mapproject: Apply a Map Projection

Description Usage Arguments Details Value References Examples

Description

Converts latitude and longitude into projected coordinates.

Usage

1
mapproject(x, y, projection="", parameters=NULL, orientation=NULL)

Arguments

x,y

two vectors giving longitude and latitude coordinates of points on the earth's surface to be projected. A list containing components named x and y, giving the coordinates of the points to be projected may also be given. Missing values (NAs) are allowed. The coordinate system is degrees of longitude east of Greenwich (so the USA is bounded by negative longitudes) and degrees north of the equator.

projection

optional character string that names a map projection to use. If the string is "" then the previous projection is used, with parameters modified by the next two arguments.

parameters

optional numeric vector of parameters for use with the projection argument. This argument is optional only in the sense that certain projections do not require additional parameters. If a projection does require additional parameters, these must be given in the parameters argument.

orientation

An optional vector c(latitude,longitude,rotation) which describes where the "North Pole" should be when computing the projection. Normally this is c(90,0), which is appropriate for cylindrical and conic projections. For a planar projection, you should set it to the desired point of tangency. The third value is a clockwise rotation (in degrees), which defaults to the midrange of the longitude coordinates in the map. This means that two maps plotted with their own default orientation may not line up. To avoid this, you should not specify a projection twice but rather default to the previous projection using projection="". See the examples.

Details

Each standard projection is displayed with the Prime Meridian (longitude 0) being a straight vertical line, along which North is up. The orientation of nonstandard projections is specified by the three parameters=c(lat,lon,rot). Imagine a transparent gridded sphere around the globe. First turn the overlay about the North Pole so that the Prime Meridian (longitude 0) of the overlay coincides with meridian lon on the globe. Then tilt the North Pole of the overlay along its Prime Meridian to latitude lat on the globe. Finally again turn the overlay about its "North Pole" so that its Prime Meridian coincides with the previous position of (the overlay) meridian rot. Project the desired map in the standard form appropriate to the overlay, but presenting information from the underlying globe.

In the descriptions that follow each projection is shown as a function call; if it requires parameters, these are shown as arguments to the function. The descriptions are grouped into families.

Equatorial projections centered on the Prime Meridian (longitude 0). Parallels are straight horizontal lines.

mercator()

equally spaced straight meridians, conformal, straight compass courses

sinusoidal()

equally spaced parallels, equal-area, same as bonne(0)

cylequalarea(lat0)

equally spaced straight meridians, equal-area, true scale on lat0

cylindrical()

central projection on tangent cylinder

rectangular(lat0)

equally spaced parallels, equally spaced straight meridians, true scale on lat0

gall(lat0)

parallels spaced stereographically on prime meridian, equally spaced straight meridians, true scale on lat0

mollweide()

(homalographic) equal-area, hemisphere is a circle

gilbert()

sphere conformally mapped on hemisphere and viewed orthographically

Azimuthal projections centered on the North Pole. Parallels are concentric circles. Meridians are equally spaced radial lines.

azequidistant()

equally spaced parallels, true distances from pole

azequalarea()

equal-area

gnomonic()

central projection on tangent plane, straight great circles

perspective(dist)

viewed along earth's axis dist earth radii from center of earth

orthographic()

viewed from infinity

stereographic()

conformal, projected from opposite pole

laue()

radius = tan(2 * colatitude) used in xray crystallography

fisheye(n)

stereographic seen through medium with refractive index n

newyorker(r)

radius = log(colatitude/r) map from viewing pedestal of radius r degrees

Polar conic projections symmetric about the Prime Meridian. Parallels are segments of concentric circles. Except in the Bonne projection, meridians are equally spaced radial lines orthogonal to the parallels.

conic(lat0)

central projection on cone tangent at lat0

simpleconic(lat0,lat1)

equally spaced parallels, true scale on lat0 and lat1

lambert(lat0,lat1)

conformal, true scale on lat0 and lat1

albers(lat0,lat1)

equal-area, true scale on lat0 and lat1

bonne(lat0)

equally spaced parallels, equal-area, parallel lat0 developed from tangent cone

Projections with bilateral symmetry about the Prime Meridian and the equator.

polyconic()

parallels developed from tangent cones, equally spaced along Prime Meridian

aitoff()

equal-area projection of globe onto 2-to-1 ellipse, based on azequalarea

lagrange()

conformal, maps whole sphere into a circle

bicentric(lon0)

points plotted at true azimuth from two centers on the equator at longitudes +lon0 and -lon0, great circles are straight lines (a stretched gnomonic projection)

elliptic(lon0)

points are plotted at true distance from two centers on the equator at longitudes +lon0 and -lon0

globular()

hemisphere is circle, circular arc meridians equally spaced on equator, circular arc parallels equally spaced on 0- and 90-degree meridians

vandergrinten()

sphere is circle, meridians as in globular, circular arc parallels resemble mercator

eisenlohr()

conformal with no singularities, shaped like polyconic

Doubly periodic conformal projections.

guyou

W and E hemispheres are square

square

world is square with Poles at diagonally opposite corners

tetra

map on tetrahedron with edge tangent to Prime Meridian at S Pole, unfolded into equilateral triangle

hex

world is hexagon centered on N Pole, N and S hemispheres are equilateral triangles

Miscellaneous projections.

harrison(dist,angle)

oblique perspective from above the North Pole, dist earth radii from center of earth, looking along the Date Line angle degrees off vertical

trapezoidal(lat0,lat1)

equally spaced parallels, straight meridians equally spaced along parallels, true scale at lat0 and lat1 on Prime Meridian

lune(lat,angle)

conformal, polar cap above latitude lat maps to convex lune with given angle at 90E and 90W

Retroazimuthal projections. At every point the angle between vertical and a straight line to "Mecca", latitude lat0 on the prime meridian, is the true bearing of Mecca.

mecca(lat0)

equally spaced vertical meridians

homing(lat0)

distances to Mecca are true

Maps based on the spheroid. Of geodetic quality, these projections do not make sense for tilted orientations.

sp\_mercator()

Mercator on the spheroid.

sp\_albers(lat0,lat1)

Albers on the spheroid.

Value

list with components named x and y, containing the projected coordinates. NAs project to NAs. Points deemed unprojectable (such as north of 80 degrees latitude in the Mercator projection) are returned as NA. Because of the ambiguity of the first two arguments, the other arguments must be given by name.

Each time mapproject is called, it leaves on frame 0 the dataset .Last.projection, which is a list with components projection, parameters, and orientation giving the arguments from the call to mapproject or as constructed (for orientation). Subsequent calls to mapproject will get missing information from .Last.projection. Since map uses mapproject to do its projections, calls to mapproject after a call to map need not supply any arguments other than the data.

References

Richard A. Becker, and Allan R. Wilks, "Maps in S", AT\&T Bell Laboratories Statistics Research Report, 1991. http://www.research.att.com/areas/stat/doc/93.2.ps

M. D. McIlroy, Documentation from the Tenth Edition UNIX Manual, Volume 1, Saunders College Publishing, 1990.

Examples

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library(maps)
# Bonne equal-area projection with state abbreviations
map("state",proj='bonne', param=45)
data(state)
text(mapproject(state.center), state.abb)

# this does not work because the default orientations are different:
map("state",proj='bonne', param=45)
text(mapproject(state.center,proj='bonne',param=45),state.abb)

map("state",proj="albers",par=c(30,40))
map("state",par=c(20,50)) # another Albers projection

map("world",proj="gnomonic",orient=c(0,-100,0)) # example of orient
# see map.grid for more examples

# tests of projections added RSB 091101
projlist <- c("aitoff", "albers", "azequalarea", "azequidist", "bicentric",
 "bonne", "conic", "cylequalarea", "cylindrical", "eisenlohr", "elliptic",
 "fisheye", "gall", "gilbert", "guyou", "harrison", "hex", "homing",
 "lagrange", "lambert", "laue", "lune", "mercator", "mollweide", "newyorker",
 "orthographic", "perspective", "polyconic", "rectangular", "simpleconic",
 "sinusoidal", "tetra", "trapezoidal")
x <- seq(-100, 0, 10)
y <- seq(-45, 45, 10)
xy <- expand.grid(x=x, y=y)
pf <- c(0, 2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 2,
 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2)
res <- vector(mode="list", length=length(projlist))
for (i in seq(along=projlist)) {
 if (pf[i] == 0) res[[i]] <- mapproject(xy$x, xy$y, projlist[i])
 else if (pf[i] == 1) res[[i]] <- mapproject(xy$x, xy$y, projlist[i], 0)
 else res[[i]] <- mapproject(xy$x, xy$y, projlist[i], c(0,0))
}
names(res) <- projlist
lapply(res, function(p) rbind(p$x, p$y))

Example output

Loading required package: maps
Warning message:
In map("world", proj = "gnomonic", orient = c(0, -100, 0)) :
  projection failed for some data
$aitoff
           [,1]       [,2]       [,3]       [,4]        [,5]       [,6]
[1,] -0.4665820 -0.3749122 -0.2821419 -0.1885496 -0.09441113  0.0000000
[2,] -0.5520135 -0.5480850 -0.5450562 -0.5429070 -0.54162312 -0.5411961
            [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.09441113  0.1885496  0.2821419  0.3749122  0.4665820 -0.5245276
[2,] -0.54162312 -0.5429070 -0.5450562 -0.5480850 -0.5520135 -0.4345271
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] -0.4212017 -0.3168209 -0.2116513 -0.1059567  0.0000000  0.1059567
[2,] -0.4311568 -0.4285627 -0.4267243 -0.4256270 -0.4252622 -0.4256270
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.2116513  0.3168209  0.4212017  0.5245276 -0.5676126 -0.4555939
[2,] -0.4267243 -0.4285627 -0.4311568 -0.4345271 -0.3131456 -0.3105766
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.3425721 -0.2287987 -0.1145245  0.0000000  0.1145245  0.2287987
[2,] -0.3086017 -0.3072033 -0.3063691 -0.3060918 -0.3063691 -0.3072033
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.3425721  0.4555939  0.5676126 -0.5961727 -0.4783805 -0.3596273
[2,] -0.3086017 -0.3105766 -0.3131456 -0.1889932 -0.1873891 -0.1861568
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] -0.2401527 -0.1201967  0.0000000  0.1201967  0.2401527  0.3596273
[2,] -0.1852847 -0.1847647 -0.1845919 -0.1847647 -0.1852847 -0.1861568
          [,43]      [,44]      [,45]      [,46]      [,47]       [,48]
[1,]  0.4783805  0.5961727 -0.6104065 -0.4897339 -0.3681233 -0.24580777
[2,] -0.1873891 -0.1889932 -0.0631819 -0.0626369 -0.0622184 -0.06192231
           [,49]       [,50]       [,51]       [,52]      [,53]      [,54]
[1,] -0.12302165  0.00000000  0.12302165  0.24580777  0.3681233  0.4897339
[2,] -0.06174579 -0.06168713 -0.06174579 -0.06192231 -0.0622184 -0.0626369
          [,55]      [,56]      [,57]      [,58]       [,59]       [,60]
[1,]  0.6104065 -0.6104065 -0.4897339 -0.3681233 -0.24580777 -0.12302165
[2,] -0.0631819  0.0631819  0.0626369  0.0622184  0.06192231  0.06174579
             [,61]      [,62]      [,63]     [,64]     [,65]     [,66]
[1,] -1.510899e-17 0.12302165 0.24580777 0.3681233 0.4897339 0.6104065
[2,]  6.168713e-02 0.06174579 0.06192231 0.0622184 0.0626369 0.0631819
          [,67]      [,68]      [,69]      [,70]      [,71]         [,72]
[1,] -0.5961727 -0.4783805 -0.3596273 -0.2401527 -0.1201967 -4.521198e-17
[2,]  0.1889932  0.1873891  0.1861568  0.1852847  0.1847647  1.845919e-01
         [,73]     [,74]     [,75]     [,76]     [,77]      [,78]      [,79]
[1,] 0.1201967 0.2401527 0.3596273 0.4783805 0.5961727 -0.5676126 -0.4555939
[2,] 0.1847647 0.1852847 0.1861568 0.1873891 0.1889932  0.3131456  0.3105766
          [,80]      [,81]      [,82]         [,83]     [,84]     [,85]
[1,] -0.3425721 -0.2287987 -0.1145245 -7.497088e-17 0.1145245 0.2287987
[2,]  0.3086017  0.3072033  0.3063691  3.060918e-01 0.3063691 0.3072033
         [,86]     [,87]     [,88]      [,89]      [,90]      [,91]      [,92]
[1,] 0.3425721 0.4555939 0.5676126 -0.5245276 -0.4212017 -0.3168209 -0.2116513
[2,] 0.3086017 0.3105766 0.3131456  0.4345271  0.4311568  0.4285627  0.4267243
          [,93]         [,94]     [,95]     [,96]     [,97]     [,98]     [,99]
[1,] -0.1059567 -1.041592e-16 0.1059567 0.2116513 0.3168209 0.4212017 0.5245276
[2,]  0.4256270  4.252622e-01 0.4256270 0.4267243 0.4285627 0.4311568 0.4345271
         [,100]     [,101]     [,102]     [,103]      [,104]        [,105]
[1,] -0.4665820 -0.3749122 -0.2821419 -0.1885496 -0.09441113 -1.325548e-16
[2,]  0.5520135  0.5480850  0.5450562  0.5429070  0.54162312  5.411961e-01
         [,106]    [,107]    [,108]    [,109]    [,110]
[1,] 0.09441113 0.1885496 0.2821419 0.3749122 0.4665820
[2,] 0.54162312 0.5429070 0.5450562 0.5480850 0.5520135

