Geant4 11.2.2
Toolkit for the simulation of the passage of particles through matter
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Transform3D.cc
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1// -*- C++ -*-
2// ---------------------------------------------------------------------------
3//
4// This file is a part of the CLHEP - a Class Library for High Energy Physics.
5//
6// Hep geometrical 3D Transformation library
7//
8// Author: Evgeni Chernyaev <[email protected]>
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
17namespace HepGeom {
18
19 const Transform3D Transform3D::Identity = Transform3D ();
20
21 // T R A N S F O R M A T I O N -------------------------------------------
22
23 double Transform3D::operator () (int i, int j) const {
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: bad indices "
46 << "(" << i << "," << j << ")" << std::endl;
47 return 0.0;
48 }
49
50 //--------------------------------------------------------------------------
51 Transform3D Transform3D::operator*(const Transform3D & b) const {
52 return Transform3D
53 (xx_*b.xx_+xy_*b.yx_+xz_*b.zx_, xx_*b.xy_+xy_*b.yy_+xz_*b.zy_,
54 xx_*b.xz_+xy_*b.yz_+xz_*b.zz_, xx_*b.dx_+xy_*b.dy_+xz_*b.dz_+dx_,
55 yx_*b.xx_+yy_*b.yx_+yz_*b.zx_, yx_*b.xy_+yy_*b.yy_+yz_*b.zy_,
56 yx_*b.xz_+yy_*b.yz_+yz_*b.zz_, yx_*b.dx_+yy_*b.dy_+yz_*b.dz_+dy_,
57 zx_*b.xx_+zy_*b.yx_+zz_*b.zx_, zx_*b.xy_+zy_*b.yy_+zz_*b.zy_,
58 zx_*b.xz_+zy_*b.yz_+zz_*b.zz_, zx_*b.dx_+zy_*b.dy_+zz_*b.dz_+dz_);
59 }
60
61 // -------------------------------------------------------------------------
62 Transform3D::Transform3D(const Point3D<double> & fr0,
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 Date: 24.09.96 *
71 * Author: E.Chernyaev (IHEP/Protvino) Revised: *
72 * *
73 * Function: Create 3D Transformation from one coordinate system *
74 * defined by its origin "fr0" and two axes "fr0->fr1", *
75 * "fr0->fr2" to another coordinate system "to0", "to0->to1" *
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::abs(1.0-cos2) <= 0.000001) {
93 std::cerr << "Transform3D: zero angle between axes" << std::endl;
94 setIdentity();
95 }else{
96 if (std::abs(cos1-cos2) > 0.000001) {
97 std::cerr << "Transform3D: angles between axes are not equal"
98 << std::endl;
99 }
100
101 // F I N D R O T A T I O N M A T R I X
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()*y1.z());
110 double detxy = -(y1.x()*z1.z() - z1.x()*y1.z());
111 double detxz = (y1.x()*z1.y() - z1.x()*y1.y());
112 double detyx = -(x1.y()*z1.z() - z1.y()*x1.z());
113 double detyy = (x1.x()*z1.z() - z1.x()*x1.z());
114 double detyz = -(x1.x()*z1.y() - z1.x()*x1.y());
115 double detzx = (x1.y()*y1.z() - y1.y()*x1.z());
116 double detzy = -(x1.x()*y1.z() - y1.x()*x1.z());
117 double detzz = (x1.x()*y1.y() - y1.x()*x1.y());
118
119 double txx = x2.x()*detxx + y2.x()*detyx + z2.x()*detzx;
120 double txy = x2.x()*detxy + y2.x()*detyy + z2.x()*detzy;
121 double txz = x2.x()*detxz + y2.x()*detyz + z2.x()*detzz;
122 double tyx = x2.y()*detxx + y2.y()*detyx + z2.y()*detzx;
123 double tyy = x2.y()*detxy + y2.y()*detyy + z2.y()*detzy;
124 double tyz = x2.y()*detxz + y2.y()*detyz + z2.y()*detzz;
125 double tzx = x2.z()*detxx + y2.z()*detyx + z2.z()*detzx;
126 double tzy = x2.z()*detxy + y2.z()*detyy + z2.z()*detzy;
127 double tzz = x2.z()*detxz + y2.z()*detyz + z2.z()*detzz;
128
129 // S E T T R A N S F O R M A T I O N
130
131 double dx1 = fr0.x(), dy1 = fr0.y(), dz1 = fr0.z();
132 double dx2 = to0.x(), dy2 = to0.y(), dz2 = to0.z();
133
134 setTransform(txx, txy, txz, dx2-txx*dx1-txy*dy1-txz*dz1,
135 tyx, tyy, tyz, dy2-tyx*dx1-tyy*dy1-tyz*dz1,
136 tzx, tzy, tzz, dz2-tzx*dx1-tzy*dy1-tzz*dz1);
137 }
138 }
139
140 // -------------------------------------------------------------------------
141 Transform3D Transform3D::inverse() const
142 /***********************************************************************
143 * *
144 * Name: Transform3D::inverse Date: 24.09.96 *
145 * Author: E.Chernyaev (IHEP/Protvino) Revised: *
146 * *
147 * Function: Find inverse affine transformation *
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_*detxz;
155 if (det == 0) {
156 std::cerr << "Transform3D::inverse error: zero determinant" << std::endl;
157 return Transform3D();
158 }
159 det = 1./det; detxx *= det; detxy *= det; detxz *= 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*dy_-detzx*dz_,
168 -detxy, detyy, -detzy, detxy*dx_-detyy*dy_+detzy*dz_,
169 detxz, -detyz, detzz, -detxz*dx_+detyz*dy_-detzz*dz_);
170 }
171
172 // -------------------------------------------------------------------------
173 void Transform3D::getDecomposition(Scale3D & scale,
174 Rotate3D & rotation,
175 Translate3D & translation) const
