Sin(V) * (Sin(U)*XDirection - Cos(U)*YDirection)
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real R1 = MinorRadius * cos(V);
Standard_Real R2 = MinorRadius * sin(V);
Standard_Real R = MajorRadius + R1;
Standard_Real A1 = R * CosU;
Standard_Real A2 = R * SinU;
Standard_Real A3 = R2 * CosU;
Standard_Real A4 = R2 * SinU;
Standard_Real A5 = R1 * CosU;
Standard_Real A6 = R1 * SinU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
Standard_Real eps = 10.*(MinorRadius + MajorRadius)*RealEpsilon();
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
if (Abs(A3) <= eps)
A3 = 0.;
if (Abs(A4) <= eps)
A4 = 0.;
if (Abs(A5) <= eps)
A5 = 0.;
if (Abs(A6) <= eps)
A6 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
Standard_Real R2ZX = R2 * ZDir.X();
Standard_Real R2ZY = R2 * ZDir.Y();
Standard_Real R2ZZ = R2 * ZDir.Z();
P .SetX( Som1X + R2ZX + PLoc.X());
P .SetY( Som1Y + R2ZY + PLoc.Y());
P .SetZ( Som1Z + R2ZZ + PLoc.Z());
Vu .SetX(- A2 * XDir.X() + A1 * YDir.X());
Vu .SetY(- A2 * XDir.Y() + A1 * YDir.Y());
Vu .SetZ(- A2 * XDir.Z() + A1 * YDir.Z());
Vv .SetX(- A3 * XDir.X() - A4 * YDir.X() + R1 * ZDir.X());
Vv .SetY(- A3 * XDir.Y() - A4 * YDir.Y() + R1 * ZDir.Y());
Vv .SetZ(- A3 * XDir.Z() - A4 * YDir.Z() + R1 * ZDir.Z());
Vuu.SetX(- Som1X);
Vuu.SetY(- Som1Y);
Vuu.SetZ(- Som1Z);
Vvv.SetX(- A5 * XDir.X() - A6 * YDir.X() - R2ZX);
Vvv.SetY(- A5 * XDir.Y() - A6 * YDir.Y() - R2ZY);
Vvv.SetZ(- A5 * XDir.Z() - A6 * YDir.Z() - R2ZZ);
Vuv.SetX( A4 * XDir.X() - A3 * YDir.X());
Vuv.SetY( A4 * XDir.Y() - A3 * YDir.Y());
Vuv.SetZ( A4 * XDir.Z() - A3 * YDir.Z());
}
void ElSLib::ConeD3 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
gp_Pnt& P,
gp_Vec& Vu, gp_Vec& Vv,
gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv,
gp_Vec& Vuuu, gp_Vec& Vvvv,
gp_Vec& Vuuv, gp_Vec& Vuvv)
{
// Z = V * Cos(SAngle)
// M(U,V) = Location() + V * Cos(SAngle) * Direction() +
// (Radius + V*Sin(SAng)) * (Cos(U) * XDirection() + Sin(U) * YDirection())
// DU =
//(Radius + V*Sin(SAng)) * (-Sin(U) * XDirection() + Cos(U) * YDirection())
// DV =
// Direction() *Cos(SAngle) + Sin(SAng) * (Cos(U) * XDirection() +
// Sin(U) * YDirection())
// D2U =
//(Radius + V*Sin(SAng)) * (-Cos(U) * XDirection() - Sin(U) * YDirection())
// D2V = 0.0
// DUV =
//Sin(SAng) * (-Sin(U) * XDirection() + Cos(U) * YDirection())
// D3U =
//(Radius + V*Sin(SAng)) * (Sin(U) * XDirection() - Cos(U) * YDirection())
// DUVV = 0.0
// D3V = 0.0
// DUUV = Sin(SAng) * (-Cos(U)*XDirection()-Sin(U) * YDirection()) +
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real CosA = cos(SAngle);
