[688] | 1 | #include "intersection_ym.hpp" |
---|
| 2 | #include "elt.hpp" |
---|
| 3 | #include "clipper.hpp" |
---|
| 4 | #include "gridRemap.hpp" |
---|
| 5 | #include "triple.hpp" |
---|
| 6 | #include "polyg.hpp" |
---|
| 7 | #include <vector> |
---|
| 8 | #include <stdlib.h> |
---|
| 9 | #include <limits> |
---|
| 10 | |
---|
| 11 | #define epsilon 1e-3 // epsilon distance ratio over side lenght for approximate small circle by great circle |
---|
| 12 | #define fusion_vertex 1e-13 |
---|
| 13 | |
---|
| 14 | namespace sphereRemap { |
---|
| 15 | |
---|
| 16 | using namespace std; |
---|
| 17 | using namespace ClipperLib ; |
---|
| 18 | |
---|
| 19 | double intersect_ym(Elt *a, Elt *b) |
---|
| 20 | { |
---|
| 21 | |
---|
| 22 | // transform small circle into piece of great circle if necessary |
---|
| 23 | |
---|
| 24 | vector<Coord> srcPolygon ; |
---|
| 25 | createGreatCirclePolygon(*b, srcGrid.pole, srcPolygon) ; |
---|
| 26 | vector<Coord> dstPolygon ; |
---|
| 27 | createGreatCirclePolygon(*a, tgtGrid.pole, dstPolygon) ; |
---|
| 28 | |
---|
| 29 | // compute coordinates of the polygons into the gnomonique plane tangent to barycenter C of dst polygon |
---|
| 30 | // transform system coordinate : Z axis along OC |
---|
| 31 | int na=dstPolygon.size() ; |
---|
| 32 | Coord *a_gno = new Coord[na]; |
---|
| 33 | int nb=srcPolygon.size() ; |
---|
| 34 | Coord *b_gno = new Coord[nb]; |
---|
| 35 | |
---|
| 36 | Coord OC=barycentre(a->vertex,a->n) ; |
---|
| 37 | Coord Oz=OC ; |
---|
| 38 | Coord Ox=crossprod(Coord(0,0,1),Oz) ; |
---|
| 39 | // choose Ox not too small to avoid rounding error |
---|
| 40 | if (norm(Ox)< 0.1) Ox=crossprod(Coord(0,1,0),Oz) ; |
---|
| 41 | Ox=Ox*(1./norm(Ox)) ; |
---|
| 42 | Coord Oy=crossprod(Oz,Ox) ; |
---|
| 43 | double cos_alpha; |
---|
| 44 | |
---|
| 45 | for(int n=0; n<na;n++) |
---|
| 46 | { |
---|
| 47 | cos_alpha=scalarprod(OC,dstPolygon[n]) ; |
---|
| 48 | a_gno[n].x=scalarprod(dstPolygon[n],Ox)/cos_alpha ; |
---|
| 49 | a_gno[n].y=scalarprod(dstPolygon[n],Oy)/cos_alpha ; |
---|
| 50 | a_gno[n].z=scalarprod(dstPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
---|
| 51 | } |
---|
| 52 | |
---|
| 53 | for(int n=0; n<nb;n++) |
---|
| 54 | { |
---|
| 55 | cos_alpha=scalarprod(OC,srcPolygon[n]) ; |
---|
| 56 | b_gno[n].x=scalarprod(srcPolygon[n],Ox)/cos_alpha ; |
---|
| 57 | b_gno[n].y=scalarprod(srcPolygon[n],Oy)/cos_alpha ; |
---|
| 58 | b_gno[n].z=scalarprod(srcPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
---|
| 59 | } |
---|
| 60 | |
---|
| 61 | |
---|
| 62 | |
---|
| 63 | // Compute intersections using clipper |
---|
| 64 | // 1) Compute offset and scale factor to rescale polygon |
---|
| 65 | |
---|
| 66 | double xmin, xmax, ymin,ymax ; |
---|
| 67 | xmin=xmax=a_gno[0].x ; |
---|
| 68 | ymin=ymax=a_gno[0].y ; |
---|
| 69 | |
---|
| 70 | for(int n=0; n<na;n++) |
---|
| 71 | { |
---|
