| 1 | MODULE spherical_geom_mod |
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| 2 | USE genmod |
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| 3 | |
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| 4 | |
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| 5 | |
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| 6 | CONTAINS |
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| 7 | |
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| 8 | |
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| 9 | |
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| 10 | |
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| 11 | SUBROUTINE lonlat2xyz(lon,lat,xyz) |
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| 12 | IMPLICIT NONE |
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| 13 | REAL(rstd),INTENT(IN) :: lon |
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| 14 | REAL(rstd),INTENT(IN) :: lat |
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| 15 | REAL(rstd),INTENT(OUT) :: xyz(3) |
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| 16 | |
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| 17 | xyz(1)=cos(lon)*cos(lat) |
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| 18 | xyz(2)=sin(lon)*cos(lat) |
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| 19 | xyz(3)=sin(lat) |
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| 20 | |
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| 21 | END SUBROUTINE lonlat2xyz |
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| 22 | |
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| 23 | |
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| 24 | SUBROUTINE xyz2lonlat(xyz,lon,lat) |
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| 25 | IMPLICIT NONE |
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| 26 | REAL(rstd),INTENT(IN) :: xyz(3) |
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| 27 | REAL(rstd),INTENT(OUT) :: lon |
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| 28 | REAL(rstd),INTENT(OUT) :: lat |
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| 29 | |
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| 30 | REAL(rstd) :: xyzn(3) |
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| 31 | |
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| 32 | xyzn(:)=xyz(:)/sqrt(sum(xyz(:)**2)) |
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| 33 | |
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| 34 | lat=asin(xyzn(3)) |
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| 35 | lon=atan2(xyzn(2),xyzn(1)) |
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| 36 | END SUBROUTINE xyz2lonlat |
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| 37 | |
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| 38 | |
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| 39 | SUBROUTINE rotate_Ox(xyz_in, theta, xyz_out) |
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| 40 | IMPLICIT NONE |
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| 41 | REAL(rstd),INTENT(IN) :: xyz_in(3) |
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| 42 | REAL(rstd),INTENT(IN) :: theta |
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| 43 | REAL(rstd),INTENT(OUT) :: xyz_out(3) |
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| 44 | REAL(rstd) :: x,y,z |
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| 45 | REAL(rstd) :: sint, cost |
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| 46 | x= xyz_in(1) ; y=xyz_in(2) ; z= xyz_in(3) |
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| 47 | sint=sin(theta) ; cost = cos(theta) |
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| 48 | |
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| 49 | xyz_out(1) = x |
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| 50 | xyz_out(2) = y*cost-z*sint |
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| 51 | xyz_out(3) = y*sint+z*cost |
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| 52 | END SUBROUTINE rotate_Ox |
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| 53 | |
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| 54 | SUBROUTINE rotate_Oy(xyz_in, theta, xyz_out) |
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| 55 | IMPLICIT NONE |
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| 56 | REAL(rstd),INTENT(IN) :: xyz_in(3) |
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| 57 | REAL(rstd),INTENT(IN) :: theta |
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| 58 | REAL(rstd),INTENT(OUT) :: xyz_out(3) |
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| 59 | REAL(rstd) :: x,y,z |
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| 60 | REAL(rstd) :: sint, cost |
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| 61 | x= xyz_in(1) ; y=xyz_in(2) ; z= xyz_in(3) |
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| 62 | sint=sin(theta) ; cost = cos(theta) |
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| 63 | |
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| 64 | xyz_out(1) = x*cost + z*sint |
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| 65 | xyz_out(2) = y |
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| 66 | xyz_out(3) = -x*sint+z*cost |
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| 67 | END SUBROUTINE rotate_Oy |
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| 68 | |
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| 69 | SUBROUTINE rotate_Oz(xyz_in, theta, xyz_out) |
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| 70 | IMPLICIT NONE |
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| 71 | REAL(rstd),INTENT(IN) :: xyz_in(3) |
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| 72 | REAL(rstd),INTENT(IN) :: theta |
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| 73 | REAL(rstd),INTENT(OUT) :: xyz_out(3) |
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| 74 | REAL(rstd) :: x,y,z |
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| 75 | REAL(rstd) :: sint, cost |