Standard_Real SinA = sin(SAngle);
Standard_Real R = Radius + V * SinA;
Standard_Real A3 = V * CosA;
Standard_Real A1 = R * CosU;
Standard_Real A2 = R * SinU;
Standard_Real R1 = SinA * CosU;
Standard_Real R2 = SinA * SinU;
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
Standard_Real Som2X = R1 * XDir.X() + R2 * YDir.X();
Standard_Real Som2Y = R1 * XDir.Y() + R2 * YDir.Y();
Standard_Real Som2Z = R1 * XDir.Z() + R2 * YDir.Z();
Standard_Real Dif1X = A2 * XDir.X() - A1 * YDir.X();
Standard_Real Dif1Y = A2 * XDir.Y() - A1 * YDir.Y();
Standard_Real Dif1Z = A2 * XDir.Z() - A1 * YDir.Z();
P .SetX( Som1X + A3 * ZDir.X() + PLoc.X());
P .SetY( Som1Y + A3 * ZDir.Y() + PLoc.Y());
P .SetZ( Som1Z + A3 * ZDir.Z() + PLoc.Z());
Vu .SetX(- Dif1X);
Vu .SetY(- Dif1Y);
Vu .SetZ(- Dif1Z);
Vv .SetX( Som2X + CosA * ZDir.X());
Vv .SetY( Som2Y + CosA * ZDir.Y());
Vv .SetZ( Som2Z + CosA * ZDir.Z());
Vuu .SetX(- Som1X);
Vuu .SetY(- Som1Y);
Vuu .SetZ(- Som1Z);
Vvv .SetX( 0.0);
Vvv .SetY( 0.0);
Vvv .SetZ( 0.0);
Vuv .SetX(- R2 * XDir.X() + R1 * YDir.X());
Vuv .SetY(- R2 * XDir.Y() + R1 * YDir.Y());
Vuv .SetZ(- R2 * XDir.Z() + R1 * YDir.Z());
Vuuu.SetX( Dif1X);
Vuuu.SetY( Dif1Y);
Vuuu.SetZ( Dif1Z);
Vvvv.SetX( 0.0);
Vvvv.SetY( 0.0);
Vvvv.SetZ( 0.0);
Vuvv.SetX( 0.0);
Vuvv.SetY( 0.0);
Vuvv.SetZ( 0.0);
Vuuv.SetX(- Som2X);
Vuuv.SetY(- Som2Y);
Vuuv.SetZ(- Som2Z);
}
void ElSLib::CylinderD3 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P,
gp_Vec& Vu, gp_Vec& Vv,
gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv,
gp_Vec& Vuuu, gp_Vec& Vvvv,
gp_Vec& Vuuv, gp_Vec& Vuvv)
{
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real A1 = Radius * cos(U);
Standard_Real A2 = Radius * sin(U);
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
Standard_Real Dif1X = A2 * XDir.X() - A1 * YDir.X();
Standard_Real Dif1Y = A2 * XDir.Y() - A1 * YDir.Y();
Standard_Real Dif1Z = A2 * XDir.Z() - A1 * YDir.Z();
P .SetX( Som1X + V * ZDir.X() + PLoc.X());
P .SetY( Som1Y + V * ZDir.Y() + PLoc.Y());
P .SetZ( Som1Z + V * ZDir.Z() + PLoc.Z());
Vu .SetX(- Dif1X);
Vu .SetY(- Dif1Y);
Vu .SetZ(- Dif1Z);
Vv .SetX( ZDir.X());
Vv .SetY( ZDir.Y());
Vv .SetZ( ZDir.Z());
Vuu .SetX(- Som1X);
Vuu .SetY(- Som1Y);
Vuu .SetZ(- Som1Z);
Vvv .SetX( 0.0);
Vvv .SetY( 0.0);
Vvv .SetZ( 0.0);
Vuv .SetX( 0.0);
Vuv .SetY( 0.0);
Vuv .SetZ( 0.0);
Vuuu.SetX( Dif1X);
Vuuu.SetY( Dif1Y);
Vuuu.SetZ( Dif1Z);
Vvvv.SetX( 0.0);
Vvvv.SetY( 0.0);
Vvvv.SetZ( 0.0);
Vuvv.SetX( 0.0);
Vuvv.SetY( 0.0);
Vuvv.SetZ( 0.0);
Vuuv.SetX( 0.0);
Vuuv.SetY( 0.0);
Vuuv.SetZ( 0.0);
