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0033661: Data Exchange, Step Import - Tessellated GDTs are not imported
[occt.git] / src / gp / gp_Torus.cxx
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b311480e 1// Copyright (c) 1995-1999 Matra Datavision
973c2be1 2// Copyright (c) 1999-2014 OPEN CASCADE SAS
b311480e 3//
973c2be1 4// This file is part of Open CASCADE Technology software library.
b311480e 5//
d5f74e42 6// This library is free software; you can redistribute it and/or modify it under
7// the terms of the GNU Lesser General Public License version 2.1 as published
973c2be1 8// by the Free Software Foundation, with special exception defined in the file
9// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
10// distribution for complete text of the license and disclaimer of any warranty.
b311480e 11//
973c2be1 12// Alternatively, this file may be used under the terms of Open CASCADE
13// commercial license or contractual agreement.
7fd59977 14
d5477f8c 15#include <gp_Torus.hxx>
42cf5bc1 16
42cf5bc1 17#include <gp_Ax1.hxx>
18#include <gp_Ax2.hxx>
19#include <gp_Ax3.hxx>
20#include <gp_Pnt.hxx>
42cf5bc1 21#include <gp_Trsf.hxx>
7fd59977 22#include <Standard_DimensionError.hxx>
23
0b4abfb9 24void gp_Torus::Coefficients (TColStd_Array1OfReal& theCoef) const
7fd59977 25{
0b4abfb9 26 // R = majorRadius;
27 // r = minorRadius.
28
29 // X = (R + r*cos(V))*cos(U)
30 // Y = (R + r*cos(V))*sin(U)
31 // Z = r*sin(V)
32
33 //Therefore,
34 // 4*R*R*(r*r - Z*Z) = (X*X + Y*Y + Z*Z - R*R - r*r)^2
35 //Or
36 // X^4+Y^4+Z^4+
37 // 2*((X*Y)^2+(X*Z)^2+(Y*Z)^2)-
38 // 2*(R^2+r^2)*(X^2+Y^2)+
39 // 2*(R^2-r^2)*Z^2+(R^2-r^2)^2 = 0.0
40
41 const Standard_Integer aLowIndex = theCoef.Lower();
42 Standard_DimensionError_Raise_if (theCoef.Length() < 35,
43 "gp_Torus::theCoefficients(): Dimension mismatch");
44
45 gp_Trsf aTr;
46 aTr.SetTransformation (pos);
47 const Standard_Real aT11 = aTr.Value (1, 1);
48 const Standard_Real aT12 = aTr.Value (1, 2);
49 const Standard_Real aT13 = aTr.Value (1, 3);
50 const Standard_Real aT14 = aTr.Value (1, 4);
51 const Standard_Real aT21 = aTr.Value (2, 1);
52 const Standard_Real aT22 = aTr.Value (2, 2);
53 const Standard_Real aT23 = aTr.Value (2, 3);
54 const Standard_Real aT24 = aTr.Value (2, 4);
55 const Standard_Real aT31 = aTr.Value (3, 1);
56 const Standard_Real aT32 = aTr.Value (3, 2);
57 const Standard_Real aT33 = aTr.Value (3, 3);
58 const Standard_Real aT34 = aTr.Value (3, 4);
59
60 const Standard_Real aTcol1sq = aT11*aT11 + aT21*aT21 + aT31*aT31;
