包括兩種計算方法：精確計算和近似計算（思考：local density=單位面積的點數 vs  local density =1/單個點所佔的面積）

每種方法可以實現三種模式的點雲密度計算，CC裡面的點雲端計算依賴於 給定的近鄰半徑所對應的最佳八叉樹層級 （通過findBestLevelForAGivenNeighbourhoodSizeExtraction()方法實現）

在GeometricalAnalysisTools類檔案中實現。

//volume of a unit sphere
static double s_UnitSphereVolume = 4.0 * M_PI / 3.0
 
;

 1.精確計算

 1 int GeometricalAnalysisTools::computeLocalDensity(    GenericIndexedCloudPersist* theCloud,
 2                                                     Density densityType,
 3                                                     PointCoordinateType kernelRadius,
 4                                                     GenericProgressCallback* progressCb/*
 
=0*/,
 5                                                     DgmOctree* inputOctree/*=0*/)
 6 {
 7     if (!theCloud)
 8         return -1;
 9 
10     unsigned numberOfPoints = theCloud->size();
11     if (numberOfPoints < 3)
12         return -2;
13 
14     //compute the right dimensional coef based on the expected output
 

15     double dimensionalCoef = 1.0;
16     switch (densityType)
17     {
18     case DENSITY_KNN:
19         dimensionalCoef = 1.0;
20         break;
21     case DENSITY_2D:
22         dimensionalCoef = M_PI * (static_cast<double>(kernelRadius) * kernelRadius);
23         break;
24     case DENSITY_3D:
25         dimensionalCoef = s_UnitSphereVolume * ((static_cast<double>(kernelRadius) * kernelRadius) * kernelRadius);
26         break;
27     default:
28         assert(false);
29         return -5;
30     }
31 
32     DgmOctree* theOctree = inputOctree;
33     if (!theOctree)
34     {
35         theOctree = new DgmOctree(theCloud);
36         if (theOctree->build(progressCb) < 1)
37         {
38             delete theOctree;
39             return -3;
40         }
41     }
42 
43     theCloud->enableScalarField();
44 
45     //determine best octree level to perform the computation
46     unsigned char level = theOctree->findBestLevelForAGivenNeighbourhoodSizeExtraction(kernelRadius);
47 
48     //parameters
49     void* additionalParameters[] = {    static_cast<void*>(&kernelRadius),
50                                         static_cast<void*>(&dimensionalCoef) };
51 
52     int result = 0;
53 
54     if (theOctree->executeFunctionForAllCellsAtLevel(    level,
55                                                         &computePointsDensityInACellAtLevel,
56                                                         additionalParameters,
57                                                         true,
58                                                         progressCb,
59                                                         "Local Density Computation") == 0)
60     {
61         //something went wrong
62         result = -4;
63     }
64 
65     if (!inputOctree)
66         delete theOctree;
67 
68     return result;
69 }

 1 //"PER-CELL" METHOD: LOCAL DENSITY
 2 //ADDITIONNAL PARAMETERS (2):
 3 // [0] -> (PointCoordinateType*) kernelRadius : spherical neighborhood radius
 4 // [1] -> (ScalarType*) sphereVolume : spherical neighborhood volume
 5 bool GeometricalAnalysisTools::computePointsDensityInACellAtLevel(    const DgmOctree::octreeCell& cell, 
 6                                                                     void** additionalParameters,
 7                                                                     NormalizedProgress* nProgress/*=0*/)
 8 {
 9     //parameter(s)
10     PointCoordinateType radius = *static_cast<PointCoordinateType*>(additionalParameters[0]);
11     double dimensionalCoef = *static_cast<double*>(additionalParameters[1]);
12     
13     assert(dimensionalCoef > 0);
14 
15     //structure for nearest neighbors search
16     DgmOctree::NearestNeighboursSphericalSearchStruct nNSS;
17     nNSS.level = cell.level;
18     nNSS.prepare(radius,cell.parentOctree->getCellSize(nNSS.level));
19     cell.parentOctree->getCellPos(cell.truncatedCode,cell.level,nNSS.cellPos,true);
20     cell.parentOctree->computeCellCenter(nNSS.cellPos,cell.level,nNSS.cellCenter);
21 
22     unsigned n = cell.points->size(); //number of points in the current cell
23     
24     //for each point in the cell
25     for (unsigned i=0; i<n; ++i)
26     {
27         cell.points->getPoint(i,nNSS.queryPoint);
28 
29         //look for neighbors inside a sphere
30         //warning: there may be more points at the end of nNSS.pointsInNeighbourhood than the actual nearest neighbors (neighborCount)!
31         unsigned neighborCount = cell.parentOctree->findNeighborsInASphereStartingFromCell(nNSS,radius,false);
32         //數目/體積
33         ScalarType density = static_cast<ScalarType>(neighborCount/dimensionalCoef);
34         cell.points->setPointScalarValue(i,density);
35 
36         if (nProgress && !nProgress->oneStep())
37         {
38             return false;
39         }
40     }
41 
42     return true;
43 }