$albers
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] -100  -90  -80  -70  -60  -50  -40  -30  -20   -10     0  -100   -90   -80
[2,]  -45  -45  -45  -45  -45  -45  -45  -45  -45   -45   -45   -35   -35   -35
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,]   -70   -60   -50   -40   -30   -20   -10     0  -100   -90   -80   -70
[2,]   -35   -35   -35   -35   -35   -35   -35   -35   -25   -25   -25   -25
     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,]   -60   -50   -40   -30   -20   -10     0  -100   -90   -80   -70   -60
[2,]   -25   -25   -25   -25   -25   -25   -25   -15   -15   -15   -15   -15
     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
[1,]   -50   -40   -30   -20   -10     0  -100   -90   -80   -70   -60   -50
[2,]   -15   -15   -15   -15   -15   -15    -5    -5    -5    -5    -5    -5
     [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
[1,]   -40   -30   -20   -10     0  -100   -90   -80   -70   -60   -50   -40
[2,]    -5    -5    -5    -5    -5     5     5     5     5     5     5     5
     [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
[1,]   -30   -20   -10     0  -100   -90   -80   -70   -60   -50   -40   -30
[2,]     5     5     5     5    15    15    15    15    15    15    15    15
     [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,]   -20   -10     0  -100   -90   -80   -70   -60   -50   -40   -30   -20
[2,]    15    15    15    25    25    25    25    25    25    25    25    25
     [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,]   -10     0  -100   -90   -80   -70   -60   -50   -40   -30   -20   -10
[2,]    25    25    35    35    35    35    35    35    35    35    35    35
     [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
[1,]     0   -100    -90    -80    -70    -60    -50    -40    -30    -20
[2,]    35     45     45     45     45     45     45     45     45     45
     [,109] [,110]
[1,]    -10      0
[2,]     45     45

$azequalarea
           [,1]       [,2]       [,3]       [,4]       [,5]      [,6]
[1,] -1.0008853 -0.8398425 -0.6532815 -0.4468709 -0.2268823  0.000000
[2,] -0.8398425 -1.0008853 -1.1315167 -1.2277676 -1.2867133 -1.306563
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.2268823  0.4468709  0.6532815  0.8398425  1.0008853 -0.9609436
[2,] -1.2867133 -1.2277676 -1.1315167 -1.0008853 -0.8398425 -0.8063274
          [,13]      [,14]      [,15]      [,16]     [,17]      [,18]
[1,] -0.8063274 -0.6272114 -0.4290378 -0.2178282  0.000000  0.2178282
[2,] -0.9609436 -1.0863620 -1.1787718 -1.2353653 -1.254423 -1.2353653
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.4290378  0.6272114  0.8063274  0.9609436 -0.9136885 -0.7666757
[2,] -1.1787718 -1.0863620 -0.9609436 -0.8063274 -0.7666757 -0.9136885
          [,25]      [,26]      [,27]     [,28]      [,29]      [,30]
[1,] -0.5963678 -0.4079396 -0.2071164  0.000000  0.2071164  0.4079396
[2,] -1.0329393 -1.1208049 -1.1746153 -1.192736 -1.1746153 -1.1208049
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.5963678  0.7666757  0.9136885 -0.8594797 -0.7211891 -0.5609855
[2,] -1.0329393 -0.9136885 -0.7666757 -0.7211891 -0.8594797 -0.9716554
          [,37]      [,38]     [,39]      [,40]      [,41]      [,42]
[1,] -0.3837367 -0.1948282  0.000000  0.1948282  0.3837367  0.5609855
[2,] -1.0543079 -1.1049258 -1.121971 -1.1049258 -1.0543079 -0.9716554
          [,43]      [,44]      [,45]      [,46]      [,47]      [,48]
[1,]  0.7211891  0.8594797 -0.7987297 -0.6702138 -0.5213338 -0.3566133
[2,] -0.8594797 -0.7211891 -0.6702138 -0.7987297 -0.9029766 -0.9797871
          [,49]     [,50]      [,51]      [,52]      [,53]      [,54]
[1,] -0.1810573  0.000000  0.1810573  0.3566133  0.5213338  0.6702138
[2,] -1.0268271 -1.042668 -1.0268271 -0.9797871 -0.9029766 -0.7987297
          [,55]      [,56]      [,57]      [,58]      [,59]      [,60]
[1,]  0.7987297 -0.7319009 -0.6141378 -0.4777144 -0.3267759 -0.1659085
[2,] -0.6702138 -0.6141378 -0.7319009 -0.8274256 -0.8978094 -0.9409137
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,]  0.0000000  0.1659085  0.3267759  0.4777144  0.6141378  0.7319009
[2,] -0.9554288 -0.9409137 -0.8978094 -0.8274256 -0.7319009 -0.6141378
          [,67]      [,68]      [,69]      [,70]      [,71]      [,72]
[1,] -0.6595020 -0.5533879 -0.4304593 -0.2944515 -0.1494970  0.0000000
[2,] -0.5533879 -0.6595020 -0.7455774 -0.8089989 -0.8478394 -0.8609187
          [,73]      [,74]      [,75]      [,76]      [,77]      [,78]
[1,]  0.1494970  0.2944515  0.4304593  0.5533879  0.6595020 -0.5820838
[2,] -0.8478394 -0.8089989 -0.7455774 -0.6595020 -0.5533879 -0.4884263
          [,79]      [,80]      [,81]      [,82]      [,83]      [,84]
[1,] -0.4884263 -0.3799282 -0.2598862 -0.1319477  0.0000000  0.1319477
[2,] -0.5820838 -0.6580549 -0.7140314 -0.7483125 -0.7598564 -0.7483125
          [,85]      [,86]      [,87]      [,88]      [,89]      [,90]
[1,]  0.2598862  0.3799282  0.4884263  0.5820838 -0.5002356 -0.4197475
[2,] -0.7140314 -0.6580549 -0.5820838 -0.4884263 -0.4197475 -0.5002356
          [,91]      [,92]      [,93]      [,94]      [,95]      [,96]
[1,] -0.3265056 -0.2233430 -0.1133942  0.0000000  0.1133942  0.2233430
[2,] -0.5655242 -0.6136298 -0.6430904 -0.6530112 -0.6430904 -0.6136298
          [,97]      [,98]      [,99]     [,100]     [,101]     [,102]
[1,]  0.3265056  0.4197475  0.5002356 -0.4145803 -0.3478741 -0.2705981
[2,] -0.5655242 -0.5002356 -0.4197475 -0.3478741 -0.4145803 -0.4686896
        [,103]      [,104]     [,105]      [,106]    [,107]     [,108]
[1,] -0.185100 -0.09397772  0.0000000  0.09397772  0.185100  0.2705981
[2,] -0.508558 -0.53297412 -0.5411961 -0.53297412 -0.508558 -0.4686896
         [,109]     [,110]
[1,]  0.3478741  0.4145803
[2,] -0.4145803 -0.3478741

