1 | MODULE spherical_geom_mod |
---|
2 | USE genmod |
---|
3 | |
---|
4 | |
---|
5 | |
---|
6 | CONTAINS |
---|
7 | |
---|
8 | |
---|
9 | |
---|
10 | |
---|
11 | SUBROUTINE lonlat2xyz(lon,lat,xyz) |
---|
12 | IMPLICIT NONE |
---|
13 | REAL(rstd),INTENT(IN) :: lon |
---|
14 | REAL(rstd),INTENT(IN) :: lat |
---|
15 | REAL(rstd),INTENT(OUT) :: xyz(3) |
---|
16 | |
---|
17 | xyz(1)=cos(lon)*cos(lat) |
---|
18 | xyz(2)=sin(lon)*cos(lat) |
---|
19 | xyz(3)=sin(lat) |
---|
20 | |
---|
21 | END SUBROUTINE lonlat2xyz |
---|
22 | |
---|
23 | |
---|
24 | SUBROUTINE xyz2lonlat(xyz,lon,lat) |
---|
25 | IMPLICIT NONE |
---|
26 | REAL(rstd),INTENT(IN) :: xyz(3) |
---|
27 | REAL(rstd),INTENT(OUT) :: lon |
---|
28 | REAL(rstd),INTENT(OUT) :: lat |
---|
29 | |
---|
30 | REAL(rstd) :: coslat |
---|
31 | REAL(rstd) :: xyzn(3) |
---|
32 | |
---|
33 | xyzn(:)=xyz(:)/sqrt(sum(xyz(:)**2)) |
---|
34 | |
---|
35 | lat=asin(xyzn(3)) |
---|
36 | lon=atan2(xyzn(2),xyzn(1)) |
---|
37 | END SUBROUTINE xyz2lonlat |
---|
38 | |
---|
39 | ! lat/lon with respect to a displaced pole (rotated basis) : |
---|
40 | ! ( cos(lon0)*sin(lat0), sin(lon0)*sin(lat0), -cos(lat0)) |
---|
41 | ! (-sin(lon0), cos(lon0), 0) |
---|
42 | ! ( cos(lon0)*cos(lat0), sin(lon0)*cos(lat0), sin(lat0)) |
---|
43 | |
---|
44 | SUBROUTINE lonlat2xyz_relative(lon,lat,lon0,lat0, xyz) |
---|
45 | IMPLICIT NONE |
---|
46 | REAL(rstd),INTENT(IN) :: lon0, lat0, lon,lat |
---|
47 | REAL(rstd),INTENT(OUT) :: xyz(3) |
---|
48 | REAL(rstd) :: xx,yy,zz |
---|
49 | xx = cos(lon)*cos(lat) |
---|
50 | yy = sin(lon)*cos(lat) |
---|
51 | zz = sin(lat) |
---|
52 | xyz(1) = cos(lon0)*(sin(lat0)*xx+cos(lat0)*zz)-sin(lon0)*yy |
---|
53 | xyz(2) = sin(lon0)*(sin(lat0)*xx+cos(lat0)*zz)+cos(lon0)*yy |
---|
54 | xyz(3) = sin(lat0)*zz-cos(lat0)*xx |
---|
55 | END SUBROUTINE lonlat2xyz_relative |
---|
56 | |
---|
57 | SUBROUTINE xyz2lonlat_relative(xyz,lon0,lat0, lon,lat) |
---|
58 | IMPLICIT NONE |
---|
59 | REAL(rstd),INTENT(IN) :: xyz(3), lon0, lat0 |
---|
60 | REAL(rstd),INTENT(OUT) :: lon,lat |
---|
61 | REAL(rstd) :: xx,yy,zz |
---|
62 | xx = sin(lat0)*(xyz(1)*cos(lon0)+xyz(2)*sin(lon0))-cos(lat0)*xyz(3) |
---|
63 | yy = xyz(2)*cos(lon0)-xyz(1)*sin(lon0) |
---|
64 | zz = cos(lat0)*(xyz(1)*cos(lon0)+xyz(2)*sin(lon0))+sin(lat0)*xyz(3) |
---|
65 | lon = atan2(yy,xx) |
---|
66 | lat = asin(zz) |
---|
67 | END SUBROUTINE xyz2lonlat_relative |
---|
68 | |
---|
69 | SUBROUTINE schmidt_transform(xyz,cc, lon0, lat0) |
---|
70 | ! Based on formula (12) from Guo & Drake, JCP 2005 |
---|
71 | IMPLICIT NONE |
---|
72 | REAL(rstd),INTENT(INOUT) :: xyz(3) |
---|
73 | REAL(rstd), INTENT(IN) :: cc, lon0, lat0 ! stretching factor>0, lon/lat of zoomed area |
---|
74 | REAL(rstd) :: lat,lon,mu |
---|
75 | CALL xyz2lonlat_relative(xyz,lon0,lat0, lon,lat) |
---|
76 | mu = sin(lat) |
---|
77 | mu = ((cc-1)+mu*(cc+1)) / ((cc+1)+mu*(cc-1)) |
---|
