[688] | 1 | #include <list> |
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| 2 | #include "elt.hpp" |
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| 3 | #include "polyg.hpp" |
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[1613] | 4 | #include "intersection_ym.hpp" |
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| 5 | #include "earcut.hpp" |
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| 6 | #include <vector> |
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[688] | 7 | |
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| 8 | namespace sphereRemap { |
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| 9 | |
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| 10 | using namespace std; |
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| 11 | |
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[1613] | 12 | double computePolygoneArea(Elt& a, const Coord &pole) |
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| 13 | { |
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| 14 | using N = uint32_t; |
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| 15 | using Point = array<double, 2>; |
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| 16 | vector<Point> vect_points; |
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| 17 | vector< vector<Point> > polyline; |
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| 18 | |
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| 19 | vector<Coord> dstPolygon ; |
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| 20 | createGreatCirclePolygon(a, pole, dstPolygon) ; |
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| 21 | |
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| 22 | int na=dstPolygon.size() ; |
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| 23 | Coord *a_gno = new Coord[na]; |
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| 24 | |
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| 25 | Coord OC=barycentre(a.vertex,a.n) ; |
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| 26 | Coord Oz=OC ; |
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| 27 | Coord Ox=crossprod(Coord(0,0,1),Oz) ; |
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| 28 | // choose Ox not too small to avoid rounding error |
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| 29 | if (norm(Ox)< 0.1) Ox=crossprod(Coord(0,1,0),Oz) ; |
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| 30 | Ox=Ox*(1./norm(Ox)) ; |
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| 31 | Coord Oy=crossprod(Oz,Ox) ; |
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| 32 | double cos_alpha; |
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| 33 | |
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| 34 | for(int n=0; n<na;n++) |
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| 35 | { |
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| 36 | cos_alpha=scalarprod(OC,dstPolygon[n]) ; |
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| 37 | a_gno[n].x=scalarprod(dstPolygon[n],Ox)/cos_alpha ; |
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| 38 | a_gno[n].y=scalarprod(dstPolygon[n],Oy)/cos_alpha ; |
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| 39 | a_gno[n].z=scalarprod(dstPolygon[n],Oz)/cos_alpha ; // must be equal to 1 |
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| 40 | |
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| 41 | vect_points.push_back( array<double, 2>() ); |
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| 42 | vect_points[n][0] = a_gno[n].x; |
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| 43 | vect_points[n][1] = a_gno[n].y; |
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| 44 | |
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| 45 | } |
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| 46 | |
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| 47 | polyline.push_back(vect_points); |
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| 48 | vector<N> indices_a_gno = mapbox::earcut<N>(polyline); |
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| 49 | |
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| 50 | double area_a_gno=0 ; |
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| 51 | for(int i=0;i<indices_a_gno.size()/3;++i) |
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| 52 | { |
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| 53 | 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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| 54 | 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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| 55 | 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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| 56 | area_a_gno+=triarea(x0 * (1./norm(x0)),x1* (1./norm(x1)), x2* (1./norm(x2))) ; |
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| 57 | } |
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| 58 | |
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| 59 | vect_points.clear(); |
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| 60 | polyline.clear(); |
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| 61 | indices_a_gno.clear(); |
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| 62 | return area_a_gno ; |
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| 63 | } |
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| 64 | |
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| 65 | |
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[688] | 66 | void cptEltGeom(Elt& elt, const Coord &pole) |
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| 67 | { |
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[844] | 68 | orient(elt.n, elt.vertex, elt.edge, elt.d, elt.x); |
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| 69 | normals(elt, pole); |
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| 70 | Coord gg; |
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| 71 | elt.area = airbar(elt.n, elt.vertex, elt.edge, elt.d, pole, gg); |
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| 72 | elt.x = gg; |
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[1613] | 73 | // overwrite area computation |
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| 74 | |
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| 75 | elt.area = computePolygoneArea(elt, pole) ; |
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[688] | 76 | } |
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| 77 | |
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[1613] | 78 | |