61 const Standard_Real aTcol2sq = aT12*aT12 + aT22*aT22 + aT32*aT32;
62 const Standard_Real aTcol3sq = aT13*aT13 + aT23*aT23 + aT33*aT33;
63 const Standard_Real aTcol4sq = aT14*aT14 + aT24*aT24 + aT34*aT34;
64 const Standard_Real aTcol1Tcol2 = aT11*aT12 + aT21*aT22 + aT31*aT32;
65 const Standard_Real aTcol1Tcol3 = aT11*aT13 + aT21*aT23 + aT31*aT33;
66 const Standard_Real aTcol2Tcol3 = aT12*aT13 + aT22*aT23 + aT32*aT33;
67 const Standard_Real aTcol1Tcol4 = aT11*aT14 + aT21*aT24 + aT31*aT34;
68 const Standard_Real aTcol2Tcol4 = aT12*aT14 + aT22*aT24 + aT32*aT34;
69 const Standard_Real aTcol3Tcol4 = aT13*aT14 + aT23*aT24 + aT33*aT34;
70
71 const Standard_Real aSumRadius = (majorRadius*majorRadius +
72 minorRadius*minorRadius);
73 const Standard_Real aSubRadius = (majorRadius*majorRadius -
74 minorRadius*minorRadius);
75
76 /*
77 After substitution
78 Transpose([X Y Z 1]) = aTr*Transpose([X Y Z 1])
79 we will obtain:
80 */
81
82 theCoef(aLowIndex) = aTcol1sq*aTcol1sq; //X^4
83 theCoef(aLowIndex+1) = aTcol2sq*aTcol2sq; //Y^4
84 theCoef(aLowIndex+2) = aTcol3sq*aTcol3sq; //Z^4
85 theCoef(aLowIndex+3) = 4.0*aTcol1sq*aTcol1Tcol2; //X^3*Y
86 theCoef(aLowIndex+4) = 4.0*aTcol1sq*aTcol1Tcol3; //X^3*Z
87 theCoef(aLowIndex+5) = 4.0*aTcol2sq*aTcol1Tcol2; //X*Y^3
88 theCoef(aLowIndex+6) = 4.0*aTcol2sq*aTcol2Tcol3; //Y^3*Z
89 theCoef(aLowIndex+7) = 4.0*aTcol3sq*aTcol1Tcol3; //X*Z^3
90 theCoef(aLowIndex+8) = 4.0*aTcol3sq*aTcol2Tcol3; //Y*Z^3
91 theCoef(aLowIndex+9) = 2.0*(aTcol1sq*aTcol2sq +
92 2.0*aTcol1Tcol2*aTcol1Tcol2); //X^2*Y^2
93 theCoef(aLowIndex+10) = 2.0*(aTcol1sq*aTcol3sq +
94 2.0*aTcol1Tcol3*aTcol1Tcol3); //X^2*Z^2
95 theCoef(aLowIndex+11) = 2.0*(aTcol2sq*aTcol3sq +
96 2.0*aTcol2Tcol3*aTcol2Tcol3); //Y^2*Z^2
97 theCoef(aLowIndex+12) = 4.0*(aTcol1sq*aTcol2Tcol3 +
98 2.0*aTcol1Tcol2*aTcol1Tcol3); //X^2*Y*Z
99 theCoef(aLowIndex+13) = 4.0*(aTcol2sq*aTcol1Tcol3 +
100 2.0*aTcol1Tcol2*aTcol2Tcol3); //X*Y^2*Z
101 theCoef(aLowIndex+14) = 4.0*(aTcol3sq*aTcol1Tcol2 +
102 2.0*aTcol1Tcol3*aTcol2Tcol3); //X*Y*Z^2
103
104 theCoef(aLowIndex+15) = 4.0*aTcol1sq*aTcol1Tcol4; //X^3
105 theCoef(aLowIndex+16) = 4.0*aTcol2sq*aTcol2Tcol4; //Y^3
106 theCoef(aLowIndex+17) = 4.0*aTcol3sq*aTcol3Tcol4; //Z^3
107 theCoef(aLowIndex+18) = 4.0*(aTcol1sq*aTcol2Tcol4 +
108 2.0*aTcol1Tcol4*aTcol1Tcol2); //X^2*Y
109 theCoef(aLowIndex+19) = 4.0*(aTcol1sq*aTcol3Tcol4 +
110 2.0*aTcol1Tcol4*aTcol1Tcol3); //X^2*Z
111 theCoef(aLowIndex+20) = 4.0*(aTcol2sq*aTcol1Tcol4 +
112 2.0*aTcol2Tcol4*aTcol1Tcol2); //X*Y^2
113 theCoef(aLowIndex+21) = 4.0*(aTcol2sq*aTcol3Tcol4 +
