[688] | 1 | #include "intersection_ym.hpp" |
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| 2 | #include "elt.hpp" |
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| 3 | #include "clipper.hpp" |
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| 4 | #include "gridRemap.hpp" |
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| 5 | #include "triple.hpp" |
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| 6 | #include "polyg.hpp" |
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| 7 | #include <vector> |
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| 8 | #include <stdlib.h> |
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| 9 | #include <limits> |
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| 10 | |
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| 11 | #define epsilon 1e-3 // epsilon distance ratio over side lenght for approximate small circle by great circle |
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| 12 | #define fusion_vertex 1e-13 |
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| 13 | |
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| 14 | namespace sphereRemap { |
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| 15 | |
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| 16 | using namespace std; |
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| 17 | using namespace ClipperLib ; |
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| 18 | |
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| 19 | double intersect_ym(Elt *a, Elt *b) |
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| 20 | { |
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| 21 | |
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| 22 | // transform small circle into piece of great circle if necessary |
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| 23 | |
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| 24 | vector<Coord> srcPolygon ; |
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| 25 | createGreatCirclePolygon(*b, srcGrid.pole, srcPolygon) ; |
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[845] | 26 | // b->area=polygonarea(&srcPolygon[0],srcPolygon.size()) ; |
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[688] | 27 | vector<Coord> dstPolygon ; |
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| 28 | createGreatCirclePolygon(*a, tgtGrid.pole, dstPolygon) ; |
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[845] | 29 | a->area=polygonarea(&dstPolygon[0],dstPolygon.size()) ; // just for target |
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[688] | 30 | |
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| 31 | // compute coordinates of the polygons into the gnomonique plane tangent to barycenter C of dst polygon |
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| 32 | // transform system coordinate : Z axis along OC |
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| 33 | int na=dstPolygon.size() ; |
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| 34 | Coord *a_gno = new Coord[na]; |
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| 35 | int nb=srcPolygon.size() ; |
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| 36 | Coord *b_gno = new Coord[nb]; |
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| 37 | |
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| 38 | Coord OC=barycentre(a->vertex,a->n) ; |
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| 39 | Coord Oz=OC ; |
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| 40 | Coord Ox=crossprod(Coord(0,0,1),Oz) ; |
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| 41 | // choose Ox not too small to avoid rounding error |
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| 42 | if (norm(Ox)< 0.1) Ox=crossprod(Coord(0,1,0),Oz) ; |
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| 43 | Ox=Ox*(1./norm(Ox)) ; |
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| 44 | Coord Oy=crossprod(Oz,Ox) ; |
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| 45 | double cos_alpha; |
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| 46 | |
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| 47 | for(int n=0; n<na;n++) |
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| 48 | { |
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| 49 | cos_alpha=scalarprod(OC,dstPolygon[n]) ; |
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| 50 | a_gno[n].x=scalarprod(dstPolygon[n],Ox)/cos_alpha ; |
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| 51 | a_gno[n].y=scalarprod(dstPolygon[n],Oy)/cos_alpha ; |
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| 52 | a_gno[n].z=scalarprod(dstPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
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| 53 | } |
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| 54 | |
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| 55 | for(int n=0; n<nb;n++) |
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| 56 | { |
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| 57 | cos_alpha=scalarprod(OC,srcPolygon[n]) ; |
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| 58 | b_gno[n].x=scalarprod(srcPolygon[n],Ox)/cos_alpha ; |
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| 59 | b_gno[n].y=scalarprod(srcPolygon[n],Oy)/cos_alpha ; |
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| 60 | b_gno[n].z=scalarprod(srcPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
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| 61 | } |
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| 62 | |
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| 63 | |
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| 64 | |
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| 65 | // Compute intersections using clipper |
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| 66 | // 1) Compute offset and scale factor to rescale polygon |
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| 67 | |
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| 68 | double xmin, xmax, ymin,ymax ; |
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| 69 | xmin=xmax=a_gno[0].x ; |
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| 70 | ymin=ymax=a_gno[0].y ; |
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| 71 | |
