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