[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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[1580] | 10 | #include <array> |
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| 11 | #include <cstdint> |
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| 12 | #include "earcut.hpp" |
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| 13 | #include <fstream> |
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[688] | 14 | |
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[1580] | 15 | |
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[688] | 16 | #define epsilon 1e-3 // epsilon distance ratio over side lenght for approximate small circle by great circle |
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| 17 | #define fusion_vertex 1e-13 |
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| 18 | |
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| 19 | namespace sphereRemap { |
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| 20 | |
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| 21 | using namespace std; |
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| 22 | using namespace ClipperLib ; |
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[1580] | 23 | |
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[688] | 24 | |
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| 25 | double intersect_ym(Elt *a, Elt *b) |
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| 26 | { |
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| 27 | |
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[1580] | 28 | using N = uint32_t; |
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| 29 | using Point = array<double, 2>; |
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| 30 | vector<Point> vect_points; |
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| 31 | vector< vector<Point> > polyline; |
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| 32 | |
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[688] | 33 | // transform small circle into piece of great circle if necessary |
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| 34 | |
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| 35 | vector<Coord> srcPolygon ; |
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| 36 | createGreatCirclePolygon(*b, srcGrid.pole, srcPolygon) ; |
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[845] | 37 | // b->area=polygonarea(&srcPolygon[0],srcPolygon.size()) ; |
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[688] | 38 | vector<Coord> dstPolygon ; |
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| 39 | createGreatCirclePolygon(*a, tgtGrid.pole, dstPolygon) ; |
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[845] | 40 | a->area=polygonarea(&dstPolygon[0],dstPolygon.size()) ; // just for target |
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[688] | 41 | |
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| 42 | // compute coordinates of the polygons into the gnomonique plane tangent to barycenter C of dst polygon |
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| 43 | // transform system coordinate : Z axis along OC |
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| 44 | int na=dstPolygon.size() ; |
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| 45 | Coord *a_gno = new Coord[na]; |
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| 46 | int nb=srcPolygon.size() ; |
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| 47 | Coord *b_gno = new Coord[nb]; |
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| 48 | |
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| 49 | Coord OC=barycentre(a->vertex,a->n) ; |
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| 50 | Coord Oz=OC ; |
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| 51 | Coord Ox=crossprod(Coord(0,0,1),Oz) ; |
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| 52 | // choose Ox not too small to avoid rounding error |
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| 53 | if (norm(Ox)< 0.1) Ox=crossprod(Coord(0,1,0),Oz) ; |
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| 54 | Ox=Ox*(1./norm(Ox)) ; |
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| 55 | Coord Oy=crossprod(Oz,Ox) ; |
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| 56 | double cos_alpha; |
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| 57 | |
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[1580] | 58 | /// vector<p2t::Point*> polyline; |
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[688] | 59 | for(int n=0; n<na;n++) |
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| 60 | { |
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| 61 | cos_alpha=scalarprod(OC,dstPolygon[n]) ; |
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| 62 | a_gno[n].x=scalarprod(dstPolygon[n],Ox)/cos_alpha ; |
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| 63 | a_gno[n].y=scalarprod(dstPolygon[n],Oy)/cos_alpha ; |
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| 64 | a_gno[n].z=scalarprod(dstPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
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[1580] | 65 | |
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| 66 | vect_points.push_back( array<double, 2>() ); |
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| 67 | vect_points[n][0] = a_gno[n].x; |
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| 68 | vect_points[n][1] = a_gno[n].y; |
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| 69 | |
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[688] | 70 | } |
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| 71 | |
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[1580] | 72 | polyline.push_back(vect_points); |
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| 73 | vector<N> indices_a_gno = mapbox::earcut<N>(polyline); |
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| 74 | |
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| 75 | double area_a_gno=0 ; |
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| 76 | for(int i=0;i<indices_a_gno.size()/3;++i) |
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| 77 | { |
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| 78 | Coord x0 = Ox * polyline[0][indices_a_gno[3*i]][0] + Oy* polyline[0][indices_a_gno[3*i]][1] + Oz ; |
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| 79 | Coord x1 = Ox * polyline[0][indices_a_gno[3*i+1]][0] + Oy* polyline[0][indices_a_gno[3*i+1]][1] + Oz ; |
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| 80 | Coord x2 = Ox * polyline[0][indices_a_gno[3*i+2]][0] + Oy* polyline[0][indices_a_gno[3*i+2]][1] + Oz ; |