$azequidist
          [,1]      [,2]      [,3]      [,4]       [,5]      [,6]       [,7]
[1,] -1.804950 -1.514533 -1.178097 -0.805866 -0.4091489  0.000000  0.4091489
[2,] -1.514533 -1.804950 -2.040524 -2.214099 -2.3203986 -2.356194 -2.3203986
          [,8]      [,9]     [,10]     [,11]     [,12]     [,13]     [,14]
[1,]  0.805866  1.178097  1.514533  1.804950 -1.671250 -1.402345 -1.090831
[2,] -2.214099 -2.040524 -1.804950 -1.514533 -1.402345 -1.671250 -1.889374
          [,15]      [,16]     [,17]      [,18]      [,19]     [,20]     [,21]
[1,] -0.7461722 -0.3788416  0.000000  0.3788416  0.7461722  1.090831  1.402345
[2,] -2.0500913 -2.1485172 -2.181662 -2.1485172 -2.0500913 -1.889374 -1.671250
         [,22]     [,23]     [,24]     [,25]      [,26]      [,27]     [,28]
[1,]  1.671250 -1.537550 -1.290157 -1.003564 -0.6864784 -0.3485342  0.000000
[2,] -1.402345 -1.290157 -1.537550 -1.738224 -1.8860840 -1.9766358 -2.007129
          [,29]      [,30]     [,31]     [,32]     [,33]    [,34]    [,35]
[1,]  0.3485342  0.6864784  1.003564  1.290157  1.537550 -1.40385 -1.17797
[2,] -1.9766358 -1.8860840 -1.738224 -1.537550 -1.290157 -1.17797 -1.40385
          [,36]      [,37]      [,38]     [,39]      [,40]      [,41]
[1,] -0.9162979 -0.6267846 -0.3182269  0.000000  0.3182269  0.6267846
[2,] -1.5870744 -1.7220767 -1.8047545 -1.832596 -1.8047545 -1.7220767
          [,42]    [,43]    [,44]     [,45]     [,46]      [,47]      [,48]
[1,]  0.9162979  1.17797  1.40385 -1.270150 -1.065782 -0.8290314 -0.5670909
[2,] -1.5870744 -1.40385 -1.17797 -1.065782 -1.270150 -1.4359245 -1.5580694
          [,49]     [,50]      [,51]      [,52]      [,53]     [,54]     [,55]
[1,] -0.2879196  0.000000  0.2879196  0.5670909  0.8290314  1.065782  1.270150
[2,] -1.6328731 -1.658063 -1.6328731 -1.5580694 -1.4359245 -1.270150 -1.065782
          [,56]      [,57]      [,58]      [,59]      [,60]    [,61]      [,62]
[1,] -1.1364498 -0.9535946 -0.7417649 -0.5073971 -0.2576123  0.00000  0.2576123
[2,] -0.9535946 -1.1364498 -1.2847745 -1.3940621 -1.4609917 -1.48353 -1.4609917
          [,63]      [,64]      [,65]      [,66]     [,67]     [,68]      [,69]
[1,]  0.5073971  0.7417649  0.9535946  1.1364498 -1.002750 -0.841407 -0.6544985
[2,] -1.3940621 -1.2847745 -1.1364498 -0.9535946 -0.841407 -1.002750 -1.1336246
          [,70]      [,71]     [,72]      [,73]      [,74]      [,75]     [,76]
[1,] -0.4477033 -0.2273049  0.000000  0.2273049  0.4477033  0.6544985  0.841407
[2,] -1.2300548 -1.2891103 -1.308997 -1.2891103 -1.2300548 -1.1336246 -1.002750
         [,77]      [,78]      [,79]      [,80]      [,81]      [,82]     [,83]
[1,]  1.002750 -0.8690499 -0.7292194 -0.5672320 -0.3880095 -0.1969976  0.000000
[2,] -0.841407 -0.7292194 -0.8690499 -0.9824747 -1.0660475 -1.1172290 -1.134464
          [,84]      [,85]      [,86]      [,87]      [,88]      [,89]
[1,]  0.1969976  0.3880095  0.5672320  0.7292194  0.8690499 -0.7353499
[2,] -1.1172290 -1.0660475 -0.9824747 -0.8690499 -0.7292194 -0.6170318
          [,90]      [,91]      [,92]      [,93]      [,94]      [,95]
[1,] -0.6170318 -0.4799655 -0.3283158 -0.1666903  0.0000000  0.1666903
[2,] -0.7353499 -0.8313247 -0.9020402 -0.9453476 -0.9599311 -0.9453476
          [,96]      [,97]      [,98]      [,99]     [,100]     [,101]
[1,]  0.3283158  0.4799655  0.6170318  0.7353499 -0.6016499 -0.5048442
[2,] -0.9020402 -0.8313247 -0.7353499 -0.6170318 -0.5048442 -0.6016499
         [,102]     [,103]     [,104]     [,105]     [,106]     [,107]
[1,] -0.3926991 -0.2686220 -0.1363830  0.0000000  0.1363830  0.2686220
[2,] -0.6801748 -0.7380329 -0.7734662 -0.7853982 -0.7734662 -0.7380329
         [,108]     [,109]     [,110]
[1,]  0.3926991  0.5048442  0.6016499
[2,] -0.6801748 -0.6016499 -0.5048442

$bicentric
          [,1]       [,2]       [,3]       [,4]      [,5] [,6]      [,7]
[1,] -1.191754 -0.8390996 -0.5773503 -0.3639702 -0.176327    0  0.176327
[2,] -1.555724 -1.3054073 -1.1547005 -1.0641778 -1.015427   -1 -1.015427
           [,8]       [,9]      [,10]     [,11]     [,12]      [,13]      [,14]
[1,]  0.3639702  0.5773503  0.8390996  1.191754 -1.191754 -0.8390996 -0.5773503
[2,] -1.0641778 -1.1547005 -1.3054073 -1.555724 -1.089330 -0.9140560 -0.8085300
          [,15]      [,16]      [,17]      [,18]      [,19]      [,20]
[1,] -0.3639702 -0.1763270  0.0000000  0.1763270  0.3639702  0.5773503
[2,] -0.7451453 -0.7110094 -0.7002075 -0.7110094 -0.7451453 -0.8085300
          [,21]     [,22]      [,23]      [,24]      [,25]      [,26]
[1,]  0.8390996  1.191754 -1.1917536 -0.8390996 -0.5773503 -0.3639702
[2,] -0.9140560 -1.089330 -0.7254459 -0.6087214 -0.5384457 -0.4962342
          [,27]      [,28]      [,29]      [,30]      [,31]      [,32]
[1,] -0.1763270  0.0000000  0.1763270  0.3639702  0.5773503  0.8390996
[2,] -0.4735012 -0.4663077 -0.4735012 -0.4962342 -0.5384457 -0.6087214
          [,33]      [,34]      [,35]      [,36]      [,37]      [,38]
[1,]  1.1917536 -1.1917536 -0.8390996 -0.5773503 -0.3639702 -0.1763270
[2,] -0.7254459 -0.4168549 -0.3497828 -0.3094011 -0.2851456 -0.2720827
          [,39]      [,40]      [,41]      [,42]      [,43]      [,44]
[1,]  0.0000000  0.1763270  0.3639702  0.5773503  0.8390996  1.1917536
[2,] -0.2679492 -0.2720827 -0.2851456 -0.3094011 -0.3497828 -0.4168549
          [,45]      [,46]      [,47]       [,48]       [,49]       [,50]
[1,] -1.1917536 -0.8390996 -0.5773503 -0.36397023 -0.17632698  0.00000000
[2,] -0.1361082 -0.1142083 -0.1010232 -0.09310349 -0.08883832 -0.08748866
           [,51]       [,52]      [,53]      [,54]      [,55]      [,56]
[1,]  0.17632698  0.36397023  0.5773503  0.8390996  1.1917536 -1.1917536
[2,] -0.08883832 -0.09310349 -0.1010232 -0.1142083 -0.1361082  0.1361082
          [,57]      [,58]       [,59]       [,60]      [,61]      [,62]
[1,] -0.8390996 -0.5773503 -0.36397023 -0.17632698 0.00000000 0.17632698
[2,]  0.1142083  0.1010232  0.09310349  0.08883832 0.08748866 0.08883832
          [,63]     [,64]     [,65]     [,66]      [,67]      [,68]      [,69]
[1,] 0.36397023 0.5773503 0.8390996 1.1917536 -1.1917536 -0.8390996 -0.5773503
[2,] 0.09310349 0.1010232 0.1142083 0.1361082  0.4168549  0.3497828  0.3094011
          [,70]      [,71]     [,72]     [,73]     [,74]     [,75]     [,76]
[1,] -0.3639702 -0.1763270 0.0000000 0.1763270 0.3639702 0.5773503 0.8390996
[2,]  0.2851456  0.2720827 0.2679492 0.2720827 0.2851456 0.3094011 0.3497828
         [,77]      [,78]      [,79]      [,80]      [,81]      [,82]     [,83]
[1,] 1.1917536 -1.1917536 -0.8390996 -0.5773503 -0.3639702 -0.1763270 0.0000000
[2,] 0.4168549  0.7254459  0.6087214  0.5384457  0.4962342  0.4735012 0.4663077
         [,84]     [,85]     [,86]     [,87]     [,88]     [,89]      [,90]
[1,] 0.1763270 0.3639702 0.5773503 0.8390996 1.1917536 -1.191754 -0.8390996
[2,] 0.4735012 0.4962342 0.5384457 0.6087214 0.7254459  1.089330  0.9140560
          [,91]      [,92]      [,93]     [,94]     [,95]     [,96]     [,97]
[1,] -0.5773503 -0.3639702 -0.1763270 0.0000000 0.1763270 0.3639702 0.5773503
[2,]  0.8085300  0.7451453  0.7110094 0.7002075 0.7110094 0.7451453 0.8085300
         [,98]    [,99]    [,100]     [,101]     [,102]     [,103]    [,104]
[1,] 0.8390996 1.191754 -1.191754 -0.8390996 -0.5773503 -0.3639702 -0.176327
[2,] 0.9140560 1.089330  1.555724  1.3054073  1.1547005  1.0641778  1.015427
     [,105]   [,106]    [,107]    [,108]    [,109]   [,110]
[1,]      0 0.176327 0.3639702 0.5773503 0.8390996 1.191754
[2,]      1 1.015427 1.0641778 1.1547005 1.3054073 1.555724

$bonne
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] -0.6170671 -0.4936537 -0.3702402 -0.2468268 -0.1234134  0.0000000
[2,] -0.7853982 -0.7853982 -0.7853982 -0.7853982 -0.7853982 -0.7853982
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.1234134  0.2468268  0.3702402  0.4936537  0.6170671 -0.7148450
[2,] -0.7853982 -0.7853982 -0.7853982 -0.7853982 -0.7853982 -0.6108652
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] -0.5718760 -0.4289070 -0.2859380 -0.1429690  0.0000000  0.1429690
[2,] -0.6108652 -0.6108652 -0.6108652 -0.6108652 -0.6108652 -0.6108652
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.2859380  0.4289070  0.5718760  0.7148450 -0.7909027 -0.6327222
[2,] -0.6108652 -0.6108652 -0.6108652 -0.6108652 -0.4363323 -0.4363323
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.4745416 -0.3163611 -0.1581805  0.0000000  0.1581805  0.3163611
[2,] -0.4363323 -0.4363323 -0.4363323 -0.4363323 -0.4363323 -0.4363323
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.4745416  0.6327222  0.7909027 -0.8429293 -0.6743434 -0.5057576
[2,] -0.4363323 -0.4363323 -0.4363323 -0.2617994 -0.2617994 -0.2617994
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] -0.3371717 -0.1685859  0.0000000  0.1685859  0.3371717  0.5057576
[2,] -0.2617994 -0.2617994 -0.2617994 -0.2617994 -0.2617994 -0.2617994
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.6743434  0.8429293 -0.86934387 -0.69547510 -0.52160632 -0.34773755
[2,] -0.2617994 -0.2617994 -0.08726646 -0.08726646 -0.08726646 -0.08726646
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.17386877  0.00000000  0.17386877  0.34773755  0.52160632  0.69547510
[2,] -0.08726646 -0.08726646 -0.08726646 -0.08726646 -0.08726646 -0.08726646
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.86934387 -0.86934387 -0.69547510 -0.52160632 -0.34773755 -0.17386877
[2,] -0.08726646  0.08726646  0.08726646  0.08726646  0.08726646  0.08726646
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.17386877 0.34773755 0.52160632 0.69547510 0.86934387
[2,] 0.08726646 0.08726646 0.08726646 0.08726646 0.08726646 0.08726646
          [,67]      [,68]      [,69]      [,70]      [,71]     [,72]     [,73]
[1,] -0.8429293 -0.6743434 -0.5057576 -0.3371717 -0.1685859 0.0000000 0.1685859
[2,]  0.2617994  0.2617994  0.2617994  0.2617994  0.2617994 0.2617994 0.2617994
         [,74]     [,75]     [,76]     [,77]      [,78]      [,79]      [,80]
[1,] 0.3371717 0.5057576 0.6743434 0.8429293 -0.7909027 -0.6327222 -0.4745416
[2,] 0.2617994 0.2617994 0.2617994 0.2617994  0.4363323  0.4363323  0.4363323
          [,81]      [,82]     [,83]     [,84]     [,85]     [,86]     [,87]
[1,] -0.3163611 -0.1581805 0.0000000 0.1581805 0.3163611 0.4745416 0.6327222
[2,]  0.4363323  0.4363323 0.4363323 0.4363323 0.4363323 0.4363323 0.4363323
         [,88]      [,89]      [,90]      [,91]      [,92]      [,93]     [,94]
[1,] 0.7909027 -0.7148450 -0.5718760 -0.4289070 -0.2859380 -0.1429690 0.0000000
[2,] 0.4363323  0.6108652  0.6108652  0.6108652  0.6108652  0.6108652 0.6108652
         [,95]     [,96]     [,97]     [,98]     [,99]     [,100]     [,101]
[1,] 0.1429690 0.2859380 0.4289070 0.5718760 0.7148450 -0.6170671 -0.4936537
[2,] 0.6108652 0.6108652 0.6108652 0.6108652 0.6108652  0.7853982  0.7853982
         [,102]     [,103]     [,104]    [,105]    [,106]    [,107]    [,108]
[1,] -0.3702402 -0.2468268 -0.1234134 0.0000000 0.1234134 0.2468268 0.3702402
[2,]  0.7853982  0.7853982  0.7853982 0.7853982 0.7853982 0.7853982 0.7853982
        [,109]    [,110]
[1,] 0.4936537 0.6170671
[2,] 0.7853982 0.7853982