}
void ElSLib::SphereD3 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real Radius,
gp_Pnt& P,
gp_Vec& Vu, gp_Vec& Vv,
gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv,
gp_Vec& Vuuu, gp_Vec& Vvvv,
gp_Vec& Vuuv, gp_Vec& Vuvv)
{
// Vxy = CosU * XDirection + SinU * YDirection
// DVxy = -SinU * XDirection + CosU * YDirection
// P(U,V) = Location + R * CosV * Vxy + R * SinV * Direction
// Vu = R * CosV * DVxy
// Vuu = - R * CosV * Vxy
// Vuuu = - Vu
// Vv = -R * SinV * Vxy + R * CosV * Direction
// Vvv = -R * CosV * Vxy - R * SinV * Direction
// Vvvv = -Vv
// Vuv = - R * SinV * DVxy
// Vuuv = R * SinV * Vxy
// Vuvv = - R * CosV * DVxy = Vuuu = -Vu
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real R1 = Radius * cos(V);
Standard_Real R2 = Radius * sin(V);
Standard_Real A1 = R1 * CosU;
Standard_Real A2 = R1 * SinU;
Standard_Real A3 = R2 * CosU;
Standard_Real A4 = R2 * SinU;
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
Standard_Real Som3X = A3 * XDir.X() + A4 * YDir.X();
Standard_Real Som3Y = A3 * XDir.Y() + A4 * YDir.Y();
Standard_Real Som3Z = A3 * XDir.Z() + A4 * YDir.Z();
Standard_Real Dif1X = A2 * XDir.X() - A1 * YDir.X();
Standard_Real Dif1Y = A2 * XDir.Y() - A1 * YDir.Y();
Standard_Real Dif1Z = A2 * XDir.Z() - A1 * YDir.Z();
Standard_Real R1ZX = R1 * ZDir.X();
Standard_Real R1ZY = R1 * ZDir.Y();
Standard_Real R1ZZ = R1 * ZDir.Z();
Standard_Real R2ZX = R2 * ZDir.X();
Standard_Real R2ZY = R2 * ZDir.Y();
Standard_Real R2ZZ = R2 * ZDir.Z();
P .SetX( Som1X + R2ZX + PLoc.X());
P .SetY( Som1Y + R2ZY + PLoc.Y());
P .SetZ( Som1Z + R2ZZ + PLoc.Z());
Vu .SetX(- Dif1X);
Vu .SetY(- Dif1Y);
Vu .SetZ(- Dif1Z);
Vv .SetX(- Som3X + R1ZX);
Vv .SetY(- Som3Y + R1ZY);
Vv .SetZ(- Som3Z + R1ZZ);
Vuu .SetX(- Som1X);
Vuu .SetY(- Som1Y);
Vuu .SetZ(- Som1Z);
Vvv .SetX(- Som1X - R2ZX);
Vvv .SetY(- Som1Y - R2ZY);
Vvv .SetZ(- Som1Z - R2ZZ);
Vuv .SetX( A4 * XDir.X() - A3 * YDir.X());
Vuv .SetY( A4 * XDir.Y() - A3 * YDir.Y());
Vuv .SetZ( A4 * XDir.Z() - A3 * YDir.Z());
Vuuu.SetX( Dif1X);
Vuuu.SetY( Dif1Y);
Vuuu.SetZ( Dif1Z);
Vvvv.SetX( Som3X - R1ZX);
Vvvv.SetY( Som3Y - R1ZY);
Vvvv.SetZ( Som3Z - R1ZZ);
Vuvv.SetX( Dif1X);
Vuvv.SetY( Dif1Y);
Vuvv.SetZ( Dif1Z);
Vuuv.SetX( Som3X);
Vuuv.SetY( Som3Y);
Vuuv.SetZ( Som3Z);
}
void ElSLib::TorusD3 (const Standard_Real U,
const Standard_Real V,
const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
gp_Pnt& P,
gp_Vec& Vu, gp_Vec& Vv,
gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv,
gp_Vec& Vuuu, gp_Vec& Vvvv,
gp_Vec& Vuuv, gp_Vec& Vuvv)
{
//P(U,V) =