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| 81 | area_a_gno+=triarea(x0 * (1./norm(x0)),x1* (1./norm(x1)), x2* (1./norm(x2))) ; |
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| 82 | } |
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| 83 | |
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| 84 | vect_points.clear(); |
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| 85 | polyline.clear(); |
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| 86 | indices_a_gno.clear(); |
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| 87 | |
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| 88 | |
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| 89 | |
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[688] | 90 | for(int n=0; n<nb;n++) |
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| 91 | { |
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| 92 | cos_alpha=scalarprod(OC,srcPolygon[n]) ; |
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| 93 | b_gno[n].x=scalarprod(srcPolygon[n],Ox)/cos_alpha ; |
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| 94 | b_gno[n].y=scalarprod(srcPolygon[n],Oy)/cos_alpha ; |
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| 95 | b_gno[n].z=scalarprod(srcPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
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[1580] | 96 | |
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| 97 | vect_points.push_back( array<double, 2>() ); |
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| 98 | vect_points[n][0] = b_gno[n].x; |
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| 99 | vect_points[n][1] = b_gno[n].y; |
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[688] | 100 | } |
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| 101 | |
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| 102 | |
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[1580] | 103 | polyline.push_back(vect_points); |
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| 104 | vector<N> indices_b_gno = mapbox::earcut<N>(polyline); |
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[688] | 105 | |
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[1580] | 106 | double area_b_gno=0 ; |
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| 107 | for(int i=0;i<indices_b_gno.size()/3;++i) |
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| 108 | { |
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| 109 | Coord x0 = Ox * polyline[0][indices_b_gno[3*i]][0] + Oy* polyline[0][indices_b_gno[3*i]][1] + Oz ; |
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| 110 | Coord x1 = Ox * polyline[0][indices_b_gno[3*i+1]][0] + Oy* polyline[0][indices_b_gno[3*i+1]][1] + Oz ; |
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| 111 | Coord x2 = Ox * polyline[0][indices_b_gno[3*i+2]][0] + Oy* polyline[0][indices_b_gno[3*i+2]][1] + Oz ; |
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| 112 | area_b_gno+=triarea(x0 * (1./norm(x0)),x1* (1./norm(x1)), x2* (1./norm(x2))) ; |
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| 113 | } |
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| 114 | |
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| 115 | vect_points.clear(); |
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| 116 | polyline.clear(); |
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| 117 | indices_b_gno.clear(); |
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| 118 | |
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| 119 | |
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[688] | 120 | // Compute intersections using clipper |
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| 121 | // 1) Compute offset and scale factor to rescale polygon |
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| 122 | |
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| 123 | double xmin, xmax, ymin,ymax ; |
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| 124 | xmin=xmax=a_gno[0].x ; |
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| 125 | ymin=ymax=a_gno[0].y ; |
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| 126 | |
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| 127 | for(int n=0; n<na;n++) |
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| 128 | { |
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| 129 | if (a_gno[n].x< xmin) xmin=a_gno[n].x ; |
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| 130 | else if (a_gno[n].x > xmax) xmax=a_gno[n].x ; |
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| 131 | |
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| 132 | if (a_gno[n].y< ymin) ymin=a_gno[n].y ; |
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| 133 | else if (a_gno[n].y > ymax) ymax=a_gno[n].y ; |
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| 134 | } |
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| 135 | |
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| 136 | for(int n=0; n<nb;n++) |
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| 137 | { |
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| 138 | if (b_gno[n].x< xmin) xmin=b_gno[n].x ; |
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| 139 | else if (b_gno[n].x > xmax) xmax=b_gno[n].x ; |
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| 140 | |
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| 141 | if (b_gno[n].y< ymin) ymin=b_gno[n].y ; |
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| 142 | else if (b_gno[n].y > ymax) ymax=b_gno[n].y ; |
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| 143 | } |
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| 144 | |
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| 145 | double xoffset=(xmin+xmax)*0.5 ; |
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| 146 | double yoffset=(ymin+ymax)*0.5 ; |
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| 147 | double xscale= 1e-4*0.5*hiRange/(xmax-xoffset) ; |
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| 148 | double yscale= 1e-4*0.5*hiRange/(ymax-yoffset) ; |
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| 149 | // Problem with numerical precision if using larger scaling factor |
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| 150 | |
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| 151 | // 2) Compute intersection with clipper |
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| 152 | // clipper use only long integer value for vertex => offset and rescale |
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| 153 | |
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| 154 | Paths src(1), dst(1), intersection; |