$conic
           [,1]       [,2]       [,3]       [,4]       [,5] [,6]       [,7]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329    0  0.1745329
[2,] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000   -1 -1.0000000
           [,8]       [,9]      [,10]      [,11]      [,12]      [,13]
[1,]  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317
[2,] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -0.7002075 -0.7002075
          [,14]      [,15]      [,16]      [,17]      [,18]      [,19]
[1,] -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659
[2,] -0.7002075 -0.7002075 -0.7002075 -0.7002075 -0.7002075 -0.7002075
          [,20]      [,21]      [,22]      [,23]      [,24]      [,25]
[1,]  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] -0.7002075 -0.7002075 -0.7002075 -0.4663077 -0.4663077 -0.4663077
          [,26]      [,27]      [,28]      [,29]      [,30]      [,31]
[1,] -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659  0.5235988
[2,] -0.4663077 -0.4663077 -0.4663077 -0.4663077 -0.4663077 -0.4663077
          [,32]      [,33]      [,34]      [,35]      [,36]      [,37]
[1,]  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659
[2,] -0.4663077 -0.4663077 -0.2679492 -0.2679492 -0.2679492 -0.2679492
          [,38]      [,39]      [,40]      [,41]      [,42]      [,43]
[1,] -0.1745329  0.0000000  0.1745329  0.3490659  0.5235988  0.6981317
[2,] -0.2679492 -0.2679492 -0.2679492 -0.2679492 -0.2679492 -0.2679492
          [,44]       [,45]       [,46]       [,47]       [,48]       [,49]
[1,]  0.8726646 -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293
[2,] -0.2679492 -0.08748866 -0.08748866 -0.08748866 -0.08748866 -0.08748866
           [,50]       [,51]       [,52]       [,53]       [,54]       [,55]
[1,]  0.00000000  0.17453293  0.34906585  0.52359878  0.69813170  0.87266463
[2,] -0.08748866 -0.08748866 -0.08748866 -0.08748866 -0.08748866 -0.08748866
           [,56]       [,57]       [,58]       [,59]       [,60]      [,61]
[1,] -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293 0.00000000
[2,]  0.08748866  0.08748866  0.08748866  0.08748866  0.08748866 0.08748866
          [,62]      [,63]      [,64]      [,65]      [,66]      [,67]
[1,] 0.17453293 0.34906585 0.52359878 0.69813170 0.87266463 -0.8726646
[2,] 0.08748866 0.08748866 0.08748866 0.08748866 0.08748866  0.2679492
          [,68]      [,69]      [,70]      [,71]     [,72]     [,73]     [,74]
[1,] -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659
[2,]  0.2679492  0.2679492  0.2679492  0.2679492 0.2679492 0.2679492 0.2679492
         [,75]     [,76]     [,77]      [,78]      [,79]      [,80]      [,81]
[1,] 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659
[2,] 0.2679492 0.2679492 0.2679492  0.4663077  0.4663077  0.4663077  0.4663077
          [,82]     [,83]     [,84]     [,85]     [,86]     [,87]     [,88]
[1,] -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988 0.6981317 0.8726646
[2,]  0.4663077 0.4663077 0.4663077 0.4663077 0.4663077 0.4663077 0.4663077
          [,89]      [,90]      [,91]      [,92]      [,93]     [,94]     [,95]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329
[2,]  0.7002075  0.7002075  0.7002075  0.7002075  0.7002075 0.7002075 0.7002075
         [,96]     [,97]     [,98]     [,99]     [,100]     [,101]     [,102]
[1,] 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] 0.7002075 0.7002075 0.7002075 0.7002075  1.0000000  1.0000000  1.0000000
         [,103]     [,104] [,105]    [,106]    [,107]    [,108]    [,109]
[1,] -0.3490659 -0.1745329      0 0.1745329 0.3490659 0.5235988 0.6981317
[2,]  1.0000000  1.0000000      1 1.0000000 1.0000000 1.0000000 1.0000000
        [,110]
[1,] 0.8726646
[2,] 1.0000000

$cylequalarea
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329  0.0000000
[2,] -0.7071068 -0.7071068 -0.7071068 -0.7071068 -0.7071068 -0.7071068
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.1745329  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646
[2,] -0.7071068 -0.7071068 -0.7071068 -0.7071068 -0.7071068 -0.5735764
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] -0.6981317 -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329
[2,] -0.5735764 -0.5735764 -0.5735764 -0.5735764 -0.5735764 -0.5735764
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317
[2,] -0.5735764 -0.5735764 -0.5735764 -0.5735764 -0.4226183 -0.4226183
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659
[2,] -0.4226183 -0.4226183 -0.4226183 -0.4226183 -0.4226183 -0.4226183
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] -0.4226183 -0.4226183 -0.4226183 -0.2588190 -0.2588190 -0.2588190
          [,37]      [,38]     [,39]      [,40]      [,41]      [,42]
[1,] -0.3490659 -0.1745329  0.000000  0.1745329  0.3490659  0.5235988
[2,] -0.2588190 -0.2588190 -0.258819 -0.2588190 -0.2588190 -0.2588190
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.6981317  0.8726646 -0.87266463 -0.69813170 -0.52359878 -0.34906585
[2,] -0.2588190 -0.2588190 -0.08715574 -0.08715574 -0.08715574 -0.08715574
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.17453293  0.00000000  0.17453293  0.34906585  0.52359878  0.69813170
[2,] -0.08715574 -0.08715574 -0.08715574 -0.08715574 -0.08715574 -0.08715574
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.87266463 -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293
[2,] -0.08715574  0.08715574  0.08715574  0.08715574  0.08715574  0.08715574
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.17453293 0.34906585 0.52359878 0.69813170 0.87266463
[2,] 0.08715574 0.08715574 0.08715574 0.08715574 0.08715574 0.08715574
          [,67]      [,68]      [,69]      [,70]      [,71]    [,72]     [,73]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.000000 0.1745329
[2,]  0.2588190  0.2588190  0.2588190  0.2588190  0.2588190 0.258819 0.2588190
         [,74]     [,75]     [,76]     [,77]      [,78]      [,79]      [,80]
[1,] 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] 0.2588190 0.2588190 0.2588190 0.2588190  0.4226183  0.4226183  0.4226183
          [,81]      [,82]     [,83]     [,84]     [,85]     [,86]     [,87]
[1,] -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988 0.6981317
[2,]  0.4226183  0.4226183 0.4226183 0.4226183 0.4226183 0.4226183 0.4226183
         [,88]      [,89]      [,90]      [,91]      [,92]      [,93]     [,94]
[1,] 0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000
[2,] 0.4226183  0.5735764  0.5735764  0.5735764  0.5735764  0.5735764 0.5735764
         [,95]     [,96]     [,97]     [,98]     [,99]     [,100]     [,101]
[1,] 0.1745329 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317
[2,] 0.5735764 0.5735764 0.5735764 0.5735764 0.5735764  0.7071068  0.7071068
         [,102]     [,103]     [,104]    [,105]    [,106]    [,107]    [,108]
[1,] -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988
[2,]  0.7071068  0.7071068  0.7071068 0.7071068 0.7071068 0.7071068 0.7071068
        [,109]    [,110]
[1,] 0.6981317 0.8726646
[2,] 0.7071068 0.7071068

$cylindrical
           [,1]       [,2]       [,3]       [,4]       [,5] [,6]       [,7]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329    0  0.1745329
[2,] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000   -1 -1.0000000
           [,8]       [,9]      [,10]      [,11]      [,12]      [,13]
[1,]  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317
[2,] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -0.7002075 -0.7002075
          [,14]      [,15]      [,16]      [,17]      [,18]      [,19]
[1,] -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659
[2,] -0.7002075 -0.7002075 -0.7002075 -0.7002075 -0.7002075 -0.7002075
          [,20]      [,21]      [,22]      [,23]      [,24]      [,25]
[1,]  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] -0.7002075 -0.7002075 -0.7002075 -0.4663077 -0.4663077 -0.4663077
          [,26]      [,27]      [,28]      [,29]      [,30]      [,31]
[1,] -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659  0.5235988
[2,] -0.4663077 -0.4663077 -0.4663077 -0.4663077 -0.4663077 -0.4663077
          [,32]      [,33]      [,34]      [,35]      [,36]      [,37]
[1,]  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659
[2,] -0.4663077 -0.4663077 -0.2679492 -0.2679492 -0.2679492 -0.2679492
          [,38]      [,39]      [,40]      [,41]      [,42]      [,43]
[1,] -0.1745329  0.0000000  0.1745329  0.3490659  0.5235988  0.6981317
[2,] -0.2679492 -0.2679492 -0.2679492 -0.2679492 -0.2679492 -0.2679492
          [,44]       [,45]       [,46]       [,47]       [,48]       [,49]
[1,]  0.8726646 -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293
[2,] -0.2679492 -0.08748866 -0.08748866 -0.08748866 -0.08748866 -0.08748866
           [,50]       [,51]       [,52]       [,53]       [,54]       [,55]
[1,]  0.00000000  0.17453293  0.34906585  0.52359878  0.69813170  0.87266463
[2,] -0.08748866 -0.08748866 -0.08748866 -0.08748866 -0.08748866 -0.08748866
           [,56]       [,57]       [,58]       [,59]       [,60]      [,61]
[1,] -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293 0.00000000
[2,]  0.08748866  0.08748866  0.08748866  0.08748866  0.08748866 0.08748866
          [,62]      [,63]      [,64]      [,65]      [,66]      [,67]
[1,] 0.17453293 0.34906585 0.52359878 0.69813170 0.87266463 -0.8726646
[2,] 0.08748866 0.08748866 0.08748866 0.08748866 0.08748866  0.2679492
          [,68]      [,69]      [,70]      [,71]     [,72]     [,73]     [,74]
[1,] -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659
[2,]  0.2679492  0.2679492  0.2679492  0.2679492 0.2679492 0.2679492 0.2679492
         [,75]     [,76]     [,77]      [,78]      [,79]      [,80]      [,81]
[1,] 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659
[2,] 0.2679492 0.2679492 0.2679492  0.4663077  0.4663077  0.4663077  0.4663077
          [,82]     [,83]     [,84]     [,85]     [,86]     [,87]     [,88]
[1,] -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988 0.6981317 0.8726646
[2,]  0.4663077 0.4663077 0.4663077 0.4663077 0.4663077 0.4663077 0.4663077
          [,89]      [,90]      [,91]      [,92]      [,93]     [,94]     [,95]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329
[2,]  0.7002075  0.7002075  0.7002075  0.7002075  0.7002075 0.7002075 0.7002075
         [,96]     [,97]     [,98]     [,99]     [,100]     [,101]     [,102]
[1,] 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] 0.7002075 0.7002075 0.7002075 0.7002075  1.0000000  1.0000000  1.0000000
         [,103]     [,104] [,105]    [,106]    [,107]    [,108]    [,109]
[1,] -0.3490659 -0.1745329      0 0.1745329 0.3490659 0.5235988 0.6981317
[2,]  1.0000000  1.0000000      1 1.0000000 1.0000000 1.0000000 1.0000000
        [,110]
[1,] 0.8726646
[2,] 1.0000000