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| 76 | x= xyz_in(1) ; y=xyz_in(2) ; z = xyz_in(3) |
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| 77 | sint=sin(theta) ; cost = cos(theta) |
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| 78 | |
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| 79 | xyz_out(1) = x*cost - y*sint |
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| 80 | xyz_out(2) = x*sint + y*cost |
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| 81 | xyz_out(3) = z |
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| 82 | END SUBROUTINE rotate_Oz |
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| 83 | |
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| 84 | ! lat/lon with respect to a displaced pole (rotated basis) : |
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| 85 | ! ( cos(lon0)*sin(lat0), sin(lon0)*sin(lat0), -cos(lat0)) |
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| 86 | ! (-sin(lon0), cos(lon0), 0) |
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| 87 | ! ( cos(lon0)*cos(lat0), sin(lon0)*cos(lat0), sin(lat0)) |
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| 88 | |
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| 89 | |
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| 90 | SUBROUTINE lonlat2xyz_relative(lon,lat,lon0,lat0, xyz) |
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| 91 | IMPLICIT NONE |
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| 92 | REAL(rstd),INTENT(IN) :: lon0, lat0, lon,lat |
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| 93 | REAL(rstd),INTENT(OUT) :: xyz(3) |
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| 94 | REAL(rstd) :: xx,yy,zz |
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| 95 | xx = cos(lon)*cos(lat) |
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| 96 | yy = sin(lon)*cos(lat) |
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| 97 | zz = sin(lat) |
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| 98 | xyz(1) = cos(lon0)*(sin(lat0)*xx+cos(lat0)*zz)-sin(lon0)*yy |
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| 99 | xyz(2) = sin(lon0)*(sin(lat0)*xx+cos(lat0)*zz)+cos(lon0)*yy |
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| 100 | xyz(3) = sin(lat0)*zz-cos(lat0)*xx |
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| 101 | END SUBROUTINE lonlat2xyz_relative |
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| 102 | |
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| 103 | SUBROUTINE xyz2lonlat_relative(xyz,lon0,lat0, lon,lat) |
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| 104 | IMPLICIT NONE |
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| 105 | REAL(rstd),INTENT(IN) :: xyz(3), lon0, lat0 |
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| 106 | REAL(rstd),INTENT(OUT) :: lon,lat |
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| 107 | REAL(rstd) :: xx,yy,zz |
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| 108 | xx = sin(lat0)*(xyz(1)*cos(lon0)+xyz(2)*sin(lon0))-cos(lat0)*xyz(3) |
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| 109 | yy = xyz(2)*cos(lon0)-xyz(1)*sin(lon0) |
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| 110 | zz = cos(lat0)*(xyz(1)*cos(lon0)+xyz(2)*sin(lon0))+sin(lat0)*xyz(3) |
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| 111 | lon = atan2(yy,xx) |
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| 112 | lat = asin(zz) |
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| 113 | END SUBROUTINE xyz2lonlat_relative |
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| 114 | |
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| 115 | SUBROUTINE schmidt_transform(xyz,cc, lon0, lat0) |
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| 116 | ! Based on formula (12) from Guo & Drake, JCP 2005 |
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| 117 | IMPLICIT NONE |
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| 118 | REAL(rstd),INTENT(INOUT) :: xyz(3) |
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| 119 | REAL(rstd), INTENT(IN) :: cc, lon0, lat0 ! stretching factor>0, lon/lat of zoomed area |
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| 120 | REAL(rstd) :: lat,lon,mu |
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| 121 | CALL xyz2lonlat_relative(xyz,lon0,lat0, lon,lat) |
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| 122 | mu = sin(lat) |
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| 123 | mu = ((cc-1)+mu*(cc+1)) / ((cc+1)+mu*(cc-1)) |
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| 124 | lat = asin(mu) |
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| 125 | CALL lonlat2xyz_relative(lon,lat, lon0,lat0, xyz) |
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| 126 | END SUBROUTINE schmidt_transform |
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| 127 | |
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| 128 | SUBROUTINE dist_cart(A,B,d) |
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| 129 | USE vector |
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| 130 | IMPLICIT NONE |
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| 131 | REAL(rstd),INTENT(IN) :: A(3) |
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| 132 | REAL(rstd),INTENT(IN) :: B(3) |
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| 133 | REAL(rstd),INTENT(OUT) :: d |
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| 134 | |
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| 135 | REAL(rstd) :: n(3) |
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| 136 | CALL cross_product2(A,B,n) |
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| 137 | d=asin(sqrt(sum(n**2))) |
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| 138 | |
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| 139 | END SUBROUTINE dist_cart |
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| 140 | |
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| 141 | |
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| 142 | SUBROUTINE dist_lonlat(lonA,latA,lonB,latB,d) |
