| Geant4 Cross Reference |
1 // -*- C++ -*- 1
2 // -------------------------------------------
3 //
4 // This file is a part of the CLHEP - a Class
5 //
6 // Hep geometrical 3D Transformation library
7 //
8 // Author: Evgeni Chernyaev <Evgueni.Tcherniae
9 //
10 // History:
11 // 24.09.96 E.Chernyaev - initial version
12
13 #include <iostream>
14 #include <cmath> // double std::abs()
15 #include "CLHEP/Geometry/Transform3D.h"
16
17 namespace HepGeom {
18
19 const Transform3D Transform3D::Identity = Tr
20
21 // T R A N S F O R M A T I O N -----------
22
23 double Transform3D::operator () (int i, int
24 if (i == 0) {
25 if (j == 0) { return xx_; }
26 if (j == 1) { return xy_; }
27 if (j == 2) { return xz_; }
28 if (j == 3) { return dx_; }
29 } else if (i == 1) {
30 if (j == 0) { return yx_; }
31 if (j == 1) { return yy_; }
32 if (j == 2) { return yz_; }
33 if (j == 3) { return dy_; }
34 } else if (i == 2) {
35 if (j == 0) { return zx_; }
36 if (j == 1) { return zy_; }
37 if (j == 2) { return zz_; }
38 if (j == 3) { return dz_; }
39 } else if (i == 3) {
40 if (j == 0) { return 0.0; }
41 if (j == 1) { return 0.0; }
42 if (j == 2) { return 0.0; }
43 if (j == 3) { return 1.0; }
44 }
45 std::cerr << "Transform3D subscripting: ba
46 << "(" << i << "," << j << ")" << std:
47 return 0.0;
48 }
49
50 //------------------------------------------
51 Transform3D Transform3D::operator*(const Tra
52 return Transform3D
53 (xx_*b.xx_+xy_*b.yx_+xz_*b.zx_, xx_*b.xy
54 xx_*b.xz_+xy_*b.yz_+xz_*b.zz_, xx_*b.dx
55 yx_*b.xx_+yy_*b.yx_+yz_*b.zx_, yx_*b.xy
56 yx_*b.xz_+yy_*b.yz_+yz_*b.zz_, yx_*b.dx
57 zx_*b.xx_+zy_*b.yx_+zz_*b.zx_, zx_*b.xy
58 zx_*b.xz_+zy_*b.yz_+zz_*b.zz_, zx_*b.dx
59 }
60
61 // -----------------------------------------
62 Transform3D::Transform3D(const Point3D<doubl
63 const Point3D<double> & fr1,
64 const Point3D<double> & fr2,
65 const Point3D<double> & to0,
66 const Point3D<double> & to1,
67 const Point3D<double> & to2)
68 /*******************************************
69 *
70 * Name: Transform3D::Transform3D
71 * Author: E.Chernyaev (IHEP/Protvino)
72 *
73 * Function: Create 3D Transformation from o
74 * defined by its origin "fr0" and
75 * "fr0->fr2" to another coordinat
76 * and "to0->to2"
77 *
78 *******************************************
79 {
80 Vector3D<double> x1,y1,z1, x2,y2,z2;
81 x1 = (fr1 - fr0).unit();
82 y1 = (fr2 - fr0).unit();
83 x2 = (to1 - to0).unit();
84 y2 = (to2 - to0).unit();
85
86 // C H E C K A N G L E S
87
88 double cos1, cos2;
89 cos1 = x1*y1;
90 cos2 = x2*y2;
91
92 if (std::abs(1.0-cos1) <= 0.000001 || std:
93 std::cerr << "Transform3D: zero angle be
94 setIdentity();
95 }else{
96 if (std::abs(cos1-cos2) > 0.000001) {
97 std::cerr << "Transform3D: angles between ax
98 << std::endl;
99 }
100
101 // F I N D R O T A T I O N M A T R
102
103 z1 = (x1.cross(y1)).unit();
104 y1 = z1.cross(x1);
105
106 z2 = (x2.cross(y2)).unit();
107 y2 = z2.cross(x2);
108
109 double detxx = (y1.y()*z1.z() - z1.y()*
110 double detxy = -(y1.x()*z1.z() - z1.x()*