$eisenlohr
           [,1]       [,2]        [,3]        [,4]        [,5]       [,6]
[1,] -0.1374332 -0.1088884 -0.08105731 -0.05375114 -0.02679004  0.0000000
[2,] -0.1613354 -0.1554967 -0.15112547 -0.14809085 -0.14630421 -0.1457143
            [,7]        [,8]        [,9]      [,10]      [,11]      [,12]
[1,]  0.02679004  0.05375114  0.08105731  0.1088884  0.1374332 -0.1452539
[2,] -0.14630421 -0.14809085 -0.15112547 -0.1554967 -0.1613354 -0.1220811
          [,13]       [,14]       [,15]       [,16]      [,17]       [,18]
[1,] -0.1148727 -0.08539369 -0.05657219 -0.02818007  0.0000000  0.02818007
[2,] -0.1174531 -0.11399746 -0.11160311 -0.11019521 -0.1097306 -0.11019521
           [,19]       [,20]      [,21]      [,22]       [,23]       [,24]
[1,]  0.05657219  0.08539369  0.1148727  0.1452539 -0.15051696 -0.11888974
[2,] -0.11160311 -0.11399746 -0.1174531 -0.1220811 -0.08549378 -0.08215493
           [,25]       [,26]       [,27]       [,28]       [,29]       [,30]
[1,] -0.08829910 -0.05845982 -0.02910944  0.00000000  0.02910944  0.05845982
[2,] -0.07966625 -0.07794409 -0.07693230 -0.07659855 -0.07693230 -0.07794409
           [,31]       [,32]       [,33]       [,34]       [,35]       [,36]
[1,]  0.08829910  0.11888974  0.15051696 -0.15377508 -0.12137252 -0.09009262
[2,] -0.07966625 -0.08215493 -0.08549378 -0.05064336 -0.04862991 -0.04713077
           [,37]       [,38]       [,39]       [,40]       [,41]       [,42]
[1,] -0.05962407 -0.02968238  0.00000000  0.02968238  0.05962407  0.09009262
[2,] -0.04609417 -0.04548547 -0.04528474 -0.04548547 -0.04609417 -0.04713077
           [,43]       [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.12137252  0.15377508 -0.15533517 -0.12256028 -0.09095005 -0.06018041
[2,] -0.04862991 -0.05064336 -0.01677511 -0.01610255 -0.01560203 -0.01525608
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.02995608  0.00000000  0.02995608  0.06018041  0.09095005  0.12256028
[2,] -0.01505298 -0.01498601 -0.01505298 -0.01525608 -0.01560203 -0.01610255
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.15533517 -0.15533517 -0.12256028 -0.09095005 -0.06018041 -0.02995608
[2,] -0.01677511  0.01677511  0.01610255  0.01560203  0.01525608  0.01505298
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.02995608 0.06018041 0.09095005 0.12256028 0.15533517
[2,] 0.01498601 0.01505298 0.01525608 0.01560203 0.01610255 0.01677511
           [,67]       [,68]       [,69]       [,70]       [,71]      [,72]
[1,] -0.15377508 -0.12137252 -0.09009262 -0.05962407 -0.02968238 0.00000000
[2,]  0.05064336  0.04862991  0.04713077  0.04609417  0.04548547 0.04528474
          [,73]      [,74]      [,75]      [,76]      [,77]       [,78]
[1,] 0.02968238 0.05962407 0.09009262 0.12137252 0.15377508 -0.15051696
[2,] 0.04548547 0.04609417 0.04713077 0.04862991 0.05064336  0.08549378
           [,79]       [,80]       [,81]       [,82]      [,83]      [,84]
[1,] -0.11888974 -0.08829910 -0.05845982 -0.02910944 0.00000000 0.02910944
[2,]  0.08215493  0.07966625  0.07794409  0.07693230 0.07659855 0.07693230
          [,85]      [,86]      [,87]      [,88]      [,89]      [,90]
[1,] 0.05845982 0.08829910 0.11888974 0.15051696 -0.1452539 -0.1148727
[2,] 0.07794409 0.07966625 0.08215493 0.08549378  0.1220811  0.1174531
           [,91]       [,92]       [,93]     [,94]      [,95]      [,96]
[1,] -0.08539369 -0.05657219 -0.02818007 0.0000000 0.02818007 0.05657219
[2,]  0.11399746  0.11160311  0.11019521 0.1097306 0.11019521 0.11160311
          [,97]     [,98]     [,99]     [,100]     [,101]      [,102]
[1,] 0.08539369 0.1148727 0.1452539 -0.1374332 -0.1088884 -0.08105731
[2,] 0.11399746 0.1174531 0.1220811  0.1613354  0.1554967  0.15112547
          [,103]      [,104]    [,105]     [,106]     [,107]     [,108]
[1,] -0.05375114 -0.02679004 0.0000000 0.02679004 0.05375114 0.08105731
[2,]  0.14809085  0.14630421 0.1457143 0.14630421 0.14809085 0.15112547
        [,109]    [,110]
[1,] 0.1088884 0.1374332
[2,] 0.1554967 0.1613354

$elliptic
          [,1]      [,2]      [,3]      [,4]       [,5]      [,6]       [,7]
[1,] -1.804950 -1.514533 -1.178097 -0.805866 -0.4091489  0.000000  0.4091489
[2,] -1.514533 -1.804950 -2.040524 -2.214099 -2.3203986 -2.356194 -2.3203986
          [,8]      [,9]     [,10]     [,11]     [,12]     [,13]     [,14]
[1,]  0.805866  1.178097  1.514533  1.804950 -1.671250 -1.402345 -1.090831
[2,] -2.214099 -2.040524 -1.804950 -1.514533 -1.402345 -1.671250 -1.889374
          [,15]      [,16]     [,17]      [,18]      [,19]     [,20]     [,21]
[1,] -0.7461722 -0.3788416  0.000000  0.3788416  0.7461722  1.090831  1.402345
[2,] -2.0500913 -2.1485172 -2.181662 -2.1485172 -2.0500913 -1.889374 -1.671250
         [,22]     [,23]     [,24]     [,25]      [,26]      [,27]     [,28]
[1,]  1.671250 -1.537550 -1.290157 -1.003564 -0.6864784 -0.3485342  0.000000
[2,] -1.402345 -1.290157 -1.537550 -1.738224 -1.8860840 -1.9766358 -2.007129
          [,29]      [,30]     [,31]     [,32]     [,33]    [,34]    [,35]
[1,]  0.3485342  0.6864784  1.003564  1.290157  1.537550 -1.40385 -1.17797
[2,] -1.9766358 -1.8860840 -1.738224 -1.537550 -1.290157 -1.17797 -1.40385
          [,36]      [,37]      [,38]     [,39]      [,40]      [,41]
[1,] -0.9162979 -0.6267846 -0.3182269  0.000000  0.3182269  0.6267846
[2,] -1.5870744 -1.7220767 -1.8047545 -1.832596 -1.8047545 -1.7220767
          [,42]    [,43]    [,44]     [,45]     [,46]      [,47]      [,48]
[1,]  0.9162979  1.17797  1.40385 -1.270150 -1.065782 -0.8290314 -0.5670909
[2,] -1.5870744 -1.40385 -1.17797 -1.065782 -1.270150 -1.4359245 -1.5580694
          [,49]     [,50]      [,51]      [,52]      [,53]     [,54]     [,55]
[1,] -0.2879196  0.000000  0.2879196  0.5670909  0.8290314  1.065782  1.270150
[2,] -1.6328731 -1.658063 -1.6328731 -1.5580694 -1.4359245 -1.270150 -1.065782
          [,56]      [,57]      [,58]      [,59]      [,60]    [,61]      [,62]
[1,] -1.1364498 -0.9535946 -0.7417649 -0.5073971 -0.2576123  0.00000  0.2576123
[2,] -0.9535946 -1.1364498 -1.2847745 -1.3940621 -1.4609917 -1.48353 -1.4609917
          [,63]      [,64]      [,65]      [,66]     [,67]     [,68]      [,69]
[1,]  0.5073971  0.7417649  0.9535946  1.1364498 -1.002750 -0.841407 -0.6544985
[2,] -1.3940621 -1.2847745 -1.1364498 -0.9535946 -0.841407 -1.002750 -1.1336246
          [,70]      [,71]     [,72]      [,73]      [,74]      [,75]     [,76]
[1,] -0.4477033 -0.2273049  0.000000  0.2273049  0.4477033  0.6544985  0.841407
[2,] -1.2300548 -1.2891103 -1.308997 -1.2891103 -1.2300548 -1.1336246 -1.002750
         [,77]      [,78]      [,79]      [,80]      [,81]      [,82]     [,83]
[1,]  1.002750 -0.8690499 -0.7292194 -0.5672320 -0.3880095 -0.1969976  0.000000
[2,] -0.841407 -0.7292194 -0.8690499 -0.9824747 -1.0660475 -1.1172290 -1.134464
          [,84]      [,85]      [,86]      [,87]      [,88]      [,89]
[1,]  0.1969976  0.3880095  0.5672320  0.7292194  0.8690499 -0.7353499
[2,] -1.1172290 -1.0660475 -0.9824747 -0.8690499 -0.7292194 -0.6170318
          [,90]      [,91]      [,92]      [,93]      [,94]      [,95]
[1,] -0.6170318 -0.4799655 -0.3283158 -0.1666903  0.0000000  0.1666903
[2,] -0.7353499 -0.8313247 -0.9020402 -0.9453476 -0.9599311 -0.9453476
          [,96]      [,97]      [,98]      [,99]     [,100]     [,101]
[1,]  0.3283158  0.4799655  0.6170318  0.7353499 -0.6016499 -0.5048442
[2,] -0.9020402 -0.8313247 -0.7353499 -0.6170318 -0.5048442 -0.6016499
         [,102]     [,103]     [,104]     [,105]     [,106]     [,107]
[1,] -0.3926991 -0.2686220 -0.1363830  0.0000000  0.1363830  0.2686220
[2,] -0.6801748 -0.7380329 -0.7734662 -0.7853982 -0.7734662 -0.7380329
         [,108]     [,109]     [,110]
[1,]  0.3926991  0.5048442  0.6016499
[2,] -0.6801748 -0.6016499 -0.5048442