78 | lat = asin(mu) |
---|
79 | CALL lonlat2xyz_relative(lon,lat, lon0,lat0, xyz) |
---|
80 | END SUBROUTINE schmidt_transform |
---|
81 | |
---|
82 | SUBROUTINE dist_cart(A,B,d) |
---|
83 | USE vector |
---|
84 | IMPLICIT NONE |
---|
85 | REAL(rstd),INTENT(IN) :: A(3) |
---|
86 | REAL(rstd),INTENT(IN) :: B(3) |
---|
87 | REAL(rstd),INTENT(OUT) :: d |
---|
88 | |
---|
89 | REAL(rstd) :: n(3) |
---|
90 | CALL cross_product2(A,B,n) |
---|
91 | d=asin(sqrt(sum(n**2))) |
---|
92 | |
---|
93 | END SUBROUTINE dist_cart |
---|
94 | |
---|
95 | |
---|
96 | SUBROUTINE dist_lonlat(lonA,latA,lonB,latB,d) |
---|
97 | IMPLICIT NONE |
---|
98 | REAL(rstd),INTENT(IN) :: lonA |
---|
99 | REAL(rstd),INTENT(IN) :: latA |
---|
100 | REAL(rstd),INTENT(IN) :: lonB |
---|
101 | REAL(rstd),INTENT(IN) :: latB |
---|
102 | REAL(rstd),INTENT(OUT) :: d |
---|
103 | |
---|
104 | d=acos(MAX(MIN(sin(latA)*sin(latB)+cos(latA)*cos(latB)*cos(lonA-lonB),1.),-1.)) |
---|
105 | |
---|
106 | END SUBROUTINE dist_lonlat |
---|
107 | |
---|
108 | SUBROUTINE surf_triangle(A,B,C,surf) |
---|
109 | REAL(rstd),INTENT(IN) :: A(3) |
---|
110 | REAL(rstd),INTENT(IN) :: B(3) |
---|
111 | REAL(rstd),INTENT(IN) :: C(3) |
---|
112 | REAL(rstd),INTENT(OUT) :: Surf |
---|
113 | |
---|
114 | REAL(rstd) :: AB,AC,BC |
---|
115 | REAL(rstd) :: s,x |
---|
116 | |
---|
117 | CALL dist_cart(A,B,AB) |
---|
118 | CALL dist_cart(A,C,AC) |
---|
119 | CALL dist_cart(B,C,BC) |
---|
120 | |
---|
121 | s=(AB+AC+BC)/2 |
---|
122 | x=tan(s/2) * tan((s-AB)/2) * tan((s-AC)/2) * tan((s-BC)/2) |
---|
123 | IF (x<0) x=0. |
---|
124 | surf=4*atan(sqrt( x)) |
---|
125 | |
---|
126 | END SUBROUTINE surf_triangle |
---|
127 | |
---|
128 | |
---|
129 | SUBROUTINE div_arc(A,B,frac,C) |
---|
130 | IMPLICIT NONE |
---|
131 | REAL(rstd),INTENT(IN) :: A(3) |
---|
132 | REAL(rstd),INTENT(IN) :: B(3) |
---|
133 | REAL(rstd),INTENT(IN) :: frac |
---|
134 | REAL(rstd),INTENT(OUT) :: C(3) |
---|
135 | |
---|
136 | REAL(rstd) :: d |
---|
137 | REAL(rstd) :: M(3,3) |
---|
138 | REAL(rstd) :: alpha(3,3) |
---|
139 | INTEGER :: IPIV(3) |
---|
140 | INTEGER :: info |
---|
141 | REAL(rstd) :: xa,xb,xc |
---|
142 | REAL(rstd) :: ya,yb,yc |
---|
143 | REAL(rstd) :: za,zb,zc |
---|
144 | REAL(rstd) :: alpha_A,alpha_B,alpha_C |
---|
145 | REAL(rstd) :: x,y,z |
---|
146 | REAL(rstd) :: a1,a2,a3 |
---|
147 | REAL(rstd) :: b1,b2,b3 |
---|
148 | |
---|
149 | |
---|
150 | xa=A(1) ; ya=A(2) ; za=A(3) |
---|
151 | xb=B(1) ; yb=B(2) ; zb=B(3) |
---|
152 | |
---|
153 | CALL dist_cart(A,B,d) |
---|
154 | |
---|
155 | C(1)=cos(frac*d) |
---|
156 | C(2)=cos((1-frac)*d) |
---|
157 | C(3)=0. |
---|
158 | |
---|
159 | xc=ya*zb-yb*za ; yc=-(xa*zb-xb*za) ; zc=xa*yb-xb*ya |
---|
160 | |
---|
161 | M(1,1)=xa ; M(1,2)=ya ; M(1,3)=za |
---|
162 | M(2,1)=xb ; M(2,2)=yb ; M(2,3)=zb |
---|
163 | M(3,1)=xc ; M(3,2)=yc ; M(3,3)=zc |
---|
164 | stop 'STOP' |
---|