// Location +
// (MajorRadius+MinorRadius*Cos(V)) *
// (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Sin(V) * Direction
//Vv = -MinorRadius * Sin(V) * (Cos(U)*XDirection + Sin(U)*YDirection) +
// MinorRadius * Cos(V) * Direction
//Vvv = -MinorRadius * Cos(V) * (Cos(U)*XDirection + Sin(U)*YDirection)
// -MinorRadius * Sin(V) * Direction
//Vvvv = - Vv
//Vu =
// (MajorRadius+MinorRadius*Cos(V)) *
// (-Sin(U)*XDirection + Cos(U)*YDirection)
//Vuu =
// -(MajorRadius+MinorRadius*Cos(V)) *
// (Cos(U)*XDirection + Sin(U)*YDirection)
//Vuuu = -Vu
//Vuv = MinorRadius * Sin(V) * (Sin(U)*XDirection - Cos(U)*YDirection)
//Vuvv = MinorRadius * Cos(V) * (Sin(U)*XDirection - Cos(U)*YDirection)
//Vuuv = MinorRadius * Sin(V) * (Cos(U)*XDirection + Sin(U)*YDirection)
const gp_XYZ& XDir = Pos.XDirection().XYZ();
const gp_XYZ& YDir = Pos.YDirection().XYZ();
const gp_XYZ& ZDir = Pos.Direction ().XYZ();
const gp_XYZ& PLoc = Pos.Location ().XYZ();
Standard_Real CosU = cos(U);
Standard_Real SinU = sin(U);
Standard_Real R1 = MinorRadius * cos(V);
Standard_Real R2 = MinorRadius * sin(V);
Standard_Real R = MajorRadius + R1;
Standard_Real A1 = R * CosU;
Standard_Real A2 = R * SinU;
Standard_Real A3 = R2 * CosU;
Standard_Real A4 = R2 * SinU;
Standard_Real A5 = R1 * CosU;
Standard_Real A6 = R1 * SinU;
// Modified by skv - Tue Sep 9 15:10:34 2003 OCC620 Begin
Standard_Real eps = 10.*(MinorRadius + MajorRadius)*RealEpsilon();
if (Abs(A1) <= eps)
A1 = 0.;
if (Abs(A2) <= eps)
A2 = 0.;
if (Abs(A3) <= eps)
A3 = 0.;
if (Abs(A4) <= eps)
A4 = 0.;
if (Abs(A5) <= eps)
A5 = 0.;
if (Abs(A6) <= eps)
A6 = 0.;
// Modified by skv - Tue Sep 9 15:10:35 2003 OCC620 End
Standard_Real Som1X = A1 * XDir.X() + A2 * YDir.X();
Standard_Real Som1Y = A1 * XDir.Y() + A2 * YDir.Y();
Standard_Real Som1Z = A1 * XDir.Z() + A2 * YDir.Z();
Standard_Real Som3X = A3 * XDir.X() + A4 * YDir.X();
Standard_Real Som3Y = A3 * XDir.Y() + A4 * YDir.Y();
Standard_Real Som3Z = A3 * XDir.Z() + A4 * YDir.Z();
Standard_Real Dif1X = A2 * XDir.X() - A1 * YDir.X();
Standard_Real Dif1Y = A2 * XDir.Y() - A1 * YDir.Y();
Standard_Real Dif1Z = A2 * XDir.Z() - A1 * YDir.Z();
Standard_Real R1ZX = R1 * ZDir.X();
Standard_Real R1ZY = R1 * ZDir.Y();
Standard_Real R1ZZ = R1 * ZDir.Z();
Standard_Real R2ZX = R2 * ZDir.X();
Standard_Real R2ZY = R2 * ZDir.Y();
Standard_Real R2ZZ = R2 * ZDir.Z();
P .SetX( Som1X + R2ZX + PLoc.X());
P .SetY( Som1Y + R2ZY + PLoc.Y());
P .SetZ( Som1Z + R2ZZ + PLoc.Z());
Vu .SetX(- Dif1X);
Vu .SetY(- Dif1Y);
Vu .SetZ(- Dif1Z);
Vv .SetX(- Som3X + R1ZX);