$fisheye
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] -100  -90  -80  -70  -60  -50  -40  -30  -20   -10     0  -100   -90   -80
[2,]  -45  -45  -45  -45  -45  -45  -45  -45  -45   -45   -45   -35   -35   -35
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,]   -70   -60   -50   -40   -30   -20   -10     0  -100   -90   -80   -70
[2,]   -35   -35   -35   -35   -35   -35   -35   -35   -25   -25   -25   -25
     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,]   -60   -50   -40   -30   -20   -10     0  -100   -90   -80   -70   -60
[2,]   -25   -25   -25   -25   -25   -25   -25   -15   -15   -15   -15   -15
     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
[1,]   -50   -40   -30   -20   -10     0  -100   -90   -80   -70   -60   -50
[2,]   -15   -15   -15   -15   -15   -15    -5    -5    -5    -5    -5    -5
     [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
[1,]   -40   -30   -20   -10     0  -100   -90   -80   -70   -60   -50   -40
[2,]    -5    -5    -5    -5    -5     5     5     5     5     5     5     5
     [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
[1,]   -30   -20   -10     0  -100   -90   -80   -70   -60   -50   -40   -30
[2,]     5     5     5     5    15    15    15    15    15    15    15    15
     [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,]   -20   -10     0  -100   -90   -80   -70   -60   -50   -40   -30   -20
[2,]    15    15    15    25    25    25    25    25    25    25    25    25
     [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,]   -10     0  -100   -90   -80   -70   -60   -50   -40   -30   -20   -10
[2,]    25    25    35    35    35    35    35    35    35    35    35    35
     [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
[1,]     0   -100    -90    -80    -70    -60    -50    -40    -30    -20
[2,]    35     45     45     45     45     45     45     45     45     45
     [,109] [,110]
[1,]    -10      0
[2,]     45     45

$gall
           [,1]       [,2]       [,3]       [,4]        [,5]       [,6]
[1,] -0.4363323 -0.3490659 -0.2617994 -0.1745329 -0.08726646  0.0000000
[2,] -0.4142136 -0.4142136 -0.4142136 -0.4142136 -0.41421356 -0.4142136
            [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.08726646  0.1745329  0.2617994  0.3490659  0.4363323 -0.4363323
[2,] -0.41421356 -0.4142136 -0.4142136 -0.4142136 -0.4142136 -0.3152988
          [,13]      [,14]      [,15]       [,16]      [,17]       [,18]
[1,] -0.3490659 -0.2617994 -0.1745329 -0.08726646  0.0000000  0.08726646
[2,] -0.3152988 -0.3152988 -0.3152988 -0.31529879 -0.3152988 -0.31529879
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.1745329  0.2617994  0.3490659  0.4363323 -0.4363323 -0.3490659
[2,] -0.3152988 -0.3152988 -0.3152988 -0.3152988 -0.2216947 -0.2216947
          [,25]      [,26]       [,27]      [,28]       [,29]      [,30]
[1,] -0.2617994 -0.1745329 -0.08726646  0.0000000  0.08726646  0.1745329
[2,] -0.2216947 -0.2216947 -0.22169466 -0.2216947 -0.22169466 -0.2216947
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.2617994  0.3490659  0.4363323 -0.4363323 -0.3490659 -0.2617994
[2,] -0.2216947 -0.2216947 -0.2216947 -0.1316525 -0.1316525 -0.1316525
          [,37]       [,38]      [,39]       [,40]      [,41]      [,42]
[1,] -0.1745329 -0.08726646  0.0000000  0.08726646  0.1745329  0.2617994
[2,] -0.1316525 -0.13165250 -0.1316525 -0.13165250 -0.1316525 -0.1316525
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.3490659  0.4363323 -0.43633231 -0.34906585 -0.26179939 -0.17453293
[2,] -0.1316525 -0.1316525 -0.04366094 -0.04366094 -0.04366094 -0.04366094
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.08726646  0.00000000  0.08726646  0.17453293  0.26179939  0.34906585
[2,] -0.04366094 -0.04366094 -0.04366094 -0.04366094 -0.04366094 -0.04366094
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.43633231 -0.43633231 -0.34906585 -0.26179939 -0.17453293 -0.08726646
[2,] -0.04366094  0.04366094  0.04366094  0.04366094  0.04366094  0.04366094
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.08726646 0.17453293 0.26179939 0.34906585 0.43633231
[2,] 0.04366094 0.04366094 0.04366094 0.04366094 0.04366094 0.04366094
          [,67]      [,68]      [,69]      [,70]       [,71]     [,72]
[1,] -0.4363323 -0.3490659 -0.2617994 -0.1745329 -0.08726646 0.0000000
[2,]  0.1316525  0.1316525  0.1316525  0.1316525  0.13165250 0.1316525
          [,73]     [,74]     [,75]     [,76]     [,77]      [,78]      [,79]
[1,] 0.08726646 0.1745329 0.2617994 0.3490659 0.4363323 -0.4363323 -0.3490659
[2,] 0.13165250 0.1316525 0.1316525 0.1316525 0.1316525  0.2216947  0.2216947
          [,80]      [,81]       [,82]     [,83]      [,84]     [,85]     [,86]
[1,] -0.2617994 -0.1745329 -0.08726646 0.0000000 0.08726646 0.1745329 0.2617994
[2,]  0.2216947  0.2216947  0.22169466 0.2216947 0.22169466 0.2216947 0.2216947
         [,87]     [,88]      [,89]      [,90]      [,91]      [,92]
[1,] 0.3490659 0.4363323 -0.4363323 -0.3490659 -0.2617994 -0.1745329
[2,] 0.2216947 0.2216947  0.3152988  0.3152988  0.3152988  0.3152988
           [,93]     [,94]      [,95]     [,96]     [,97]     [,98]     [,99]
[1,] -0.08726646 0.0000000 0.08726646 0.1745329 0.2617994 0.3490659 0.4363323
[2,]  0.31529879 0.3152988 0.31529879 0.3152988 0.3152988 0.3152988 0.3152988
         [,100]     [,101]     [,102]     [,103]      [,104]    [,105]
[1,] -0.4363323 -0.3490659 -0.2617994 -0.1745329 -0.08726646 0.0000000
[2,]  0.4142136  0.4142136  0.4142136  0.4142136  0.41421356 0.4142136
         [,106]    [,107]    [,108]    [,109]    [,110]
[1,] 0.08726646 0.1745329 0.2617994 0.3490659 0.4363323
[2,] 0.41421356 0.4142136 0.4142136 0.4142136 0.4142136

$gilbert
           [,1]       [,2]       [,3]       [,4]        [,5]       [,6]
[1,] -0.3846586 -0.3112998 -0.2355718 -0.1580510 -0.07932739  0.0000000
[2,] -0.4142136 -0.4142136 -0.4142136 -0.4142136 -0.41421356 -0.4142136
            [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.07932739  0.1580510  0.2355718  0.3112998  0.3846586 -0.4010615
[2,] -0.41421356 -0.4142136 -0.4142136 -0.4142136 -0.4142136 -0.3152988
          [,13]      [,14]      [,15]       [,16]      [,17]       [,18]
[1,] -0.3245745 -0.2456173 -0.1647908 -0.08271014  0.0000000  0.08271014
[2,] -0.3152988 -0.3152988 -0.3152988 -0.31529879 -0.3152988 -0.31529879
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.1647908  0.2456173  0.3245745  0.4010615 -0.4121019 -0.3335094
[2,] -0.3152988 -0.3152988 -0.3152988 -0.3152988 -0.2216947 -0.2216947
          [,25]      [,26]       [,27]      [,28]       [,29]      [,30]
[1,] -0.2523786 -0.1693271 -0.08498697  0.0000000  0.08498697  0.1693271
[2,] -0.2216947 -0.2216947 -0.22169466 -0.2216947 -0.22169466 -0.2216947
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.2523786  0.3335094  0.4121019 -0.4189398 -0.3390432 -0.2565663
[2,] -0.2216947 -0.2216947 -0.2216947 -0.1316525 -0.1316525 -0.1316525
          [,37]       [,38]      [,39]       [,40]      [,41]      [,42]
[1,] -0.1721367 -0.08639713  0.0000000  0.08639713  0.1721367  0.2565663
[2,] -0.1316525 -0.13165250 -0.1316525 -0.13165250 -0.1316525 -0.1316525
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.3390432  0.4189398 -0.42221526 -0.34169400 -0.25857224 -0.17348259
[2,] -0.1316525 -0.1316525 -0.04366094 -0.04366094 -0.04366094 -0.04366094
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.08707263  0.00000000  0.08707263  0.17348259  0.25857224  0.34169400
[2,] -0.04366094 -0.04366094 -0.04366094 -0.04366094 -0.04366094 -0.04366094
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.42221526 -0.42221526 -0.34169400 -0.25857224 -0.17348259 -0.08707263
[2,] -0.04366094  0.04366094  0.04366094  0.04366094  0.04366094  0.04366094
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.08707263 0.17348259 0.25857224 0.34169400 0.42221526
[2,] 0.04366094 0.04366094 0.04366094 0.04366094 0.04366094 0.04366094
          [,67]      [,68]      [,69]      [,70]       [,71]     [,72]
[1,] -0.4189398 -0.3390432 -0.2565663 -0.1721367 -0.08639713 0.0000000
[2,]  0.1316525  0.1316525  0.1316525  0.1316525  0.13165250 0.1316525
          [,73]     [,74]     [,75]     [,76]     [,77]      [,78]      [,79]
[1,] 0.08639713 0.1721367 0.2565663 0.3390432 0.4189398 -0.4121019 -0.3335094
[2,] 0.13165250 0.1316525 0.1316525 0.1316525 0.1316525  0.2216947  0.2216947
          [,80]      [,81]       [,82]     [,83]      [,84]     [,85]     [,86]
[1,] -0.2523786 -0.1693271 -0.08498697 0.0000000 0.08498697 0.1693271 0.2523786
[2,]  0.2216947  0.2216947  0.22169466 0.2216947 0.22169466 0.2216947 0.2216947
         [,87]     [,88]      [,89]      [,90]      [,91]      [,92]
[1,] 0.3335094 0.4121019 -0.4010615 -0.3245745 -0.2456173 -0.1647908
[2,] 0.2216947 0.2216947  0.3152988  0.3152988  0.3152988  0.3152988
           [,93]     [,94]      [,95]     [,96]     [,97]     [,98]     [,99]
[1,] -0.08271014 0.0000000 0.08271014 0.1647908 0.2456173 0.3245745 0.4010615
[2,]  0.31529879 0.3152988 0.31529879 0.3152988 0.3152988 0.3152988 0.3152988
         [,100]     [,101]     [,102]     [,103]      [,104]    [,105]
[1,] -0.3846586 -0.3112998 -0.2355718 -0.1580510 -0.07932739 0.0000000
[2,]  0.4142136  0.4142136  0.4142136  0.4142136  0.41421356 0.4142136
         [,106]    [,107]    [,108]    [,109]    [,110]
[1,] 0.07932739 0.1580510 0.2355718 0.3112998 0.3846586
[2,] 0.41421356 0.4142136 0.4142136 0.4142136 0.4142136