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| 72 | for(int n=0; n<na;n++) |
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| 73 | { |
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| 74 | if (a_gno[n].x< xmin) xmin=a_gno[n].x ; |
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| 75 | else if (a_gno[n].x > xmax) xmax=a_gno[n].x ; |
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| 76 | |
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| 77 | if (a_gno[n].y< ymin) ymin=a_gno[n].y ; |
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| 78 | else if (a_gno[n].y > ymax) ymax=a_gno[n].y ; |
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| 79 | } |
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| 80 | |
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| 81 | for(int n=0; n<nb;n++) |
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| 82 | { |
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| 83 | if (b_gno[n].x< xmin) xmin=b_gno[n].x ; |
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| 84 | else if (b_gno[n].x > xmax) xmax=b_gno[n].x ; |
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| 85 | |
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| 86 | if (b_gno[n].y< ymin) ymin=b_gno[n].y ; |
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| 87 | else if (b_gno[n].y > ymax) ymax=b_gno[n].y ; |
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| 88 | } |
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| 89 | |
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| 90 | double xoffset=(xmin+xmax)*0.5 ; |
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| 91 | double yoffset=(ymin+ymax)*0.5 ; |
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| 92 | double xscale= 1e-4*0.5*hiRange/(xmax-xoffset) ; |
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| 93 | double yscale= 1e-4*0.5*hiRange/(ymax-yoffset) ; |
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| 94 | // Problem with numerical precision if using larger scaling factor |
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| 95 | |
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| 96 | // 2) Compute intersection with clipper |
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| 97 | // clipper use only long integer value for vertex => offset and rescale |
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| 98 | |
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| 99 | Paths src(1), dst(1), intersection; |
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| 100 | |
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| 101 | for(int n=0; n<na;n++) |
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| 102 | src[0]<<IntPoint((a_gno[n].x-xoffset)*xscale,(a_gno[n].y-yoffset)*yscale) ; |
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| 103 | |
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| 104 | for(int n=0; n<nb;n++) |
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| 105 | dst[0]<<IntPoint((b_gno[n].x-xoffset)*xscale,(b_gno[n].y-yoffset)*yscale) ; |
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| 106 | |
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| 107 | Clipper clip ; |
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| 108 | clip.AddPaths(src, ptSubject, true); |
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| 109 | clip.AddPaths(dst, ptClip, true); |
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| 110 | clip.Execute(ctIntersection, intersection); |
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| 111 | |
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| 112 | double area=0 ; |
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[845] | 113 | |
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| 114 | for(int ni=0;ni<intersection.size(); ni++) |
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[688] | 115 | { |
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[845] | 116 | // go back into real coordinate on the sphere |
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| 117 | Coord* intersectPolygon=new Coord[intersection[ni].size()] ; |
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| 118 | for(int n=0; n < intersection[ni].size(); n++) |
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[688] | 119 | { |
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[845] | 120 | double x=intersection[ni][n].X/xscale+xoffset ; |
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| 121 | double y=intersection[ni][n].Y/yscale+yoffset ; |
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[688] | 122 | |
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| 123 | intersectPolygon[n]=Ox*x+Oy*y+Oz ; |
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| 124 | intersectPolygon[n]=intersectPolygon[n]*(1./norm(intersectPolygon[n])) ; |
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| 125 | } |
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| 126 | |
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| 127 | // remove redondants vertex |
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| 128 | int nv=0 ; |
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[845] | 129 | for(int n=0; n < intersection[ni].size(); n++) |
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[688] | 130 | { |
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[845] | 131 | if (norm(intersectPolygon[n]-intersectPolygon[(n+1)%intersection[ni].size()])>fusion_vertex) |
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[688] | 132 | { |
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| 133 | intersectPolygon[nv]=intersectPolygon[n] ; |
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| 134 | nv++ ; |
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| 135 | } |
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| 136 | } |
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| 137 | |
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| 138 | |
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| 139 | if (nv>2) |
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| 140 | { |
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| 141 | // assign intersection to source and destination polygons |
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| 142 | Polyg *is = new Polyg; |