| 72 | if (a_gno[n].x< xmin) xmin=a_gno[n].x ; |
---|
| 73 | else if (a_gno[n].x > xmax) xmax=a_gno[n].x ; |
---|
| 74 | |
---|
| 75 | if (a_gno[n].y< ymin) ymin=a_gno[n].y ; |
---|
| 76 | else if (a_gno[n].y > ymax) ymax=a_gno[n].y ; |
---|
| 77 | } |
---|
| 78 | |
---|
| 79 | for(int n=0; n<nb;n++) |
---|
| 80 | { |
---|
| 81 | if (b_gno[n].x< xmin) xmin=b_gno[n].x ; |
---|
| 82 | else if (b_gno[n].x > xmax) xmax=b_gno[n].x ; |
---|
| 83 | |
---|
| 84 | if (b_gno[n].y< ymin) ymin=b_gno[n].y ; |
---|
| 85 | else if (b_gno[n].y > ymax) ymax=b_gno[n].y ; |
---|
| 86 | } |
---|
| 87 | |
---|
| 88 | double xoffset=(xmin+xmax)*0.5 ; |
---|
| 89 | double yoffset=(ymin+ymax)*0.5 ; |
---|
| 90 | double xscale= 1e-4*0.5*hiRange/(xmax-xoffset) ; |
---|
| 91 | double yscale= 1e-4*0.5*hiRange/(ymax-yoffset) ; |
---|
| 92 | // Problem with numerical precision if using larger scaling factor |
---|
| 93 | |
---|
| 94 | // 2) Compute intersection with clipper |
---|
| 95 | // clipper use only long integer value for vertex => offset and rescale |
---|
| 96 | |
---|
| 97 | Paths src(1), dst(1), intersection; |
---|
| 98 | |
---|
| 99 | for(int n=0; n<na;n++) |
---|
| 100 | src[0]<<IntPoint((a_gno[n].x-xoffset)*xscale,(a_gno[n].y-yoffset)*yscale) ; |
---|
| 101 | |
---|
| 102 | for(int n=0; n<nb;n++) |
---|
| 103 | dst[0]<<IntPoint((b_gno[n].x-xoffset)*xscale,(b_gno[n].y-yoffset)*yscale) ; |
---|
| 104 | |
---|
| 105 | Clipper clip ; |
---|
| 106 | clip.AddPaths(src, ptSubject, true); |
---|
| 107 | clip.AddPaths(dst, ptClip, true); |
---|
| 108 | clip.Execute(ctIntersection, intersection); |
---|
| 109 | |
---|
| 110 | double area=0 ; |
---|
| 111 | if (intersection.size()==1) |
---|
| 112 | { |
---|
| 113 | // go back into real coordinate on the sphere |
---|
| 114 | Coord* intersectPolygon=new Coord[intersection[0].size()] ; |
---|
| 115 | // Coord* intersect2D=new Coord[intersection[0].size()] ; |
---|
| 116 | for(int n=0; n < intersection[0].size(); n++) |
---|
| 117 | { |
---|
| 118 | double x=intersection[0][n].X/xscale+xoffset ; |
---|
| 119 | double y=intersection[0][n].Y/yscale+yoffset ; |
---|
| 120 | // intersect2D[n].x=x ; |
---|
| 121 | // intersect2D[n].y=y ; |
---|
| 122 | // intersect2D[n].z=1. ; |
---|
| 123 | |
---|
| 124 | intersectPolygon[n]=Ox*x+Oy*y+Oz ; |
---|
| 125 | intersectPolygon[n]=intersectPolygon[n]*(1./norm(intersectPolygon[n])) ; |
---|
| 126 | } |
---|
| 127 | |
---|
| 128 | // remove redondants vertex |
---|
| 129 | int nv=0 ; |
---|
| 130 | for(int n=0; n < intersection[0].size(); n++) |
---|
| 131 | { |
---|
| 132 | if (norm(intersectPolygon[n]-intersectPolygon[(n+1)%intersection[0].size()])>fusion_vertex) |
---|
| 133 | { |
---|
| 134 | intersectPolygon[nv]=intersectPolygon[n] ; |
---|
| 135 | nv++ ; |
---|
| 136 | } |
---|
| 137 | } |
---|
| 138 | |
---|
| 139 | |
---|
| 140 | if (nv>2) |
---|
| 141 | { |
---|