$guyou
           [,1]       [,2]       [,3]       [,4]       [,5]          [,6]
[1,] -1.0818633 -0.9453492 -0.7988003 -0.6353802 -0.4369094 -1.522347e-08
[2,] -0.7909968 -0.8453217 -0.9192179 -1.0210517 -1.1717974 -1.582552e+00
           [,7]       [,8]       [,9]      [,10]      [,11]     [,12]
[1,]  0.4369094  0.6353802  0.7988003  0.9453492  1.0818633 -1.027906
[2,] -1.1717974 -1.0210517 -0.9192179 -0.8453217 -0.7909968 -0.605316
          [,13]      [,14]      [,15]      [,16]         [,17]      [,18]
[1,] -0.8727157 -0.7031356 -0.5106829 -0.2802304 -9.802070e-11  0.2802304
[2,] -0.6464281 -0.6992647 -0.7635494 -0.8316041 -8.679157e-01 -0.8316041
          [,19]      [,20]      [,21]     [,22]      [,23]      [,24]
[1,]  0.5106829  0.7031356  0.8727157  1.027906 -0.9931880 -0.8280105
[2,] -0.7635494 -0.6992647 -0.6464281 -0.605316 -0.4257917 -0.4532811
          [,25]      [,26]      [,27]         [,28]      [,29]      [,30]
[1,] -0.6491982 -0.4524450 -0.2346237 -9.802070e-11  0.2346237  0.4524450
[2,] -0.4863955 -0.5221273 -0.5527945 -5.655984e-01 -0.5527945 -0.5221273
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.6491982  0.8280105  0.9931880 -0.9728167 -0.8028471 -0.6209911
[2,] -0.4863955 -0.4532811 -0.4257917 -0.2525737 -0.2681129 -0.2860077
          [,37]      [,38]         [,39]      [,40]      [,41]      [,42]
[1,] -0.4255730 -0.2170653 -9.802070e-11  0.2170653  0.4255730  0.6209911
[2,] -0.3040146 -0.3181345 -3.236104e-01 -0.3181345 -0.3040146 -0.2860077
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.8028471  0.9728167 -0.96343444 -0.79155981 -0.60886055 -0.41468472
[2,] -0.2681129 -0.2525737 -0.08368734 -0.08869771 -0.09434327 -0.09985368
          [,49]         [,50]      [,51]       [,52]       [,53]       [,54]
[1,] -0.2103903 -9.802070e-11  0.2103903  0.41468472  0.60886055  0.79155981
[2,] -0.1040288 -1.056088e-01 -0.1040288 -0.09985368 -0.09434327 -0.08869771
           [,55]       [,56]       [,57]       [,58]       [,59]      [,60]
[1,]  0.96343444 -0.96343444 -0.79155981 -0.60886055 -0.41468472 -0.2103903
[2,] -0.08368734  0.08368734  0.08869771  0.09434327  0.09985368  0.1040288
             [,61]     [,62]      [,63]      [,64]      [,65]      [,66]
[1,] -9.802070e-11 0.2103903 0.41468472 0.60886055 0.79155981 0.96343444
[2,]  1.056088e-01 0.1040288 0.09985368 0.09434327 0.08869771 0.08368734
          [,67]      [,68]      [,69]      [,70]      [,71]         [,72]
[1,] -0.9728167 -0.8028471 -0.6209911 -0.4255730 -0.2170653 -9.802070e-11
[2,]  0.2525737  0.2681129  0.2860077  0.3040146  0.3181345  3.236104e-01
         [,73]     [,74]     [,75]     [,76]     [,77]      [,78]      [,79]
[1,] 0.2170653 0.4255730 0.6209911 0.8028471 0.9728167 -0.9931880 -0.8280105
[2,] 0.3181345 0.3040146 0.2860077 0.2681129 0.2525737  0.4257917  0.4532811
          [,80]      [,81]      [,82]         [,83]     [,84]     [,85]
[1,] -0.6491982 -0.4524450 -0.2346237 -9.802070e-11 0.2346237 0.4524450
[2,]  0.4863955  0.5221273  0.5527945  5.655984e-01 0.5527945 0.5221273
         [,86]     [,87]     [,88]     [,89]      [,90]      [,91]      [,92]
[1,] 0.6491982 0.8280105 0.9931880 -1.027906 -0.8727157 -0.7031356 -0.5106829
[2,] 0.4863955 0.4532811 0.4257917  0.605316  0.6464281  0.6992647  0.7635494
          [,93]         [,94]     [,95]     [,96]     [,97]     [,98]    [,99]
[1,] -0.2802304 -9.802070e-11 0.2802304 0.5106829 0.7031356 0.8727157 1.027906
[2,]  0.8316041  8.679157e-01 0.8316041 0.7635494 0.6992647 0.6464281 0.605316
         [,100]     [,101]     [,102]     [,103]     [,104]        [,105]
[1,] -1.0818633 -0.9453492 -0.7988003 -0.6353802 -0.4369094 -1.522347e-08
[2,]  0.7909968  0.8453217  0.9192179  1.0210517  1.1717974  1.582552e+00
        [,106]    [,107]    [,108]    [,109]    [,110]
[1,] 0.4369094 0.6353802 0.7988003 0.9453492 1.0818633
[2,] 1.1717974 1.0210517 0.9192179 0.8453217 0.7909968

$harrison
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] -100  -90  -80  -70  -60  -50  -40  -30  -20   -10     0  -100   -90   -80
[2,]  -45  -45  -45  -45  -45  -45  -45  -45  -45   -45   -45   -35   -35   -35
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,]   -70   -60   -50   -40   -30   -20   -10     0  -100   -90   -80   -70
[2,]   -35   -35   -35   -35   -35   -35   -35   -35   -25   -25   -25   -25
     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,]   -60   -50   -40   -30   -20   -10     0  -100   -90   -80   -70   -60
[2,]   -25   -25   -25   -25   -25   -25   -25   -15   -15   -15   -15   -15
     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
[1,]   -50   -40   -30   -20   -10     0  -100   -90   -80   -70   -60   -50
[2,]   -15   -15   -15   -15   -15   -15    -5    -5    -5    -5    -5    -5
     [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
[1,]   -40   -30   -20   -10     0  -100   -90   -80   -70   -60   -50   -40
[2,]    -5    -5    -5    -5    -5     5     5     5     5     5     5     5
     [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
[1,]   -30   -20   -10     0  -100   -90   -80   -70   -60   -50   -40   -30
[2,]     5     5     5     5    15    15    15    15    15    15    15    15
     [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,]   -20   -10     0  -100   -90   -80   -70   -60   -50   -40   -30   -20
[2,]    15    15    15    25    25    25    25    25    25    25    25    25
     [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,]   -10     0  -100   -90   -80   -70   -60   -50   -40   -30   -20   -10
[2,]    25    25    35    35    35    35    35    35    35    35    35    35
     [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
[1,]     0   -100    -90    -80    -70    -60    -50    -40    -30    -20
[2,]    35     45     45     45     45     45     45     45     45     45
     [,109] [,110]
[1,]    -10      0
[2,]     45     45

$hex
          [,1]      [,2]      [,3]      [,4]       [,5]          [,6]
[1,] 0.5411498 0.5797978 0.6094710 0.6301475 0.64226320  6.462460e-01
[2,] 0.2421377 0.2007288 0.1539458 0.1039659 0.05232423 -5.551115e-17
            [,7]       [,8]       [,9]      [,10]      [,11]     [,12]
[1,]  0.64226320  0.6301475  0.6094710  0.5797978  0.5411498 0.5988099
[2,] -0.05232423 -0.1039659 -0.1539458 -0.2007288 -0.2421377 0.3057689
         [,13]     [,14]     [,15]      [,16]        [,17]       [,18]
[1,] 0.6469239 0.6817265 0.7047154 0.71768853 7.218730e-01  0.71768853
[2,] 0.2502039 0.1892904 0.1264306 0.06318962 5.551115e-17 -0.06318962
          [,19]      [,20]      [,21]      [,22]     [,23]     [,24]     [,25]
[1,]  0.7047154  0.6817265  0.6469239  0.5988099 0.6687210 0.7255287 0.7623020
[2,] -0.1264306 -0.1892904 -0.2502039 -0.3057689 0.3768234 0.3010022 0.2228714
         [,26]     [,27]     [,28]      [,29]      [,30]      [,31]      [,32]
[1,] 0.7846501 0.7966350 0.8004106  0.7966350  0.7846501  0.7623020  0.7255287
[2,] 0.1466177 0.0726444 0.0000000 -0.0726444 -0.1466177 -0.2228714 -0.3010022
          [,33]     [,34]     [,35]     [,36]     [,37]      [,38]     [,39]
[1,]  0.6687210 0.7624968 0.8217299 0.8530926 0.8701550 0.87881061 0.8814748
[2,] -0.3768234 0.4567415 0.3490548 0.2510131 0.1623745 0.07976114 0.0000000
           [,40]      [,41]      [,42]      [,43]      [,44]     [,45]
[1,]  0.87881061  0.8701550  0.8530926  0.8217299  0.7624968 0.9073403
[2,] -0.07976114 -0.1623745 -0.2510131 -0.3490548 -0.4567415 0.5335524
         [,46]     [,47]     [,48]      [,49]         [,50]       [,51]
[1,] 0.9403847 0.9535963 0.9601234 0.96330732  9.642729e-01  0.96330732
[2,] 0.3822663 0.2678218 0.1711741 0.08361697 -5.551115e-17 -0.08361697
          [,52]      [,53]      [,54]      [,55]     [,56]     [,57]     [,58]
[1,]  0.9601234  0.9535963  0.9403847  0.9073403 1.1045269 1.0714826 1.0582709
[2,] -0.1711741 -0.2678218 -0.3822663 -0.5335524 0.5335524 0.3822663 0.2678218
         [,59]      [,60]         [,61]       [,62]      [,63]      [,64]
[1,] 1.0517439 1.04855991  1.047594e+00  1.04855991  1.0517439  1.0582709
[2,] 0.1711741 0.08361697 -5.551115e-17 -0.08361697 -0.1711741 -0.2678218
          [,65]      [,66]     [,67]     [,68]     [,69]     [,70]      [,71]
[1,]  1.0714826  1.1045269 1.2493705 1.1901373 1.1587746 1.1417123 1.13305663
[2,] -0.3822663 -0.5335524 0.4567415 0.3490548 0.2510131 0.1623745 0.07976114
        [,72]       [,73]      [,74]      [,75]      [,76]      [,77]     [,78]
[1,] 1.130392  1.13305663  1.1417123  1.1587746  1.1901373  1.2493705 1.3431462
[2,] 0.000000 -0.07976114 -0.1623745 -0.2510131 -0.3490548 -0.4567415 0.3768234
         [,79]     [,80]     [,81]     [,82]    [,83]      [,84]      [,85]
[1,] 1.2863385 1.2495652 1.2272171 1.2152322 1.211457  1.2152322  1.2272171
[2,] 0.3010022 0.2228714 0.1466177 0.0726444 0.000000 -0.0726444 -0.1466177
          [,86]      [,87]      [,88]     [,89]     [,90]     [,91]     [,92]
[1,]  1.2495652  1.2863385  1.3431462 1.4130573 1.3649434 1.3301407 1.3071518
[2,] -0.2228714 -0.3010022 -0.3768234 0.3057689 0.2502039 0.1892904 0.1264306
          [,93]        [,94]       [,95]      [,96]      [,97]      [,98]
[1,] 1.29417871 1.289994e+00  1.29417871  1.3071518  1.3301407  1.3649434
[2,] 0.06318962 5.551115e-17 -0.06318962 -0.1264306 -0.1892904 -0.2502039
          [,99]    [,100]    [,101]    [,102]    [,103]     [,104]
[1,]  1.4130573 1.4707175 1.4320694 1.4023962 1.3817197 1.36960404
[2,] -0.3057689 0.2421377 0.2007288 0.1539458 0.1039659 0.05232423
            [,105]      [,106]     [,107]     [,108]     [,109]     [,110]
[1,]  1.365621e+00  1.36960404  1.3817197  1.4023962  1.4320694  1.4707175
[2,] -5.551115e-17 -0.05232423 -0.1039659 -0.1539458 -0.2007288 -0.2421377