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[688] | 79 | void cptAllEltsGeom(Elt *elt, int N, const Coord &pole) |
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| 80 | { |
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[844] | 81 | for (int ne=0; ne<N; ne++) |
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| 82 | cptEltGeom(elt[ne], pole); |
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[688] | 83 | } |
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| 84 | |
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| 85 | /* for all elements of size-N-array `elt`, |
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| 86 | make centre areaweighted average centres of super mesh elements */ |
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| 87 | void update_baryc(Elt *elt, int N) |
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| 88 | { |
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[844] | 89 | for (int ne=0; ne<N; ne++) |
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| 90 | { |
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| 91 | Elt &e = elt[ne]; |
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| 92 | int ns = e.is.size(); // sous-elements |
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| 93 | Coord *sx = new Coord[ns]; |
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| 94 | int i=0; |
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| 95 | for (list<Polyg*>::iterator it = e.is.begin(); it != e.is.end(); i++, it++) |
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| 96 | { |
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| 97 | sx[i] = (*it)->x * (*it)->area; |
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| 98 | } |
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| 99 | e.x = barycentre(sx, ns); |
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| 100 | } |
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[688] | 101 | } |
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| 102 | |
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[844] | 103 | |
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| 104 | Coord gradient_old(Elt& elt, Elt **neighElts) |
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| 105 | { |
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| 106 | Coord grad = ORIGIN; |
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| 107 | Coord *neighBaryc = new Coord[elt.n]; |
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| 108 | for (int j = 0; j < elt.n; j++) |
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| 109 | { |
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| 110 | int k = (j + 1) % elt.n; |
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| 111 | neighBaryc[j] = neighElts[j]->x; |
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| 112 | Coord edgeNormal = crossprod(neighElts[k]->x, neighElts[j]->x); |
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| 113 | |
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| 114 | // use nomenclauture form paper |
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| 115 | double f_i = elt.val; |
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| 116 | double f_j = neighElts[j]->val; |
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| 117 | double f_k = neighElts[k]->val; |
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| 118 | grad = grad + edgeNormal * (0.5*(f_j + f_k) - f_i); |
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| 119 | } |
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| 120 | // area of the polygon whoes vertices are the barycentres the neighbours |
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| 121 | grad = grad * (1./polygonarea(neighBaryc, elt.n)); |
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| 122 | delete[] neighBaryc; |
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| 123 | |
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| 124 | return grad - elt.x * scalarprod(elt.x, grad); |
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| 125 | } |
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| 126 | |
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| 127 | |
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| 128 | |
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[688] | 129 | Coord gradient(Elt& elt, Elt **neighElts) |
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| 130 | { |
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[844] | 131 | |
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| 132 | Coord grad = ORIGIN; |
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| 133 | Coord neighBaryc[3] ; |
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[688] | 134 | |
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[844] | 135 | double f_i ; |
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| 136 | double f_j ; |
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| 137 | double f_k ; |
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| 138 | |
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| 139 | Coord edgeNormal ; |
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| 140 | double area=0 ; |
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| 141 | int k ; |
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[877] | 142 | int count=0 ; |
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| 143 | |
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[844] | 144 | for (int j = 0; j < elt.n; j++) |
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| 145 | { |
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| 146 | f_i = elt.val; |
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| 147 | k = (j + 1) % elt.n; |
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| 148 | if (neighElts[j]==NULL || neighElts[k]==NULL) continue ; |
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| 149 | |
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| 150 | // use nomenclauture form paper |
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| 151 | f_j = neighElts[j]->val; |
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| 152 | f_k = neighElts[k]->val; |
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| 153 | |
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| 154 | |
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| 155 | |
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| 156 | neighBaryc[0] = elt.x; |
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| 157 | neighBaryc[1] = neighElts[j]->x; |
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| 158 | neighBaryc[2] = neighElts[k]->x; |
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| 159 | |