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| 143 | is->x = exact_barycentre(intersectPolygon,nv); |
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| 144 | is->area = polygonarea(intersectPolygon,nv) ; |
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| 145 | // if (is->area < 1e-12) cout<<"Small intersection : "<<is->area<<endl ; |
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[849] | 146 | if (is->area==0.) delete is ; |
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| 147 | else |
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| 148 | { |
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| 149 | is->id = b->id; /* intersection holds id of corresponding source element (see Elt class definition for details about id) */ |
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| 150 | is->src_id = b->src_id; |
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| 151 | is->n = nv; |
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| 152 | (a->is).push_back(is); |
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| 153 | (b->is).push_back(is); |
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| 154 | area=is->area ; |
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| 155 | } |
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[845] | 156 | } |
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| 157 | delete[] intersectPolygon ; |
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[688] | 158 | } |
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| 159 | |
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| 160 | delete[] a_gno ; |
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| 161 | delete[] b_gno ; |
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| 162 | return area ; |
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| 163 | } |
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| 164 | |
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| 165 | void createGreatCirclePolygon(const Elt& element, const Coord& pole, vector<Coord>& coordinates) |
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| 166 | { |
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| 167 | int nv = element.n; |
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| 168 | |
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| 169 | double z,r ; |
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| 170 | int north ; |
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| 171 | int iterations ; |
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| 172 | |
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| 173 | Coord xa,xb,xi,xc ; |
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| 174 | Coord x1,x2,x ; |
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| 175 | |
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| 176 | for(int i=0;i < nv ;i++) |
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| 177 | { |
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| 178 | north = (scalarprod(element.edge[i], pole) < 0) ? -1 : 1; |
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| 179 | z=north*element.d[i] ; |
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| 180 | |
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| 181 | if (z != 0.0) |
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| 182 | { |
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| 183 | |
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| 184 | xa=element.vertex[i] ; |
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| 185 | xb=element.vertex[(i+1)%nv] ; |
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| 186 | iterations=0 ; |
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| 187 | |
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| 188 | // compare max distance (at mid-point) between small circle and great circle |
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| 189 | // if greater the epsilon refine the small circle by dividing it recursively. |
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| 190 | |
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| 191 | do |
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| 192 | { |
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| 193 | xc = pole * z ; |
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| 194 | r=sqrt(1-z*z) ; |
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| 195 | xi=(xa+xb)*0.5 ; |
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| 196 | x1=xc+(xi-xc)*(r/norm(xi-xc)) ; |
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| 197 | x2= xi*(1./norm(xi)) ; |
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| 198 | ++iterations; |
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| 199 | xb=x1 ; |
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| 200 | } while(norm(x1-x2)/norm(xa-xb)>epsilon) ; |
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| 201 | |
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| 202 | iterations = 1 << (iterations-1) ; |
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| 203 | |
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| 204 | // small circle divided in "iterations" great circle arc |
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| 205 | Coord delta=(element.vertex[(i+1)%nv]-element.vertex[i])*(1./iterations); |
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| 206 | x=xa ; |
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| 207 | for(int j=0; j<iterations ; j++) |
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| 208 | { |
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| 209 | //xc+(x-xc)*r/norm(x-xc) |
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| 210 | coordinates.push_back(xc+(x-xc)*(r/norm(x-xc))) ; |
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| 211 | x=x+delta ; |
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| 212 | } |
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| 213 | } |
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| 214 | else coordinates.push_back(element.vertex[i]) ; |
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| 215 | } |
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| 216 | } |
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| 217 | |
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| 218 | } |
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