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| 155 | |
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| 156 | for(int n=0; n<na;n++) |
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| 157 | src[0]<<IntPoint((a_gno[n].x-xoffset)*xscale,(a_gno[n].y-yoffset)*yscale) ; |
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| 158 | |
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| 159 | for(int n=0; n<nb;n++) |
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| 160 | dst[0]<<IntPoint((b_gno[n].x-xoffset)*xscale,(b_gno[n].y-yoffset)*yscale) ; |
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| 161 | |
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| 162 | Clipper clip ; |
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| 163 | clip.AddPaths(src, ptSubject, true); |
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| 164 | clip.AddPaths(dst, ptClip, true); |
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| 165 | clip.Execute(ctIntersection, intersection); |
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[1580] | 166 | |
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[688] | 167 | double area=0 ; |
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[845] | 168 | |
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| 169 | for(int ni=0;ni<intersection.size(); ni++) |
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[688] | 170 | { |
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[845] | 171 | Coord* intersectPolygon=new Coord[intersection[ni].size()] ; |
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| 172 | for(int n=0; n < intersection[ni].size(); n++) |
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[688] | 173 | { |
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[1580] | 174 | intersectPolygon[n].x=intersection[ni][n].X/xscale+xoffset ; |
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| 175 | intersectPolygon[n].y=intersection[ni][n].Y/yscale+yoffset ; |
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[688] | 176 | } |
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[1580] | 177 | |
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[688] | 178 | |
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[1580] | 179 | int nv=0; |
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| 180 | |
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[845] | 181 | for(int n=0; n < intersection[ni].size(); n++) |
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[688] | 182 | { |
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[1580] | 183 | double dx=intersectPolygon[n].x-intersectPolygon[(n+1)%intersection[ni].size()].x ; |
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| 184 | double dy=intersectPolygon[n].y-intersectPolygon[(n+1)%intersection[ni].size()].y ; |
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| 185 | |
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| 186 | if (dx*dx+dy*dy>fusion_vertex*fusion_vertex) |
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| 187 | { |
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| 188 | intersectPolygon[nv]=intersectPolygon[n] ; |
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| 189 | |
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| 190 | vect_points.push_back( array<double, 2>() ); |
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| 191 | vect_points[nv][0] = intersectPolygon[n].x; |
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| 192 | vect_points[nv][1] = intersectPolygon[n].y; |
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| 193 | |
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| 194 | nv++ ; |
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| 195 | } |
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| 196 | |
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| 197 | |
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[688] | 198 | } |
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| 199 | |
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[1580] | 200 | polyline.push_back(vect_points); |
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| 201 | vect_points.clear(); |
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[688] | 202 | |
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| 203 | if (nv>2) |
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| 204 | { |
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[1580] | 205 | |
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| 206 | vector<N> indices = mapbox::earcut<N>(polyline); |
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| 207 | |
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| 208 | double area2=0 ; |
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| 209 | for(int i=0;i<indices.size()/3;++i) |
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| 210 | { |
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| 211 | Coord x0 = Ox * polyline[0][indices[3*i]][0] + Oy* polyline[0][indices[3*i]][1] + Oz ; |
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| 212 | Coord x1 = Ox * polyline[0][indices[3*i+1]][0] + Oy* polyline[0][indices[3*i+1]][1] + Oz ; |
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| 213 | Coord x2 = Ox * polyline[0][indices[3*i+2]][0] + Oy* polyline[0][indices[3*i+2]][1] + Oz ; |
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| 214 | area2+=triarea(x0 * (1./norm(x0)),x1* (1./norm(x1)), x2* (1./norm(x2))) ; |
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| 215 | } |
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| 216 | |
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| 217 | polyline.clear(); |
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| 218 | |
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| 219 | for(int n=0; n < nv; n++) |
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| 220 | { |
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| 221 | intersectPolygon[n] = Ox*intersectPolygon[n].x+Oy*intersectPolygon[n].y+Oz; |
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[1588] | 222 | intersectPolygon[n] = intersectPolygon[n]*(1./norm(intersectPolygon[n])) ; |
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[1580] | 223 | } |
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| 224 | |
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| 225 | |
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[688] | 226 | // assign intersection to source and destination polygons |
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| 227 | Polyg *is = new Polyg; |
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| 228 | is->x = exact_barycentre(intersectPolygon,nv); |