111 double detxz = (y1.x()*z1.y() - z1.x()*
112 double detyx = -(x1.y()*z1.z() - z1.y()*
113 double detyy = (x1.x()*z1.z() - z1.x()*
114 double detyz = -(x1.x()*z1.y() - z1.x()*
115 double detzx = (x1.y()*y1.z() - y1.y()*
116 double detzy = -(x1.x()*y1.z() - y1.x()*
117 double detzz = (x1.x()*y1.y() - y1.x()*
118
119 double txx = x2.x()*detxx + y2.x()*detyx
120 double txy = x2.x()*detxy + y2.x()*detyy
121 double txz = x2.x()*detxz + y2.x()*detyz
122 double tyx = x2.y()*detxx + y2.y()*detyx
123 double tyy = x2.y()*detxy + y2.y()*detyy
124 double tyz = x2.y()*detxz + y2.y()*detyz
125 double tzx = x2.z()*detxx + y2.z()*detyx
126 double tzy = x2.z()*detxy + y2.z()*detyy
127 double tzz = x2.z()*detxz + y2.z()*detyz
128
129 // S E T T R A N S F O R M A T I O
130
131 double dx1 = fr0.x(), dy1 = fr0.y(), dz1
132 double dx2 = to0.x(), dy2 = to0.y(), dz2
133
134 setTransform(txx, txy, txz, dx2-txx*dx1-
135 tyx, tyy, tyz, dy2-tyx*dx1-tyy*dy1-tyz*
136 tzx, tzy, tzz, dz2-tzx*dx1-tzy*dy1-tzz*
137 }
138 }
139
140 // -----------------------------------------
141 Transform3D Transform3D::inverse() const
142 /*******************************************
143 *
144 * Name: Transform3D::inverse
145 * Author: E.Chernyaev (IHEP/Protvino)
146 *
147 * Function: Find inverse affine transformat
148 *
149 *******************************************
150 {
151 double detxx = yy_*zz_-yz_*zy_;
152 double detxy = yx_*zz_-yz_*zx_;
153 double detxz = yx_*zy_-yy_*zx_;
154 double det = xx_*detxx - xy_*detxy + xz_
155 if (det == 0) {
156 std::cerr << "Transform3D::inverse error
157 return Transform3D();
158 }
159 det = 1./det; detxx *= det; detxy *= det;
160 double detyx = (xy_*zz_ - xz_*zy_)*det;
161 double detyy = (xx_*zz_ - xz_*zx_)*det;
162 double detyz = (xx_*zy_ - xy_*zx_)*det;
163 double detzx = (xy_*yz_ - xz_*yy_)*det;
164 double detzy = (xx_*yz_ - xz_*yx_)*det;
165 double detzz = (xx_*yy_ - xy_*yx_)*det;
166 return Transform3D
167 (detxx, -detyx, detzx, -detxx*dx_+detyx
168 -detxy, detyy, -detzy, detxy*dx_-detyy
169 detxz, -detyz, detzz, -detxz*dx_+detyz
170 }
171
172 // -----------------------------------------
173 void Transform3D::getDecomposition(Scale3D &
174 Rotate3D & rotation,
175 Translate3D & translation) const
176 /*******************************************
177 *
178 * Name: Transform3D::getDecomposition
179 * Author: E.Chernyaev (IHEP/Protvino)
180 *
181 * Function: Gets decomposition of general t
182 * three consequentive specific tr
183 * Scale, then Rotation, then Tran
184 * If there was a reflection, then
185 *
186 *******************************************
187 {
188 double sx = std::sqrt(xx_*xx_ + yx_*yx_ +
189 double sy = std::sqrt(xy_*xy_ + yy_*yy_ +
190 double sz = std::sqrt(xz_*xz_ + yz_*yz_ +
191
192 if (xx_*(yy_*zz_-yz_*zy_) -
193 xy_*(yx_*zz_-yz_*zx_) +
194 xz_*(yx_*zy_-yy_*zx_) < 0) sz = -sz;
195 scale.setTransform(sx,0,0,0, 0,sy,0,0, 0,
196 rotation.setTransform(xx_/sx,xy_/sy,xz_/sz
197 yx_/sx,yy_/sy,yz_/sz,0,
198 zx_/sx,zy_/sy,zz_/sz,0);