114 2.0*aTcol2Tcol4*aTcol2Tcol3); //Y^2*Z
115 theCoef(aLowIndex+22) = 4.0*(aTcol3sq*aTcol1Tcol4 +
116 2.0*aTcol3Tcol4*aTcol1Tcol3); //X*Z^2
117 theCoef(aLowIndex+23) = 4.0*(aTcol3sq*aTcol2Tcol4 +
118 2.0*aTcol3Tcol4*aTcol2Tcol3); //Y*Z^2
119 theCoef(aLowIndex+24) = 8.0*(aTcol1Tcol2*aTcol3Tcol4 +
120 aTcol2Tcol3*aTcol1Tcol4 +
121 aTcol2Tcol4*aTcol1Tcol3); //X*Y*Z
122
123 theCoef(aLowIndex+25) = 2.0*(aSubRadius*aT31*aT31 -
124 aSumRadius*(aT11*aT11 + aT21*aT21) +
125 aTcol4sq*aTcol1sq +
126 2.0*aTcol1Tcol4*aTcol1Tcol4); //X^2
127 theCoef(aLowIndex+26) = 2.0*(aSubRadius*aT32*aT32 -
128 aSumRadius*(aT12*aT12 + aT22*aT22) +
129 aTcol4sq*aTcol2sq +
130 2.0*aTcol2Tcol4*aTcol2Tcol4); //Y^2
131 theCoef(aLowIndex+27) = 2.0*(aSubRadius*aT33*aT33 -
132 aSumRadius*(aT13*aT13 + aT23*aT23) +
133 aTcol4sq*aTcol3sq +
134 2.0*aTcol3Tcol4*aTcol3Tcol4); //Z^2
135 theCoef(aLowIndex+28) = 4.0*(aSubRadius*aT31*aT32 -
136 aSumRadius*(aT11*aT12 + aT21*aT22) +
137 aTcol4sq*aTcol1Tcol2 +
138 2.0*aTcol1Tcol4*aTcol2Tcol4); //X*Y
139 theCoef(aLowIndex+29) = 4.0*(aSubRadius*aT31*aT33 -
140 aSumRadius*(aT11*aT13 + aT21*aT23) +
141 aTcol4sq*aTcol1Tcol3 +
142 2.0*aTcol1Tcol4*aTcol3Tcol4); //X*Z
143 theCoef(aLowIndex+30) = 4.0*(aSubRadius*aT32*aT33 -
144 aSumRadius*(aT12*aT13 + aT22*aT23) +
145 aTcol4sq*aTcol2Tcol3 +
146 2.0*aTcol2Tcol4*aTcol3Tcol4); //Y*Z
147
148 theCoef(aLowIndex+31) = 4.0*(aTcol4sq*aTcol1Tcol4 +
149 aSubRadius*aT31*aT34 -
150 aSumRadius*(aT11*aT14 + aT21*aT24)); //X
151 theCoef(aLowIndex+32) = 4.0*(aTcol4sq*aTcol2Tcol4 +
152 aSubRadius*aT32*aT34 -
153 aSumRadius*(aT12*aT14 + aT22*aT24)); //Y
154 theCoef(aLowIndex+33) = 4.0*(aTcol4sq*aTcol3Tcol4 +
155 aSubRadius*aT33*aT34 -
156 aSumRadius*(aT13*aT14 + aT23*aT24)); //Z;
157
158 theCoef(aLowIndex+34) = 2.0*aSubRadius*aT34*aT34 -
159 2.0*aSumRadius*(aT14*aT14 + aT24*aT24) +
160 aTcol4sq*aTcol4sq + aSubRadius*aSubRadius;
7fd59977 161}
162
163void gp_Torus::Mirror (const gp_Pnt& P)
164{ pos.Mirror (P); }
165
166gp_Torus gp_Torus::Mirrored (const gp_Pnt& P) const
167{
168 gp_Torus C = *this;
169 C.pos.Mirror (P);
170 return C;
171}
172
173void gp_Torus::Mirror (const gp_Ax1& A1)
174{ pos.Mirror (A1); }
175
176gp_Torus gp_Torus::Mirrored (const gp_Ax1& A1) const
177{
178 gp_Torus C = *this;
179 C.pos.Mirror (A1);
180 return C;
181}
182
183void gp_Torus::Mirror (const gp_Ax2& A2)
184{ pos.Mirror (A2); }
185
186gp_Torus gp_Torus::Mirrored (const gp_Ax2& A2) const
187{
188 gp_Torus C = *this;
189 C.pos.Mirror (A2);
190 return C;
191}
192
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