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[1580] | 229 | // is->area = polygonarea(intersectPolygon,nv) ; |
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| 230 | is->area = area2 ; |
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| 231 | |
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[688] | 232 | // if (is->area < 1e-12) cout<<"Small intersection : "<<is->area<<endl ; |
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[849] | 233 | if (is->area==0.) delete is ; |
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| 234 | else |
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| 235 | { |
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| 236 | is->id = b->id; /* intersection holds id of corresponding source element (see Elt class definition for details about id) */ |
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| 237 | is->src_id = b->src_id; |
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| 238 | is->n = nv; |
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| 239 | (a->is).push_back(is); |
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| 240 | (b->is).push_back(is); |
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| 241 | area=is->area ; |
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| 242 | } |
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[845] | 243 | } |
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| 244 | delete[] intersectPolygon ; |
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[688] | 245 | } |
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| 246 | |
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| 247 | delete[] a_gno ; |
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| 248 | delete[] b_gno ; |
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| 249 | return area ; |
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[1580] | 250 | |
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[688] | 251 | } |
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| 252 | |
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[1580] | 253 | |
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| 254 | |
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[688] | 255 | void createGreatCirclePolygon(const Elt& element, const Coord& pole, vector<Coord>& coordinates) |
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| 256 | { |
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| 257 | int nv = element.n; |
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| 258 | |
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| 259 | double z,r ; |
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| 260 | int north ; |
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| 261 | int iterations ; |
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| 262 | |
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| 263 | Coord xa,xb,xi,xc ; |
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| 264 | Coord x1,x2,x ; |
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| 265 | |
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| 266 | for(int i=0;i < nv ;i++) |
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| 267 | { |
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| 268 | north = (scalarprod(element.edge[i], pole) < 0) ? -1 : 1; |
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| 269 | z=north*element.d[i] ; |
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| 270 | |
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| 271 | if (z != 0.0) |
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| 272 | { |
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| 273 | |
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| 274 | xa=element.vertex[i] ; |
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| 275 | xb=element.vertex[(i+1)%nv] ; |
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| 276 | iterations=0 ; |
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| 277 | |
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| 278 | // compare max distance (at mid-point) between small circle and great circle |
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| 279 | // if greater the epsilon refine the small circle by dividing it recursively. |
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| 280 | |
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| 281 | do |
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| 282 | { |
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| 283 | xc = pole * z ; |
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| 284 | r=sqrt(1-z*z) ; |
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| 285 | xi=(xa+xb)*0.5 ; |
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| 286 | x1=xc+(xi-xc)*(r/norm(xi-xc)) ; |
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| 287 | x2= xi*(1./norm(xi)) ; |
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| 288 | ++iterations; |
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| 289 | xb=x1 ; |
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| 290 | } while(norm(x1-x2)/norm(xa-xb)>epsilon) ; |
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| 291 | |
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| 292 | iterations = 1 << (iterations-1) ; |
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| 293 | |
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| 294 | // small circle divided in "iterations" great circle arc |
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| 295 | Coord delta=(element.vertex[(i+1)%nv]-element.vertex[i])*(1./iterations); |
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| 296 | x=xa ; |
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| 297 | for(int j=0; j<iterations ; j++) |
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| 298 | { |
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| 299 | //xc+(x-xc)*r/norm(x-xc) |
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| 300 | coordinates.push_back(xc+(x-xc)*(r/norm(x-xc))) ; |
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| 301 | x=x+delta ; |
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| 302 | } |
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| 303 | } |
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| 304 | else coordinates.push_back(element.vertex[i]) ; |
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| 305 | } |
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| 306 | } |
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| 307 | |
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| 308 | } |
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