Vv .SetY(- Som3Y + R1ZY);
Vv .SetZ(- Som3Z + R1ZZ);
Vuu .SetX(- Som1X);
Vuu .SetY(- Som1Y);
Vuu .SetZ(- Som1Z);
Vvv .SetX(- A5 * XDir.X() - A6 * YDir.X() - R2ZX);
Vvv .SetY(- A5 * XDir.Y() - A6 * YDir.Y() - R2ZY);
Vvv .SetZ(- A5 * XDir.Z() - A6 * YDir.Z() - R2ZZ);
Vuv .SetX( A4 * XDir.X() - A3 * YDir.X());
Vuv .SetY( A4 * XDir.Y() - A3 * YDir.Y());
Vuv .SetZ( A4 * XDir.Z() - A3 * YDir.Z());
Vuuu.SetX( Dif1X);
Vuuu.SetY( Dif1Y);
Vuuu.SetZ( Dif1Z);
Vvvv.SetX( Som3X - R1ZX);
Vvvv.SetY( Som3Y - R1ZY);
Vvvv.SetZ( Som3Z - R1ZZ);
Vuuv.SetX( Som3X);
Vuuv.SetY( Som3Y);
Vuuv.SetZ( Som3Z);
Vuvv.SetX( A6 * XDir.X() - A5 * YDir.X() );
Vuvv.SetY( A6 * XDir.Y() - A5 * YDir.Y() );
Vuvv.SetZ( A6 * XDir.Z() - A5 * YDir.Z() );
}
//=======================================================================
//function : PlaneParameters
//purpose :
//=======================================================================
void ElSLib::PlaneParameters (const gp_Ax3& Pos,
const gp_Pnt& P,
Standard_Real& U,
Standard_Real& V)
{
gp_Trsf T;
T.SetTransformation (Pos);
gp_Pnt Ploc = P.Transformed (T);
U = Ploc.X();
V = Ploc.Y();
}
//=======================================================================
//function : CylindreParameters
//purpose :
//=======================================================================
void ElSLib::CylinderParameters (const gp_Ax3& Pos,
const Standard_Real,
const gp_Pnt& P,
Standard_Real& U,
Standard_Real& V)
{
gp_Trsf T;
T.SetTransformation (Pos);
gp_Pnt Ploc = P.Transformed (T);
U = atan2(Ploc.Y(),Ploc.X());
if (U < -1.e-16) U += PIPI;
else if (U < 0) U = 0;
V = Ploc.Z();
}
//=======================================================================
//function : ConeParameters
//purpose :
//=======================================================================
void ElSLib::ConeParameters(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
const gp_Pnt& P,
Standard_Real& U,
Standard_Real& V)
{
gp_Trsf T;
T.SetTransformation (Pos);
gp_Pnt Ploc = P.Transformed (T);
if(Ploc.X() ==0.0 && Ploc.Y()==0.0 ) {
U = 0.0;
}
else if ( -Radius > Ploc.Z()* Tan(SAngle) ) {
// the point is at the wrong side of the apex
U = atan2(-Ploc.Y(), -Ploc.X());
}
else {
U = atan2(Ploc.Y(),Ploc.X());
}
if (U < -1.e-16) U += PIPI;
else if (U < 0) U = 0;
// Evaluate V as follows :
// P0 = Cone.Value(U,0)
// P1 = Cone.Value(U,1)
// V = P0 P1 . P0 Ploc
// After simplification obtain:
// V = Sin(Sang) * ( x cosU + y SinU - R) + z * Cos(Sang)
// Method that permits to find V of the projected point if the point
// is not actually on the cone.
