[4] | 1 | /************************************************************** ggt-head beg |
---|
| 2 | * |
---|
| 3 | * GGT: Generic Graphics Toolkit |
---|
| 4 | * |
---|
| 5 | * Original Authors: |
---|
| 6 | * Allen Bierbaum |
---|
| 7 | * |
---|
| 8 | * ----------------------------------------------------------------- |
---|
| 9 | * File: GaussPointsFit.h,v |
---|
| 10 | * Date modified: 2002/01/31 01:16:22 |
---|
| 11 | * Version: 1.3 |
---|
| 12 | * ----------------------------------------------------------------- |
---|
| 13 | * |
---|
| 14 | *********************************************************** ggt-head end */ |
---|
| 15 | /*************************************************************** ggt-cpr beg |
---|
| 16 | * |
---|
| 17 | * GGT: The Generic Graphics Toolkit |
---|
| 18 | * Copyright (C) 2001,2002 Allen Bierbaum |
---|
| 19 | * |
---|
| 20 | * This library is free software; you can redistribute it and/or |
---|
| 21 | * modify it under the terms of the GNU Lesser General Public |
---|
| 22 | * License as published by the Free Software Foundation; either |
---|
| 23 | * version 2.1 of the License, or (at your option) any later version. |
---|
| 24 | * |
---|
| 25 | * This library is distributed in the hope that it will be useful, |
---|
| 26 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
---|
| 27 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
---|
| 28 | * Lesser General Public License for more details. |
---|
| 29 | * |
---|
| 30 | * You should have received a copy of the GNU Lesser General Public |
---|
| 31 | * License along with this library; if not, write to the Free Software |
---|
| 32 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
---|
| 33 | * |
---|
| 34 | ************************************************************ ggt-cpr end */ |
---|
| 35 | // Based on code from: |
---|
| 36 | // Magic Software, Inc. |
---|
| 37 | // http://www.magic-software.com |
---|
| 38 | // |
---|
| 39 | #ifndef _GMTL_GAUSSPOINTSFIT_H |
---|
| 40 | #define _GMTL_GAUSSPOINTSFIT_H |
---|
| 41 | |
---|
| 42 | // Fit points with a Gaussian distribution. The center is the mean of the |
---|
| 43 | // points, the axes are the eigenvectors of the covariance matrix, and the |
---|
| 44 | // extents are the eigenvalues of the covariance matrix and are returned in |
---|
| 45 | // increasing order. The last two functions allow selection of valid |
---|
| 46 | // vertices from a pool. The return value is 'true' if and only if at least |
---|
| 47 | // one vertex was valid. |
---|
| 48 | |
---|
| 49 | #include <gmtl/Vec3.h> |
---|
| 50 | #include <gmtl/Point3.h> |
---|
| 51 | #include <gmtl/Numerics/Eigen.h> |
---|
| 52 | |
---|
| 53 | namespace gmtl |
---|
| 54 | { |
---|
| 55 | |
---|
| 56 | /* |
---|
| 57 | void MgcGaussPointsFit (int iQuantity, const MgcVector2* akPoint, |
---|
| 58 | MgcVector2& rkCenter, MgcVector2 akAxis[2], MgcReal afExtent[2]); |
---|
| 59 | */ |
---|
| 60 | |
---|
| 61 | void GaussPointsFit (int iQuantity, const Point3* akPoint, |
---|
| 62 | Point3& rkCenter, Vec3 akAxis[3], float afExtent[3]); |
---|
| 63 | |
---|
| 64 | /* |
---|
| 65 | bool MgcGaussPointsFit (int iQuantity, const MgcVector2* akPoint, |
---|
| 66 | const bool* abValid, MgcVector2& rkCenter, MgcVector2 akAxis[2], |