176 /***********************************************************************
177 * CLHEP-1.7 *
178 * Name: Transform3D::getDecomposition Date: 09.06.01 *
179 * Author: E.Chernyaev (IHEP/Protvino) Revised: *
180 * *
181 * Function: Gets decomposition of general transformation on *
182 * three consequentive specific transformations: *
183 * Scale, then Rotation, then Translation. *
184 * If there was a reflection, then ScaleZ will be negative. *
185 * *
186 ***********************************************************************/
187 {
188 double sx = std::sqrt(xx_*xx_ + yx_*yx_ + zx_*zx_);
189 double sy = std::sqrt(xy_*xy_ + yy_*yy_ + zy_*zy_);
190 double sz = std::sqrt(xz_*xz_ + yz_*yz_ + zz_*zz_);
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, 0,0,sz,0);
196 rotation.setTransform(xx_/sx,xy_/sy,xz_/sz,0,
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,dy_, 0,0,1,dz_);
200 }
201
202 // -------------------------------------------------------------------------
203 bool Transform3D::isNear(const Transform3D & t, double tolerance) const
204 {
205 return ( (std::abs(xx_ - t.xx_) <= tolerance) &&
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 Transform3D & t) const
221 {
222 return (this == &t) ? true :
223 (xx_==t.xx_ && xy_==t.xy_ && xz_==t.xz_ && dx_==t.dx_ &&
224 yx_==t.yx_ && yy_==t.yy_ && yz_==t.yz_ && dy_==t.dy_ &&
225 zx_==t.zx_ && zy_==t.zy_ && zz_==t.zz_ && dz_==t.dz_ );
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) : Transform3D()
233 /***********************************************************************
234 * *
235 * Name: Rotate3D::Rotate3D Date: 24.09.96 *
236 * Author: E.Chernyaev (IHEP/Protvino) Revised: *
237 * *
238 * Function: Create 3D Rotation through angle "a" (counterclockwise) *
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.y(), cz = p2.z()-p1.z();
246 double ll = std::sqrt(cx*cx + cy*cy + cz*cz);
247 if (ll == 0) {
248 std::cerr << "Rotate3D: zero axis" << std::endl;
249 }else{
250 double cosa = std::cos(a), sina = std::sin(a);
251 cx /= ll; cy /= ll; cz /= ll;
252
253 double txx = cosa + (1-cosa)*cx*cx;
254 double txy = (1-cosa)*cx*cy - sina*cz;
255 double txz = (1-cosa)*cx*cz + sina*cy;
256
257 double tyx = (1-cosa)*cy*cx + sina*cz;
258 double tyy = cosa + (1-cosa)*cy*cy;
259 double tyz = (1-cosa)*cy*cz - sina*cx;
260
261 double tzx = (1-cosa)*cz*cx - sina*cy;
262 double tzy = (1-cosa)*cz*cy + sina*cx;
263 double tzz = cosa + (1-cosa)*cz*cz;
264
265 double tdx = p1.x(), tdy = p1.y(), tdz = p1.z();
266
267 setTransform(txx, txy, txz, tdx-txx*tdx-txy*tdy-txz*tdz,
268 tyx, tyy, tyz, tdy-tyx*tdx-tyy*tdy-tyz*tdz,
269 tzx, tzy, tzz, tdz-tzx*tdx-tzy*tdy-tzz*tdz);
270 }
271 }
272
273 // 3 D R E F L E C T I O N ---------------------------------------------
274
275 Reflect3D::Reflect3D(double a, double b, double c, double d)
276 /***********************************************************************
277 * *
278 * Name: Reflect3D::Reflect3D Date: 24.09.96 *
279 * Author: E.Chernyaev (IHEP/Protvino) Revised: *
280 * *
281 * Function: Create 3D Reflection in a plane a*x + b*y + c*z + d = 0 *
282 * *
283 ***********************************************************************/
284 {
285 double ll = a*a+b*b+c*c;
286 if (ll == 0) {
287 std::cerr << "Reflect3D: zero normal" << std::endl;
288 setIdentity();
289 }else{
290 ll = 1/ll;
291 double aa = a*a*ll, ab = a*b*ll, ac = a*c*ll, ad = a*d*ll,
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-ac, -ad-ad,
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 */
HepGeom::BasicVector3D::cross
BasicVector3D< T > cross(const BasicVector3D< T > &v) const
Definition BasicVector3D.h:281
HepGeom::BasicVector3D::unit
BasicVector3D< T > unit() const
Definition BasicVector3D.h:310
HepGeom::Transform3D::operator()
double operator()(int, int) const
Definition Transform3D.cc:23
HepGeom::Transform3D::Identity
static DLL_API const Transform3D Identity
Definition Transform3D.h:196
HepGeom::Transform3D::isNear
bool isNear(const Transform3D &t, double tolerance=2.2E-14) const
Definition Transform3D.cc:203
HepGeom::Transform3D::operator*
Transform3D operator*(const Transform3D &b) const
Definition Transform3D.cc:51
HepGeom::Transform3D::operator==
bool operator==(const Transform3D &transform) const
Definition Transform3D.cc:220
HepGeom::Transform3D::getDecomposition
void getDecomposition(Scale3D &scale, Rotate3D &rotation, Translate3D &translation) const
Definition Transform3D.cc:173
HepGeom::Transform3D::setTransform
void setTransform(double XX, double XY, double XZ, double DX, double YX, double YY, double YZ, double DY, double ZX, double ZY, double ZZ, double DZ)
Definition Transform3D.h:185
HepGeom::Transform3D::inverse
Transform3D inverse() const
Definition Transform3D.cc:141