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| 143 | IMPLICIT NONE |
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| 144 | REAL(rstd),INTENT(IN) :: lonA |
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| 145 | REAL(rstd),INTENT(IN) :: latA |
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| 146 | REAL(rstd),INTENT(IN) :: lonB |
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| 147 | REAL(rstd),INTENT(IN) :: latB |
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| 148 | REAL(rstd),INTENT(OUT) :: d |
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| 149 | |
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| 150 | d=acos(MAX(MIN(sin(latA)*sin(latB)+cos(latA)*cos(latB)*cos(lonA-lonB),1.),-1.)) |
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| 151 | |
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| 152 | END SUBROUTINE dist_lonlat |
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| 153 | |
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| 154 | SUBROUTINE surf_triangle(A,B,C,surf) |
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| 155 | REAL(rstd),INTENT(IN) :: A(3) |
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| 156 | REAL(rstd),INTENT(IN) :: B(3) |
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| 157 | REAL(rstd),INTENT(IN) :: C(3) |
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| 158 | REAL(rstd),INTENT(OUT) :: Surf |
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| 159 | |
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| 160 | REAL(rstd) :: AB,AC,BC |
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| 161 | REAL(rstd) :: s,x |
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| 162 | |
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| 163 | CALL dist_cart(A,B,AB) |
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| 164 | CALL dist_cart(A,C,AC) |
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| 165 | CALL dist_cart(B,C,BC) |
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| 166 | |
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| 167 | s=(AB+AC+BC)/2 |
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| 168 | x=tan(s/2) * tan((s-AB)/2) * tan((s-AC)/2) * tan((s-BC)/2) |
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| 169 | IF (x<0) x=0. |
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| 170 | surf=4*atan(sqrt( x)) |
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| 171 | |
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| 172 | END SUBROUTINE surf_triangle |
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| 173 | |
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| 174 | |
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| 175 | SUBROUTINE div_arc(A,B,frac,C) |
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| 176 | IMPLICIT NONE |
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| 177 | REAL(rstd),INTENT(IN) :: A(3) |
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| 178 | REAL(rstd),INTENT(IN) :: B(3) |
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| 179 | REAL(rstd),INTENT(IN) :: frac |
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| 180 | REAL(rstd),INTENT(OUT) :: C(3) |
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| 181 | |
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| 182 | REAL(rstd) :: d |
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| 183 | REAL(rstd) :: M(3,3) |
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| 184 | REAL(rstd) :: xa,xb,xc |
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| 185 | REAL(rstd) :: ya,yb,yc |
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| 186 | REAL(rstd) :: za,zb,zc |
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| 187 | |
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| 188 | |
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| 189 | xa=A(1) ; ya=A(2) ; za=A(3) |
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| 190 | xb=B(1) ; yb=B(2) ; zb=B(3) |
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| 191 | |
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| 192 | CALL dist_cart(A,B,d) |
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| 193 | |
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| 194 | C(1)=cos(frac*d) |
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| 195 | C(2)=cos((1-frac)*d) |
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| 196 | C(3)=0. |
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| 197 | |
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| 198 | xc=ya*zb-yb*za ; yc=-(xa*zb-xb*za) ; zc=xa*yb-xb*ya |
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| 199 | |
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| 200 | M(1,1)=xa ; M(1,2)=ya ; M(1,3)=za |
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| 201 | M(2,1)=xb ; M(2,2)=yb ; M(2,3)=zb |
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| 202 | M(3,1)=xc ; M(3,2)=yc ; M(3,3)=zc |
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| 203 | stop 'STOP' |
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| 204 | ! CALL DGESV(3,1,M,3,IPIV,C,3,info) |
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| 205 | |
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| 206 | END SUBROUTINE div_arc |
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| 207 | |
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| 208 | SUBROUTINE div_arc_bis(A,B,frac,C) |
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| 209 | IMPLICIT NONE |
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| 210 | REAL(rstd),INTENT(IN) :: A(3) |
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| 211 | REAL(rstd),INTENT(IN) :: B(3) |
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| 212 | REAL(rstd),INTENT(IN) :: frac |
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| 213 | REAL(rstd),INTENT(OUT) :: C(3) |
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| 214 | |
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| 215 | C=A*(1-frac)+B*frac |
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| 216 | C=C/sqrt(sum(C**2)) |