---|
| 67 | MgcReal afExtent[2]); |
---|
| 68 | */ |
---|
| 69 | |
---|
| 70 | bool GaussPointsFit (int iQuantity, const Vec3* akPoint, |
---|
| 71 | const bool* abValid, Vec3& rkCenter, Vec3 akAxis[3], |
---|
| 72 | float afExtent[3]); |
---|
| 73 | |
---|
| 74 | |
---|
| 75 | // --- Implementations ---- // |
---|
| 76 | void GaussPointsFit (int iQuantity, const Point3* akPoint, |
---|
| 77 | Point3& rkCenter, Vec3 akAxis[3], float afExtent[3]) |
---|
| 78 | { |
---|
| 79 | // compute mean of points |
---|
| 80 | rkCenter = akPoint[0]; |
---|
| 81 | unsigned i; |
---|
| 82 | for (i = 1; i < iQuantity; i++) |
---|
| 83 | rkCenter += akPoint[i]; |
---|
| 84 | float fInvQuantity = 1.0f/iQuantity; |
---|
| 85 | rkCenter *= fInvQuantity; |
---|
| 86 | |
---|
| 87 | // compute covariances of points |
---|
| 88 | float fSumXX = 0.0, fSumXY = 0.0, fSumXZ = 0.0; |
---|
| 89 | float fSumYY = 0.0, fSumYZ = 0.0, fSumZZ = 0.0; |
---|
| 90 | for (i = 0; i < iQuantity; i++) |
---|
| 91 | { |
---|
| 92 | Vec3 kDiff = akPoint[i] - rkCenter; |
---|
| 93 | fSumXX += kDiff[Xelt]*kDiff[Xelt]; |
---|
| 94 | fSumXY += kDiff[Xelt]*kDiff[Yelt]; |
---|
| 95 | fSumXZ += kDiff[Xelt]*kDiff[Zelt]; |
---|
| 96 | fSumYY += kDiff[Yelt]*kDiff[Yelt]; |
---|
| 97 | fSumYZ += kDiff[Yelt]*kDiff[Zelt]; |
---|
| 98 | fSumZZ += kDiff[Zelt]*kDiff[Zelt]; |
---|
| 99 | } |
---|
| 100 | fSumXX *= fInvQuantity; |
---|
| 101 | fSumXY *= fInvQuantity; |
---|
| 102 | fSumXZ *= fInvQuantity; |
---|
| 103 | fSumYY *= fInvQuantity; |
---|
| 104 | fSumYZ *= fInvQuantity; |
---|
| 105 | fSumZZ *= fInvQuantity; |
---|
| 106 | |
---|
| 107 | // compute eigenvectors for covariance matrix |
---|
| 108 | gmtl::Eigen kES(3); |
---|
| 109 | kES.Matrix(0,0) = fSumXX; |
---|
| 110 | kES.Matrix(0,1) = fSumXY; |
---|
| 111 | kES.Matrix(0,2) = fSumXZ; |
---|
| 112 | kES.Matrix(1,0) = fSumXY; |
---|
| 113 | kES.Matrix(1,1) = fSumYY; |
---|
| 114 | kES.Matrix(1,2) = fSumYZ; |
---|
| 115 | kES.Matrix(2,0) = fSumXZ; |
---|
| 116 | kES.Matrix(2,1) = fSumYZ; |
---|
| 117 | kES.Matrix(2,2) = fSumZZ; |
---|
| 118 | kES.IncrSortEigenStuff3(); |
---|
| 119 | |
---|
| 120 | akAxis[0][Xelt] = kES.GetEigenvector(0,0); |
---|
| 121 | akAxis[0][Yelt] = kES.GetEigenvector(1,0); |
---|
| 122 | akAxis[0][Zelt] = kES.GetEigenvector(2,0); |
---|
| 123 | |
---|
| 124 | akAxis[1][Xelt] = kES.GetEigenvector(0,1); |
---|
| 125 | akAxis[1][Yelt] = kES.GetEigenvector(1,1); |
---|
| 126 | akAxis[1][Zelt] = kES.GetEigenvector(2,1); |
---|
| 127 | |
---|
| 128 | akAxis[2][Xelt] = kES.GetEigenvector(0,2); |
---|
| 129 | akAxis[2][Yelt] = kES.GetEigenvector(1,2); |
---|
| 130 | akAxis[2][Zelt] = kES.GetEigenvector(2,2); |
---|
| 131 | |
---|
| 132 | afExtent[0] = kES.GetEigenvalue(0); |
---|
| 133 | afExtent[1] = kES.GetEigenvalue(1); |
---|
| 134 | afExtent[2] = kES.GetEigenvalue(2); |
---|
| 135 | } |
---|
| 136 | |
---|
| 137 | |
---|
| 138 | // |
---|
| 139 | bool GaussPointsFit (int iQuantity, const Vec3* akPoint, |
---|
| 140 | const bool* abValid, Vec3& rkCenter, Vec3 akAxis[3], |
---|
| 141 | float afExtent[3]) |
---|
| 142 | { |
---|
| 143 | // compute mean of points |
---|
| 144 | rkCenter = ZeroVec3; |
---|
| 145 | int i, iValidQuantity = 0; |