199 translation.setTransform(1,0,0,dx_, 0,1,0,
200 }
201
202 // -----------------------------------------
203 bool Transform3D::isNear(const Transform3D &
204 {
205 return ( (std::abs(xx_ - t.xx_) <= toleran
206 (std::abs(xy_ - t.xy_) <= tolerance) &&
207 (std::abs(xz_ - t.xz_) <= tolerance) &&
208 (std::abs(dx_ - t.dx_) <= tolerance) &&
209 (std::abs(yx_ - t.yx_) <= tolerance) &&
210 (std::abs(yy_ - t.yy_) <= tolerance) &&
211 (std::abs(yz_ - t.yz_) <= tolerance) &&
212 (std::abs(dy_ - t.dy_) <= tolerance) &&
213 (std::abs(zx_ - t.zx_) <= tolerance) &&
214 (std::abs(zy_ - t.zy_) <= tolerance) &&
215 (std::abs(zz_ - t.zz_) <= tolerance) &&
216 (std::abs(dz_ - t.dz_) <= tolerance) );
217 }
218
219 // -----------------------------------------
220 bool Transform3D::operator==(const Transform
221 {
222 return (this == &t) ? true :
223 (xx_==t.xx_ && xy_==t.xy_ && xz_==t.xz_
224 yx_==t.yx_ && yy_==t.yy_ && yz_==t.yz_
225 zx_==t.zx_ && zy_==t.zy_ && zz_==t.zz_
226 }
227
228 // 3 D R O T A T I O N -----------------
229
230 Rotate3D::Rotate3D(double a,
231 const Point3D<double> & p1,
232 const Point3D<double> & p2) : Transfo
233 /*******************************************
234 *
235 * Name: Rotate3D::Rotate3D
236 * Author: E.Chernyaev (IHEP/Protvino)
237 *
238 * Function: Create 3D Rotation through angl
239 * around the axis p1->p2
240 *
241 *******************************************
242 {
243 if (a == 0) return;
244
245 double cx = p2.x()-p1.x(), cy = p2.y()-p1.
246 double ll = std::sqrt(cx*cx + cy*cy + cz*c
247 if (ll == 0) {
248 std::cerr << "Rotate3D: zero axis" << st
249 }else{
250 double cosa = std::cos(a), sina = std::s
251 cx /= ll; cy /= ll; cz /= ll;
252
253 double txx = cosa + (1-cosa)*cx*cx;
254 double txy = (1-cosa)*cx*cy - sin
255 double txz = (1-cosa)*cx*cz + sin
256
257 double tyx = (1-cosa)*cy*cx + sin
258 double tyy = cosa + (1-cosa)*cy*cy;
259 double tyz = (1-cosa)*cy*cz - sin
260
261 double tzx = (1-cosa)*cz*cx - sin
262 double tzy = (1-cosa)*cz*cy + sin
263 double tzz = cosa + (1-cosa)*cz*cz;
264
265 double tdx = p1.x(), tdy = p1.y(), tdz =
266
267 setTransform(txx, txy, txz, tdx-txx*tdx-
268 tyx, tyy, tyz, tdy-tyx*tdx-tyy*tdy-tyz*
269 tzx, tzy, tzz, tdz-tzx*tdx-tzy*tdy-tzz*
270 }
271 }
272
273 // 3 D R E F L E C T I O N -------------
274
275 Reflect3D::Reflect3D(double a, double b, dou
276 /*******************************************
277 *
278 * Name: Reflect3D::Reflect3D
279 * Author: E.Chernyaev (IHEP/Protvino)
280 *
281 * Function: Create 3D Reflection in a plane
282 *
283 *******************************************
284 {
285 double ll = a*a+b*b+c*c;
286 if (ll == 0) {
287 std::cerr << "Reflect3D: zero normal" <<
288 setIdentity();
289 }else{
290 ll = 1/ll;
291 double aa = a*a*ll, ab = a*b*ll, ac = a*
292 bb = b*b*ll, bc = b*c*ll, bd = b*d*ll,
293 cc = c*c*ll, cd = c*d*ll;
294 setTransform(-aa+bb+cc, -ab-ab, -ac-a
295 -ab-ab, aa-bb+cc, -bc-bc, -bd-bd
296 -ac-ac, -bc-bc, aa+bb-cc, -cd-cd
297 }
298 }
299 } /* namespace HepGeom */
300