 2. 近似計算

 1 int GeometricalAnalysisTools::computeLocalDensityApprox(GenericIndexedCloudPersist* theCloud,
 2                                                         Density densityType,
 3                                                         GenericProgressCallback* progressCb/*=0*/,
 4                                                         DgmOctree* inputOctree/*=0*/)
 5 {
 6     if (!theCloud)
 7         return -1;
 8 
 9     unsigned numberOfPoints = theCloud->size();
10     if (numberOfPoints < 3)
11         return -2;
12 
13     DgmOctree* theOctree = inputOctree;
14     if (!theOctree)
15     {
16         theOctree = new DgmOctree(theCloud);
17         if (theOctree->build(progressCb) < 1)
18         {
19             delete theOctree;
20             return -3;
21         }
22     }
23 
24     theCloud->enableScalarField();
25 
26     //determine best octree level to perform the computation
27     unsigned char level = theOctree->findBestLevelForAGivenPopulationPerCell(3);
28 
29     //parameters
30     void* additionalParameters[] = { static_cast<void*>(&densityType) };
31 
32     int result = 0;
33 
34     if (theOctree->executeFunctionForAllCellsAtLevel(    level,
35                                                         &computeApproxPointsDensityInACellAtLevel,
36                                                         additionalParameters,
37                                                         true,
38                                                         progressCb,
39                                                         "Approximate Local Density Computation") == 0)
40     {
41         //something went wrong
42         result = -4;
43     }
44 
45     if (!inputOctree)
46         delete theOctree;
47 
48     return result;
49 }

 1 //"PER-CELL" METHOD: APPROXIMATE LOCAL DENSITY
 2 //ADDITIONAL PARAMETERS (0): NONE
 3 bool GeometricalAnalysisTools::computeApproxPointsDensityInACellAtLevel(const DgmOctree::octreeCell& cell,
 4                                                                         void** additionalParameters,
 5                                                                         NormalizedProgress* nProgress/*=0*/)
 6 {
 7     //extract additional parameter(s)
 8     Density densityType = *static_cast<Density*>(additionalParameters[0]);
 9     
10     DgmOctree::NearestNeighboursSearchStruct nNSS;
11     nNSS.level                                = cell.level;
12     nNSS.alreadyVisitedNeighbourhoodSize    = 0;
13     nNSS.minNumberOfNeighbors                = 2;
14     cell.parentOctree->getCellPos(cell.truncatedCode,cell.level,nNSS.cellPos,true);
15     cell.parentOctree->computeCellCenter(nNSS.cellPos,cell.level,nNSS.cellCenter);
16 
17     unsigned n = cell.points->size();
18     for (unsigned i=0; i<n; ++i)
19     {
20         cell.points->getPoint(i,nNSS.queryPoint);
21 
22         //the first point is always the point itself!
23         if (cell.parentOctree->findNearestNeighborsStartingFromCell(nNSS) > 1)
24         {
25             double R2 = nNSS.pointsInNeighbourhood[1].squareDistd;
26 
27             ScalarType density = NAN_VALUE;
28             if (R2 > ZERO_TOLERANCE)
29             {
30                 switch (densityType)
31                 {
32                 case DENSITY_KNN:
33                     {
34                         //we return in fact the (inverse) distance to the nearest neighbor
35                         density = static_cast<ScalarType>(1.0 / sqrt(R2));
36                     }
37                     break;
38                 case DENSITY_2D:
39                     {
40                         //circle area (2D approximation)
41                         double circleArea = M_PI * R2;
42                         density = static_cast<ScalarType>(1.0 / circleArea);
43                     }
44                     break;
45                 case DENSITY_3D:
46                     {
47                         //sphere area
48                         double sphereArea =  s_UnitSphereVolume * R2 * sqrt(R2);
49                         density = static_cast<ScalarType>(1.0 / sphereArea);
50                     }
51                     break;
52                 default:
53                     assert(false);
54                     break;
55                 }
56             }
57             cell.points->setPointScalarValue(i,density);
58         }
59         else
60         {
61             //shouldn't happen! Apart if the cloud has only one point...
62             cell.points->setPointScalarValue(i,NAN_VALUE);
63         }
64 
65         if (nProgress && !nProgress->oneStep())
66         {
67             return false;
68         }
69     }
70 
71     return true;
72 }

 double R2 = nNSS.pointsInNeighbourhood[1].squareDistd;  //索引為1的點，表示最近鄰點。pi點與最近鄰點之間距離的平方。