---|
| 146 | for (i = 0; i < iQuantity; i++) |
---|
| 147 | { |
---|
| 148 | if ( abValid[i] ) |
---|
| 149 | { |
---|
| 150 | rkCenter += akPoint[i]; |
---|
| 151 | iValidQuantity++; |
---|
| 152 | } |
---|
| 153 | } |
---|
| 154 | if ( iValidQuantity == 0 ) |
---|
| 155 | return false; |
---|
| 156 | |
---|
| 157 | float fInvQuantity = 1.0/iValidQuantity; |
---|
| 158 | rkCenter *= fInvQuantity; |
---|
| 159 | |
---|
| 160 | // compute covariances of points |
---|
| 161 | float fSumXX = 0.0, fSumXY = 0.0, fSumXZ = 0.0; |
---|
| 162 | float fSumYY = 0.0, fSumYZ = 0.0, fSumZZ = 0.0; |
---|
| 163 | for (i = 0; i < iQuantity; i++) |
---|
| 164 | { |
---|
| 165 | if ( abValid[i] ) |
---|
| 166 | { |
---|
| 167 | Vec3 kDiff = akPoint[i] - rkCenter; |
---|
| 168 | fSumXX += kDiff[Xelt]*kDiff[Xelt]; |
---|
| 169 | fSumXY += kDiff[Xelt]*kDiff[Yelt]; |
---|
| 170 | fSumXZ += kDiff[Xelt]*kDiff[Zelt]; |
---|
| 171 | fSumYY += kDiff[Yelt]*kDiff[Yelt]; |
---|
| 172 | fSumYZ += kDiff[Yelt]*kDiff[Zelt]; |
---|
| 173 | fSumZZ += kDiff[Zelt]*kDiff[Zelt]; |
---|
| 174 | } |
---|
| 175 | } |
---|
| 176 | fSumXX *= fInvQuantity; |
---|
| 177 | fSumXY *= fInvQuantity; |
---|
| 178 | fSumXZ *= fInvQuantity; |
---|
| 179 | fSumYY *= fInvQuantity; |
---|
| 180 | fSumYZ *= fInvQuantity; |
---|
| 181 | fSumZZ *= fInvQuantity; |
---|
| 182 | |
---|
| 183 | // compute eigenvectors for covariance matrix |
---|
| 184 | Eigen kES(3); |
---|
| 185 | kES.Matrix(0,0) = fSumXX; |
---|
| 186 | kES.Matrix(0,1) = fSumXY; |
---|
| 187 | kES.Matrix(0,2) = fSumXZ; |
---|
| 188 | kES.Matrix(1,0) = fSumXY; |
---|
| 189 | kES.Matrix(1,1) = fSumYY; |
---|
| 190 | kES.Matrix(1,2) = fSumYZ; |
---|
| 191 | kES.Matrix(2,0) = fSumXZ; |
---|
| 192 | kES.Matrix(2,1) = fSumYZ; |
---|
| 193 | kES.Matrix(2,2) = fSumZZ; |
---|
| 194 | kES.IncrSortEigenStuff3(); |
---|
| 195 | |
---|
| 196 | akAxis[0][Xelt] = kES.GetEigenvector(0,0); |
---|
| 197 | akAxis[0][Yelt] = kES.GetEigenvector(1,0); |
---|
| 198 | akAxis[0][Zelt] = kES.GetEigenvector(2,0); |
---|
| 199 | |
---|
| 200 | akAxis[1][Xelt] = kES.GetEigenvector(0,1); |
---|
| 201 | akAxis[1][Yelt] = kES.GetEigenvector(1,1); |
---|
| 202 | akAxis[1][Zelt] = kES.GetEigenvector(2,1); |
---|
| 203 | |
---|
| 204 | akAxis[2][Xelt] = kES.GetEigenvector(0,2); |
---|
| 205 | akAxis[2][Yelt] = kES.GetEigenvector(1,2); |
---|
| 206 | akAxis[2][Zelt] = kES.GetEigenvector(2,2); |
---|
| 207 | |
---|
| 208 | afExtent[0] = kES.GetEigenvalue(0); |
---|
| 209 | afExtent[1] = kES.GetEigenvalue(1); |
---|
| 210 | afExtent[2] = kES.GetEigenvalue(2); |
---|
| 211 | |
---|
| 212 | return true; |
---|
| 213 | } |
---|
| 214 | |
---|
| 215 | }; |
---|
| 216 | |
---|
| 217 | /* |
---|
| 218 | void MgcGaussPointsFit (int iQuantity, const MgcVector2* akPoint, |
---|
| 219 | MgcVector2& rkCenter, MgcVector2 akAxis[2], float afExtent[2]) |
---|
| 220 | { |
---|
| 221 | // compute mean of points |
---|
| 222 | rkCenter = akPoint[0]; |
---|
| 223 | int i; |
---|
| 224 | for (i = 1; i < iQuantity; i++) |
---|
| 225 | rkCenter += akPoint[i]; |
---|
| 226 | float fInvQuantity = 1.0/iQuantity; |
---|
| 227 | rkCenter *= fInvQuantity; |
---|
| 228 | |
---|
| 229 | // compute covariances of points |
---|