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| 160 | edgeNormal = crossprod(neighElts[k]->x, neighElts[j]->x); |
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| 161 | grad = grad + edgeNormal * (0.5*(f_k + f_j) - f_i); |
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| 162 | |
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| 163 | edgeNormal = crossprod(neighElts[j]->x, elt.x); |
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| 164 | grad = grad + edgeNormal * (0.5*(f_j + f_i) - f_i); |
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| 165 | |
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| 166 | edgeNormal = crossprod(elt.x, neighElts[k]->x); |
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| 167 | grad = grad + edgeNormal * (0.5*(f_i + f_k) - f_i); |
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| 168 | |
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| 169 | // area of the polygon whoes vertices are the barycentres the neighbours |
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| 170 | |
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| 171 | area+=polygonarea(neighBaryc, 3) ; |
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[877] | 172 | count++ ; |
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[844] | 173 | |
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| 174 | } |
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[877] | 175 | if (count>0) |
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| 176 | { |
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| 177 | grad=grad*(1./area) ; |
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| 178 | return grad - elt.x * scalarprod(elt.x, grad); |
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| 179 | } |
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| 180 | else return grad ; |
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[688] | 181 | } |
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| 182 | |
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[844] | 183 | |
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| 184 | |
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| 185 | |
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[688] | 186 | void computeGradients(Elt **elts, int N) |
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| 187 | { |
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[844] | 188 | |
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| 189 | for (int j = 0; j < N; j++) |
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| 190 | elts[j]->val = 0; |
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[688] | 191 | |
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[844] | 192 | Elt *neighbours[NMAX]; |
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| 193 | for (int j = 0; j < N; j++) |
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| 194 | { |
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| 195 | for (int i = 0; i < elts[j]->n; i++) |
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[1581] | 196 | if ( elts[j]->neighbour[i]== NOT_FOUND) neighbours[i]=NULL ; // no neighbour |
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| 197 | else if (elts[elts[j]->neighbour[i]]->is.size() == 0) neighbours[i]=NULL ; // neighbour has none supermesh cell |
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[844] | 198 | else neighbours[i] = elts[elts[j]->neighbour[i]]; |
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[688] | 199 | |
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[844] | 200 | for (int i = 0; i < elts[j]->n; i++) |
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| 201 | if (neighbours[i]!=NULL) neighbours[i]->val = 0; |
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| 202 | |
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| 203 | for (int i = 0; i < elts[j]->n; i++) |
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| 204 | { |
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| 205 | if (neighbours[i]!=NULL) |
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| 206 | { |
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| 207 | elts[j]->neighId[i] = neighbours[i]->src_id; |
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| 208 | /* for weight computation all values are always kept zero and only set to one when used .. */ |
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| 209 | neighbours[i]->val = 1; |
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| 210 | elts[j]->gradNeigh[i] = gradient(*(elts[j]), neighbours); |
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| 211 | /* .. and right after zeroed again */ |
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| 212 | neighbours[i]->val = 0; |
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| 213 | } |
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| 214 | else |
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| 215 | { |
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| 216 | elts[j]->neighId[i].rank = -1; // mark end |
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| 217 | elts[j]->neighId[i].ind = -1; // mark end |
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| 218 | } |
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| 219 | } |
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| 220 | |
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| 221 | for(int i = elts[j]->n ; i < NMAX; i++) |
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| 222 | { |
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| 223 | elts[j]->neighId[i].rank = -1; // mark end |
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| 224 | elts[j]->neighId[i].ind = -1; // mark end |
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| 225 | } |
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| 226 | /* For the most naive algorithm the case where the element itself is one must also be considered. |
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| 227 | Thomas says this can later be optimized out. */ |
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| 228 | elts[j]->val = 1; |
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| 229 | elts[j]->grad = gradient(*(elts[j]), neighbours); |
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| 230 | elts[j]->val = 0; |
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| 231 | } |
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[688] | 232 | } |
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| 233 | |
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| 234 | } |
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