V = sin(SAngle) * ( Ploc.X() * cos(U) + Ploc.Y() * sin(U) - Radius)
+ cos(SAngle) * Ploc.Z();
}
//=======================================================================
//function : SphereParameters
//purpose :
//=======================================================================
void ElSLib::SphereParameters(const gp_Ax3& Pos,
const Standard_Real,
const gp_Pnt& P,
Standard_Real& U,
Standard_Real& V)
{
gp_Trsf T;
T.SetTransformation (Pos);
gp_Pnt Ploc = P.Transformed (T);
Standard_Real x, y, z;
Ploc.Coord (x, y, z);
Standard_Real l = sqrt (x * x + y * y);
if (l < gp::Resolution()) { // point on axis Z of the sphere
if (z > 0.)
V = M_PI_2; // PI * 0.5
else
V = - M_PI_2; // PI * 0.5
U = 0.;
}
else {
V = atan(z/l);
U = atan2(y,x);
if (U < -1.e-16) U += PIPI;
else if (U < 0) U = 0;
}
}
//=======================================================================
//function : TorusParameters
//purpose :
//=======================================================================
void ElSLib::TorusParameters(const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
const gp_Pnt& P,
Standard_Real& U,
Standard_Real& V)
{
gp_Trsf Tref;
Tref.SetTransformation (Pos);
gp_Pnt Ploc = P.Transformed (Tref);
Standard_Real x, y, z;
Ploc.Coord (x, y, z);
// all that to process case of Major < Minor.
U = atan2(y,x);
if (MajorRadius < MinorRadius){
Standard_Real cosu = cos(U);
Standard_Real sinu = sin(U);
Standard_Real z2 = z * z;
Standard_Real MinR2 = MinorRadius * MinorRadius;
Standard_Real RCosU = MajorRadius * cosu;
Standard_Real RSinU = MajorRadius * sinu;
Standard_Real xm = x - RCosU;
Standard_Real ym = y - RSinU;
Standard_Real xp = x + RCosU;
Standard_Real yp = y + RSinU;
Standard_Real D1 = xm * xm + ym * ym + z2 - MinR2;
Standard_Real D2 = xp * xp + yp * yp + z2 - MinR2;
Standard_Real AD1 = D1;
if (AD1 < 0) AD1 = - AD1;
Standard_Real AD2 = D2;
if (AD2 < 0) AD2 = - AD2;
if (AD2 < AD1) U += M_PI;
}
if (U < -1.e-16) U += PIPI;
else if (U < 0) U = 0;
Standard_Real cosu = cos(U);
Standard_Real sinu = sin(U);
gp_Dir dx(cosu,sinu,0.);
gp_Dir dP(x - MajorRadius * cosu,
y - MajorRadius * sinu,
z);
V = dx.AngleWithRef(dP,dx^gp::DZ());
if (V < -1.e-16) V += PIPI;
else if (V < 0) V = 0;
}
//=======================================================================
//function : PlaneUIso
//purpose :
//=======================================================================
gp_Lin ElSLib::PlaneUIso(const gp_Ax3& Pos,
const Standard_Real U)
{
gp_Lin L(Pos.Location(),Pos.YDirection());
gp_Vec Ve(Pos.XDirection());
Ve *= U;
L.Translate(Ve);
return L;
}
//=======================================================================
//function : CylinderUIso
//purpose :
//=======================================================================
gp_Lin ElSLib::CylinderUIso(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real U)
{
gp_Pnt P;
gp_Vec DU,DV;
CylinderD1(U,0.,Pos,Radius,P,DU,DV);
gp_Lin L(P,DV);
return L;
}
//=======================================================================
//function : ConeUIso
//purpose :
//=======================================================================
gp_Lin ElSLib::ConeUIso(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
const Standard_Real U)
{
gp_Pnt P;
gp_Vec DU,DV;
ConeD1(U,0,Pos,Radius,SAngle,P,DU,DV);
gp_Lin L(P,DV);
return L;
}
//=======================================================================