| 230 | float fSumXX = 0.0, fSumXY = 0.0, fSumYY = 0.0; |
---|
| 231 | for (i = 0; i < iQuantity; i++) |
---|
| 232 | { |
---|
| 233 | MgcVector2 kDiff = akPoint[i] - rkCenter; |
---|
| 234 | fSumXX += kDiff.x*kDiff.x; |
---|
| 235 | fSumXY += kDiff.x*kDiff.y; |
---|
| 236 | fSumYY += kDiff.y*kDiff.y; |
---|
| 237 | } |
---|
| 238 | fSumXX *= fInvQuantity; |
---|
| 239 | fSumXY *= fInvQuantity; |
---|
| 240 | fSumYY *= fInvQuantity; |
---|
| 241 | |
---|
| 242 | // solve eigensystem of covariance matrix |
---|
| 243 | MgcEigen kES(2); |
---|
| 244 | kES.Matrix(0,0) = fSumXX; |
---|
| 245 | kES.Matrix(0,1) = fSumXY; |
---|
| 246 | kES.Matrix(1,0) = fSumXY; |
---|
| 247 | kES.Matrix(1,1) = fSumYY; |
---|
| 248 | kES.IncrSortEigenStuff2(); |
---|
| 249 | |
---|
| 250 | akAxis[0].x = kES.GetEigenvector(0,0); |
---|
| 251 | akAxis[0].y = kES.GetEigenvector(1,0); |
---|
| 252 | akAxis[1].x = kES.GetEigenvector(0,1); |
---|
| 253 | akAxis[1].y = kES.GetEigenvector(1,1); |
---|
| 254 | |
---|
| 255 | afExtent[0] = kES.GetEigenvalue(0); |
---|
| 256 | afExtent[1] = kES.GetEigenvalue(1); |
---|
| 257 | } |
---|
| 258 | */ |
---|
| 259 | |
---|
| 260 | |
---|
| 261 | /* |
---|
| 262 | bool MgcGaussPointsFit (int iQuantity, const MgcVector2* akPoint, |
---|
| 263 | const bool* abValid, MgcVector2& rkCenter, MgcVector2 akAxis[2], |
---|
| 264 | float afExtent[2]) |
---|
| 265 | { |
---|
| 266 | // compute mean of points |
---|
| 267 | rkCenter = MgcVector2::ZERO; |
---|
| 268 | int i, iValidQuantity = 0; |
---|
| 269 | for (i = 0; i < iQuantity; i++) |
---|
| 270 | { |
---|
| 271 | if ( abValid[i] ) |
---|
| 272 | { |
---|
| 273 | rkCenter += akPoint[i]; |
---|
| 274 | iValidQuantity++; |
---|
| 275 | } |
---|
| 276 | } |
---|
| 277 | if ( iValidQuantity == 0 ) |
---|
| 278 | return false; |
---|
| 279 | |
---|
| 280 | float fInvQuantity = 1.0/iValidQuantity; |
---|
| 281 | rkCenter *= fInvQuantity; |
---|
| 282 | |
---|
| 283 | // compute covariances of points |
---|
| 284 | float fSumXX = 0.0, fSumXY = 0.0, fSumYY = 0.0; |
---|
| 285 | for (i = 0; i < iQuantity; i++) |
---|
| 286 | { |
---|
| 287 | if ( abValid[i] ) |
---|
| 288 | { |
---|
| 289 | MgcVector2 kDiff = akPoint[i] - rkCenter; |
---|
| 290 | fSumXX += kDiff.x*kDiff.x; |
---|
| 291 | fSumXY += kDiff.x*kDiff.y; |
---|
| 292 | fSumYY += kDiff.y*kDiff.y; |
---|
| 293 | } |
---|
| 294 | } |
---|
| 295 | fSumXX *= fInvQuantity; |
---|
| 296 | fSumXY *= fInvQuantity; |
---|
| 297 | fSumYY *= fInvQuantity; |
---|
| 298 | |
---|
| 299 | // solve eigensystem of covariance matrix |
---|
| 300 | MgcEigen kES(2); |
---|
| 301 | kES.Matrix(0,0) = fSumXX; |
---|
| 302 | kES.Matrix(0,1) = fSumXY; |
---|
| 303 | kES.Matrix(1,0) = fSumXY; |
---|
| 304 | kES.Matrix(1,1) = fSumYY; |
---|
| 305 | kES.IncrSortEigenStuff2(); |
---|
| 306 | |
---|
| 307 | akAxis[0].x = kES.GetEigenvector(0,0); |
---|
| 308 | akAxis[0].y = kES.GetEigenvector(1,0); |
---|
| 309 | akAxis[1].x = kES.GetEigenvector(0,1); |
---|
| 310 | akAxis[1].y = kES.GetEigenvector(1,1); |
---|
| 311 | |
---|
| 312 | afExtent[0] = kES.GetEigenvalue(0); |
---|
| 313 | afExtent[1] = kES.GetEigenvalue(1); |
---|
| 314 | |
---|
| 315 | return true; |
---|
| 316 | } |
---|
| 317 | */ |
---|
| 318 | |
---|
| 319 | #endif |
---|