| 142 | // assign intersection to source and destination polygons |
---|
| 143 | Polyg *is = new Polyg; |
---|
| 144 | is->x = exact_barycentre(intersectPolygon,nv); |
---|
| 145 | is->area = polygonarea(intersectPolygon,nv) ; |
---|
| 146 | // if (is->area < 1e-12) cout<<"Small intersection : "<<is->area<<endl ; |
---|
| 147 | is->id = b->id; /* intersection holds id of corresponding source element (see Elt class definition for details about id) */ |
---|
| 148 | is->src_id = b->src_id; |
---|
| 149 | is->n = nv; |
---|
| 150 | (a->is).push_back(is); |
---|
| 151 | (b->is).push_back(is); |
---|
| 152 | area=is->area ; |
---|
| 153 | } |
---|
| 154 | delete[] intersectPolygon ; |
---|
| 155 | } |
---|
| 156 | else if (intersection.size()>1) |
---|
| 157 | { |
---|
| 158 | |
---|
| 159 | cout<<"Intersection Size > 1 : "<< intersection.size()<<endl ; |
---|
| 160 | } |
---|
| 161 | |
---|
| 162 | delete[] a_gno ; |
---|
| 163 | delete[] b_gno ; |
---|
| 164 | return area ; |
---|
| 165 | } |
---|
| 166 | |
---|
| 167 | void createGreatCirclePolygon(const Elt& element, const Coord& pole, vector<Coord>& coordinates) |
---|
| 168 | { |
---|
| 169 | int nv = element.n; |
---|
| 170 | |
---|
| 171 | double z,r ; |
---|
| 172 | int north ; |
---|
| 173 | int iterations ; |
---|
| 174 | |
---|
| 175 | Coord xa,xb,xi,xc ; |
---|
| 176 | Coord x1,x2,x ; |
---|
| 177 | |
---|
| 178 | for(int i=0;i < nv ;i++) |
---|
| 179 | { |
---|
| 180 | north = (scalarprod(element.edge[i], pole) < 0) ? -1 : 1; |
---|
| 181 | z=north*element.d[i] ; |
---|
| 182 | |
---|
| 183 | if (z != 0.0) |
---|
| 184 | { |
---|
| 185 | |
---|
| 186 | xa=element.vertex[i] ; |
---|
| 187 | xb=element.vertex[(i+1)%nv] ; |
---|
| 188 | iterations=0 ; |
---|
| 189 | |
---|
| 190 | // compare max distance (at mid-point) between small circle and great circle |
---|
| 191 | // if greater the epsilon refine the small circle by dividing it recursively. |
---|
| 192 | |
---|
| 193 | do |
---|
| 194 | { |
---|
| 195 | xc = pole * z ; |
---|
| 196 | r=sqrt(1-z*z) ; |
---|
| 197 | xi=(xa+xb)*0.5 ; |
---|
| 198 | x1=xc+(xi-xc)*(r/norm(xi-xc)) ; |
---|
| 199 | x2= xi*(1./norm(xi)) ; |
---|
| 200 | ++iterations; |
---|
| 201 | xb=x1 ; |
---|
| 202 | } while(norm(x1-x2)/norm(xa-xb)>epsilon) ; |
---|
| 203 | |
---|
| 204 | iterations = 1 << (iterations-1) ; |
---|
| 205 | |
---|
| 206 | // small circle divided in "iterations" great circle arc |
---|
| 207 | Coord delta=(element.vertex[(i+1)%nv]-element.vertex[i])*(1./iterations); |
---|
| 208 | x=xa ; |
---|
| 209 | for(int j=0; j<iterations ; j++) |
---|
| 210 | { |
---|
| 211 | //xc+(x-xc)*r/norm(x-xc) |
---|
| 212 | coordinates.push_back(xc+(x-xc)*(r/norm(x-xc))) ; |
---|
| 213 | x=x+delta ; |
---|
| 214 | } |
---|
| 215 | } |
---|
| 216 | else coordinates.push_back(element.vertex[i]) ; |
---|
| 217 | } |
---|
| 218 | } |
---|
| 219 | |
---|
| 220 | } |
---|