//function : SphereUIso
//purpose :
//=======================================================================
gp_Circ ElSLib::SphereUIso(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real U)
{
gp_Vec dx = Pos.XDirection();
gp_Vec dy = Pos.YDirection();
gp_Dir dz = Pos.Direction ();
gp_Dir cx = cos(U) * dx + sin(U) * dy;
gp_Ax2 axes(Pos.Location(),
cx.Crossed(dz),
cx);
gp_Circ Circ(axes,Radius);
return Circ;
}
//=======================================================================
//function : TorusUIso
//purpose :
//=======================================================================
gp_Circ ElSLib::TorusUIso(const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
const Standard_Real U)
{
gp_Vec dx = Pos.XDirection();
gp_Vec dy = Pos.YDirection();
gp_Dir dz = Pos.Direction ();
gp_Dir cx = cos(U) * dx + sin(U) * dy;
gp_Ax2 axes(Pos.Location(),
cx.Crossed(dz),
cx);
gp_Vec Ve = cx;
Ve *= MajorRadius;
axes.Translate(Ve);
gp_Circ Circ(axes,MinorRadius);
return Circ;
}
//=======================================================================
//function : PlaneVIso
//purpose :
//=======================================================================
gp_Lin ElSLib::PlaneVIso(const gp_Ax3& Pos,
const Standard_Real V)
{
gp_Lin L(Pos.Location(),Pos.XDirection());
gp_Vec Ve(Pos.YDirection());
Ve *= V;
L.Translate(Ve);
return L;
}
//=======================================================================
//function : CylinderVIso
//purpose :
//=======================================================================
gp_Circ ElSLib::CylinderVIso(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real V)
{
gp_Ax2 axes = Pos.Ax2();
gp_Vec Ve(Pos.Direction());
Ve.Multiply(V);
axes.Translate(Ve);
gp_Circ C(axes,Radius);
return C;
}
//=======================================================================
//function : ConeVIso
//purpose :
//=======================================================================
gp_Circ ElSLib::ConeVIso(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real SAngle,
const Standard_Real V)
{
gp_Ax3 axes(Pos);
gp_Vec Ve(Pos.Direction());
Ve.Multiply(V * cos(SAngle));
axes.Translate(Ve);
Standard_Real R = Radius + V * sin(SAngle);
if (R < 0) {
axes.XReverse();
axes.YReverse();
R = - R;
}
gp_Circ C(axes.Ax2(),R);
return C;
}
//=======================================================================
//function : SphereVIso
//purpose :
//=======================================================================
gp_Circ ElSLib::SphereVIso(const gp_Ax3& Pos,
const Standard_Real Radius,
const Standard_Real V)
{
gp_Ax2 axes = Pos.Ax2();
gp_Vec Ve(Pos.Direction());
Ve.Multiply(Radius * sin(V));
axes.Translate(Ve);
Standard_Real radius = Radius * cos(V);
gp_Circ Circ(axes,radius);
return Circ;
}
//=======================================================================
//function : TorusVIso
//purpose :
//=======================================================================
gp_Circ ElSLib::TorusVIso(const gp_Ax3& Pos,
const Standard_Real MajorRadius,
const Standard_Real MinorRadius,
const Standard_Real V)
{
gp_Ax3 axes = Pos.Ax2();
gp_Vec Ve(Pos.Direction());
Ve.Multiply(MinorRadius * sin(V));
axes.Translate(Ve);
Standard_Real R = MajorRadius + MinorRadius * cos(V);
if (R < 0) {
axes.XReverse();
axes.YReverse();
R = - R;
}
gp_Circ Circ(axes.Ax2(),R);
return Circ;
}
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