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| 217 | END SUBROUTINE div_arc_bis |
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| 218 | |
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| 219 | |
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| 220 | SUBROUTINE circumcenter(A0,B0,C0,center) |
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| 221 | USE vector |
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| 222 | IMPLICIT NONE |
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| 223 | REAL(rstd), INTENT(IN) :: A0(3),B0(3),C0(3) |
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| 224 | REAL(rstd), INTENT(OUT) :: Center(3) |
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| 225 | |
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| 226 | REAL(rstd) :: a(3),b(3),c(3), ac(3), ab(3), p1(3), q(3), p2(3) |
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| 227 | |
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| 228 | a=A0/sqrt(sum(A0**2)) |
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| 229 | b=B0/sqrt(sum(B0**2)) |
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| 230 | c=C0/sqrt(sum(C0**2)) |
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| 231 | |
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| 232 | ab=b-a |
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| 233 | ac=c-a |
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| 234 | CALL Cross_product2(ab,ac,p1) |
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| 235 | IF(.FALSE.) THEN ! Direct solution, round-off error |
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| 236 | center=p1/norm(p1) |
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| 237 | ELSE ! Two-step solution, stable |
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| 238 | q = SUM(ac**2)*ab-SUM(ab**2)*ac |
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| 239 | CALL Cross_product2(p1,q,p2) |
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| 240 | p2 = a + p2/(2.*SUM(p1**2)) |
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| 241 | center = p2/norm(p2) |
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| 242 | END IF |
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| 243 | END SUBROUTINE circumcenter |
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| 244 | |
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| 245 | |
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| 246 | SUBROUTINE compute_centroid(points,n,centr) |
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| 247 | USE vector |
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| 248 | IMPLICIT NONE |
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| 249 | INTEGER :: n |
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| 250 | REAL(rstd), INTENT(IN) :: points(3,n) |
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| 251 | REAL(rstd), INTENT(OUT) :: Centr(3) |
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| 252 | |
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| 253 | REAL(rstd) :: p1(3),p2(3),cross(3), cc(3) |
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| 254 | REAL(rstd) :: norm_cross, area |
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| 255 | INTEGER :: i,j |
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| 256 | |
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| 257 | centr(:)=0 |
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| 258 | IF(.FALSE.) THEN |
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| 259 | ! Gauss formula (subject to round-off error) |
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| 260 | DO i=1,n |
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| 261 | j=MOD(i,n)+1 |
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| 262 | p1=points(:,i)/norm(points(:,i)) |
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| 263 | p2=points(:,j)/norm(points(:,j)) |
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| 264 | CALL cross_product2(p1,p2,cross) |
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| 265 | norm_cross=norm(cross) |
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| 266 | if (norm_cross<1e-10) CYCLE |
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| 267 | centr(:)=centr(:)+asin(norm_cross)*cross(:)/norm_cross |
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| 268 | ENDDO |
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| 269 | ELSE |
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| 270 | ! Simple area-weighted average (second-order accurate, stable) |
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| 271 | cc=SUM(points,2) ! arithmetic average used as center |
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| 272 | cc=cc/norm(cc) |
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| 273 | DO i=1,n |
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| 274 | j=MOD(i,n)+1 |
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| 275 | p1=points(:,i)/norm(points(:,i)) |
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| 276 | p2=points(:,j)/norm(points(:,j)) |
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| 277 | CALL surf_triangle(cc,p1,p2,area) |
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| 278 | centr(:)=centr(:)+area*(p1+p2+cc) |
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| 279 | ENDDO |
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| 280 | END IF |
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| 281 | |
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| 282 | centr(:)=centr(:)/norm(centr(:)) |
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| 283 | |
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| 284 | END SUBROUTINE compute_centroid |
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| 285 | |
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| 286 | END MODULE spherical_geom_mod |
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| 287 | |
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| 288 | |
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