165 | ! CALL DGESV(3,1,M,3,IPIV,C,3,info) |
---|
166 | |
---|
167 | END SUBROUTINE div_arc |
---|
168 | |
---|
169 | SUBROUTINE div_arc_bis(A,B,frac,C) |
---|
170 | IMPLICIT NONE |
---|
171 | REAL(rstd),INTENT(IN) :: A(3) |
---|
172 | REAL(rstd),INTENT(IN) :: B(3) |
---|
173 | REAL(rstd),INTENT(IN) :: frac |
---|
174 | REAL(rstd),INTENT(OUT) :: C(3) |
---|
175 | |
---|
176 | C=A*(1-frac)+B*frac |
---|
177 | C=C/sqrt(sum(C**2)) |
---|
178 | END SUBROUTINE div_arc_bis |
---|
179 | |
---|
180 | |
---|
181 | SUBROUTINE circumcenter(A0,B0,C0,center) |
---|
182 | USE vector |
---|
183 | IMPLICIT NONE |
---|
184 | REAL(rstd), INTENT(IN) :: A0(3),B0(3),C0(3) |
---|
185 | REAL(rstd), INTENT(OUT) :: Center(3) |
---|
186 | |
---|
187 | REAL(rstd) :: a(3),b(3),c(3), ac(3), ab(3), p1(3), q(3), p2(3) |
---|
188 | |
---|
189 | a=A0/sqrt(sum(A0**2)) |
---|
190 | b=B0/sqrt(sum(B0**2)) |
---|
191 | c=C0/sqrt(sum(C0**2)) |
---|
192 | |
---|
193 | ab=b-a |
---|
194 | ac=c-a |
---|
195 | CALL Cross_product2(ab,ac,p1) |
---|
196 | IF(.FALSE.) THEN ! Direct solution, round-off error |
---|
197 | center=p1/norm(p1) |
---|
198 | ELSE ! Two-step solution, stable |
---|
199 | q = SUM(ac**2)*ab-SUM(ab**2)*ac |
---|
200 | CALL Cross_product2(p1,q,p2) |
---|
201 | p2 = a + p2/(2.*SUM(p1**2)) |
---|
202 | center = p2/norm(p2) |
---|
203 | END IF |
---|
204 | END SUBROUTINE circumcenter |
---|
205 | |
---|
206 | |
---|
207 | SUBROUTINE compute_centroid(points,n,centr) |
---|
208 | USE vector |
---|
209 | IMPLICIT NONE |
---|
210 | INTEGER :: n |
---|
211 | REAL(rstd), INTENT(IN) :: points(3,n) |
---|
212 | REAL(rstd), INTENT(OUT) :: Centr(3) |
---|
213 | |
---|
214 | REAL(rstd) :: p1(3),p2(3),cross(3), cc(3) |
---|
215 | REAL(rstd) :: norm_cross, area |
---|
216 | INTEGER :: i,j |
---|
217 | |
---|
218 | centr(:)=0 |
---|
219 | IF(.FALSE.) THEN |
---|
220 | ! Gauss formula (subject to round-off error) |
---|
221 | DO i=1,n |
---|
222 | j=MOD(i,n)+1 |
---|
223 | p1=points(:,i)/norm(points(:,i)) |
---|
224 | p2=points(:,j)/norm(points(:,j)) |
---|
225 | CALL cross_product2(p1,p2,cross) |
---|
226 | norm_cross=norm(cross) |
---|
227 | if (norm_cross<1e-10) CYCLE |
---|
228 | centr(:)=centr(:)+asin(norm_cross)*cross(:)/norm_cross |
---|
229 | ENDDO |
---|
230 | ELSE |
---|
231 | ! Simple area-weighted average (second-order accurate, stable) |
---|
232 | cc=SUM(points,2) ! arithmetic average used as center |
---|
233 | cc=cc/norm(cc) |
---|
234 | DO i=1,n |
---|
235 | j=MOD(i,n)+1 |
---|
236 | p1=points(:,i)/norm(points(:,i)) |
---|
237 | p2=points(:,j)/norm(points(:,j)) |
---|
238 | CALL surf_triangle(cc,p1,p2,area) |
---|
239 | centr(:)=centr(:)+area*(p1+p2+cc) |
---|
240 | ENDDO |
---|
241 | END IF |
---|
242 | |
---|
243 | centr(:)=centr(:)/norm(centr(:)) |
---|
244 | |
---|
245 | END SUBROUTINE compute_centroid |
---|
246 | |
---|
247 | END MODULE spherical_geom_mod |
---|
248 | |
---|
249 | |
---|