$homing
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] -0.9451221 -0.7634399 -0.5766339 -0.3862761 -0.1936793  0.0000000
[2,] -0.5607721 -0.6433485 -0.7062294 -0.7504417 -0.7766931 -0.7853982
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.1936793  0.3862761  0.5766339  0.7634399  0.9451221 -0.9157302
[2,] -0.7766931 -0.7504417 -0.7062294 -0.6433485 -0.5607721 -0.4407297
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] -0.7367676 -0.5548674 -0.3709535 -0.1857799  0.0000000  0.1857799
[2,] -0.5036261 -0.5512405 -0.5845813 -0.6043261 -0.6108652 -0.6043261
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.3709535  0.5548674  0.7367676  0.9157302 -0.8943480 -0.7175198
[2,] -0.5845813 -0.5512405 -0.5036261 -0.4407297 -0.3171526 -0.3613837
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.5392519 -0.3600049 -0.1801486  0.0000000  0.1801486  0.3600049
[2,] -0.3947304 -0.4180139 -0.4317779 -0.4363323 -0.4317779 -0.4180139
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.5392519  0.7175198  0.8943480 -0.8804021 -0.7050352 -0.5291637
[2,] -0.3947304 -0.3613837 -0.3171526 -0.1912013 -0.2174671 -0.2372176
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] -0.3529508 -0.1765261  0.0000000  0.1765261  0.3529508  0.5291637
[2,] -0.2509831 -0.2591113 -0.2617994 -0.2591113 -0.2509831 -0.2372176
          [,43]      [,44]       [,45]      [,46]       [,47]       [,48]
[1,]  0.7050352  0.8804021 -0.87352056 -0.6988946 -0.52421326 -0.34949461
[2,] -0.2174671 -0.1912013 -0.06388261 -0.0725929 -0.07913428 -0.08368943
           [,49]       [,50]       [,51]       [,52]       [,53]      [,54]
[1,] -0.17475283  0.00000000  0.17475283  0.34949461  0.52421326  0.6988946
[2,] -0.08637767 -0.08726646 -0.08637767 -0.08368943 -0.07913428 -0.0725929
           [,55]       [,56]      [,57]       [,58]       [,59]       [,60]
[1,]  0.87352056 -0.87352056 -0.6988946 -0.52421326 -0.34949461 -0.17475283
[2,] -0.06388261  0.06388261  0.0725929  0.07913428  0.08368943  0.08637767
          [,61]      [,62]      [,63]      [,64]     [,65]      [,66]
[1,] 0.00000000 0.17475283 0.34949461 0.52421326 0.6988946 0.87352056
[2,] 0.08726646 0.08637767 0.08368943 0.07913428 0.0725929 0.06388261
          [,67]      [,68]      [,69]      [,70]      [,71]     [,72]     [,73]
[1,] -0.8804021 -0.7050352 -0.5291637 -0.3529508 -0.1765261 0.0000000 0.1765261
[2,]  0.1912013  0.2174671  0.2372176  0.2509831  0.2591113 0.2617994 0.2591113
         [,74]     [,75]     [,76]     [,77]      [,78]      [,79]      [,80]
[1,] 0.3529508 0.5291637 0.7050352 0.8804021 -0.8943480 -0.7175198 -0.5392519
[2,] 0.2509831 0.2372176 0.2174671 0.1912013  0.3171526  0.3613837  0.3947304
          [,81]      [,82]     [,83]     [,84]     [,85]     [,86]     [,87]
[1,] -0.3600049 -0.1801486 0.0000000 0.1801486 0.3600049 0.5392519 0.7175198
[2,]  0.4180139  0.4317779 0.4363323 0.4317779 0.4180139 0.3947304 0.3613837
         [,88]      [,89]      [,90]      [,91]      [,92]      [,93]     [,94]
[1,] 0.8943480 -0.9157302 -0.7367676 -0.5548674 -0.3709535 -0.1857799 0.0000000
[2,] 0.3171526  0.4407297  0.5036261  0.5512405  0.5845813  0.6043261 0.6108652
         [,95]     [,96]     [,97]     [,98]     [,99]     [,100]     [,101]
[1,] 0.1857799 0.3709535 0.5548674 0.7367676 0.9157302 -0.9451221 -0.7634399
[2,] 0.6043261 0.5845813 0.5512405 0.5036261 0.4407297  0.5607721  0.6433485
         [,102]     [,103]     [,104]    [,105]    [,106]    [,107]    [,108]
[1,] -0.5766339 -0.3862761 -0.1936793 0.0000000 0.1936793 0.3862761 0.5766339
[2,]  0.7062294  0.7504417  0.7766931 0.7853982 0.7766931 0.7504417 0.7062294
        [,109]    [,110]
[1,] 0.7634399 0.9451221
[2,] 0.6433485 0.5607721

$lagrange
           [,1]       [,2]       [,3]        [,4]        [,5]       [,6]
[1,] -0.2107830 -0.1677904 -0.1253598 -0.08334478 -0.04160419  0.0000000
[2,] -0.2269784 -0.2232609 -0.2204241 -0.21842651 -0.21723923 -0.2168453
            [,7]        [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.04160419  0.08334478  0.1253598  0.1677904  0.2107830 -0.2156153
[2,] -0.21723923 -0.21842651 -0.2204241 -0.2232609 -0.2269784 -0.1695083
          [,13]      [,14]       [,15]       [,16]      [,17]       [,18]
[1,] -0.1715727 -0.1281489 -0.08518191 -0.04251616  0.0000000  0.04251616
[2,] -0.1666694 -0.1645046 -0.16298090 -0.16207558 -0.1617753 -0.16207558
           [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.08518191  0.1281489  0.1715727  0.2156153 -0.2187661 -0.1740373
[2,] -0.16298090 -0.1645046 -0.1666694 -0.1695083 -0.1176876 -0.1156883
          [,25]       [,26]       [,27]      [,28]       [,29]       [,30]
[1,] -0.1299655 -0.08637809 -0.04310984  0.0000000  0.04310984  0.08637809
[2,] -0.1141644 -0.11309210 -0.11245513 -0.1122439 -0.11245513 -0.11309210
          [,31]      [,32]      [,33]       [,34]       [,35]      [,36]
[1,]  0.1299655  0.1740373  0.2187661 -0.22067821 -0.17553239 -0.1310671
[2,] -0.1141644 -0.1156883 -0.1176876 -0.06934849 -0.06816028 -0.0672548
           [,37]       [,38]       [,39]       [,40]       [,41]      [,42]
[1,] -0.08710333 -0.04346974  0.00000000  0.04346974  0.08710333  0.1310671
[2,] -0.06661780 -0.06623946 -0.06611398 -0.06623946 -0.06661780 -0.0672548
           [,43]       [,44]      [,45]       [,46]       [,47]       [,48]
[1,]  0.17553239  0.22067821 -0.2215837 -0.17624025 -0.13158861 -0.08744661
[2,] -0.06816028 -0.06934849 -0.0229138 -0.02251961 -0.02221926 -0.02200798
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.04364008  0.00000000  0.04364008  0.08744661  0.13158861  0.17624025
[2,] -0.02188250 -0.02184089 -0.02188250 -0.02200798 -0.02221926 -0.02251961
          [,55]      [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.2215837 -0.2215837 -0.17624025 -0.13158861 -0.08744661 -0.04364008
[2,] -0.0229138  0.0229138  0.02251961  0.02221926  0.02200798  0.02188250
          [,61]      [,62]      [,63]      [,64]      [,65]     [,66]
[1,] 0.00000000 0.04364008 0.08744661 0.13158861 0.17624025 0.2215837
[2,] 0.02184089 0.02188250 0.02200798 0.02221926 0.02251961 0.0229138
           [,67]       [,68]      [,69]       [,70]       [,71]      [,72]
[1,] -0.22067821 -0.17553239 -0.1310671 -0.08710333 -0.04346974 0.00000000
[2,]  0.06934849  0.06816028  0.0672548  0.06661780  0.06623946 0.06611398
          [,73]      [,74]     [,75]      [,76]      [,77]      [,78]
[1,] 0.04346974 0.08710333 0.1310671 0.17553239 0.22067821 -0.2187661
[2,] 0.06623946 0.06661780 0.0672548 0.06816028 0.06934849  0.1176876
          [,79]      [,80]       [,81]       [,82]     [,83]      [,84]
[1,] -0.1740373 -0.1299655 -0.08637809 -0.04310984 0.0000000 0.04310984
[2,]  0.1156883  0.1141644  0.11309210  0.11245513 0.1122439 0.11245513
          [,85]     [,86]     [,87]     [,88]      [,89]      [,90]      [,91]
[1,] 0.08637809 0.1299655 0.1740373 0.2187661 -0.2156153 -0.1715727 -0.1281489
[2,] 0.11309210 0.1141644 0.1156883 0.1176876  0.1695083  0.1666694  0.1645046
           [,92]       [,93]     [,94]      [,95]      [,96]     [,97]
[1,] -0.08518191 -0.04251616 0.0000000 0.04251616 0.08518191 0.1281489
[2,]  0.16298090  0.16207558 0.1617753 0.16207558 0.16298090 0.1645046
         [,98]     [,99]     [,100]     [,101]     [,102]      [,103]
[1,] 0.1715727 0.2156153 -0.2107830 -0.1677904 -0.1253598 -0.08334478
[2,] 0.1666694 0.1695083  0.2269784  0.2232609  0.2204241  0.21842651
          [,104]    [,105]     [,106]     [,107]    [,108]    [,109]    [,110]
[1,] -0.04160419 0.0000000 0.04160419 0.08334478 0.1253598 0.1677904 0.2107830
[2,]  0.21723923 0.2168453 0.21723923 0.21842651 0.2204241 0.2232609 0.2269784

$lambert
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329  0.0000000
[2,] -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.8813736
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.1745329  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646
[2,] -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.6528366
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] -0.6981317 -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329
[2,] -0.6528366 -0.6528366 -0.6528366 -0.6528366 -0.6528366 -0.6528366
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317
[2,] -0.6528366 -0.6528366 -0.6528366 -0.6528366 -0.4508753 -0.4508753
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659
[2,] -0.4508753 -0.4508753 -0.4508753 -0.4508753 -0.4508753 -0.4508753
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] -0.4508753 -0.4508753 -0.4508753 -0.2648422 -0.2648422 -0.2648422
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659  0.5235988
[2,] -0.2648422 -0.2648422 -0.2648422 -0.2648422 -0.2648422 -0.2648422
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.6981317  0.8726646 -0.87266463 -0.69813170 -0.52359878 -0.34906585
[2,] -0.2648422 -0.2648422 -0.08737744 -0.08737744 -0.08737744 -0.08737744
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.17453293  0.00000000  0.17453293  0.34906585  0.52359878  0.69813170
[2,] -0.08737744 -0.08737744 -0.08737744 -0.08737744 -0.08737744 -0.08737744
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.87266463 -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293
[2,] -0.08737744  0.08737744  0.08737744  0.08737744  0.08737744  0.08737744
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.17453293 0.34906585 0.52359878 0.69813170 0.87266463
[2,] 0.08737744 0.08737744 0.08737744 0.08737744 0.08737744 0.08737744
          [,67]      [,68]      [,69]      [,70]      [,71]     [,72]     [,73]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329
[2,]  0.2648422  0.2648422  0.2648422  0.2648422  0.2648422 0.2648422 0.2648422
         [,74]     [,75]     [,76]     [,77]      [,78]      [,79]      [,80]
[1,] 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] 0.2648422 0.2648422 0.2648422 0.2648422  0.4508753  0.4508753  0.4508753
          [,81]      [,82]     [,83]     [,84]     [,85]     [,86]     [,87]
[1,] -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988 0.6981317
[2,]  0.4508753  0.4508753 0.4508753 0.4508753 0.4508753 0.4508753 0.4508753
         [,88]      [,89]      [,90]      [,91]      [,92]      [,93]     [,94]
[1,] 0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000
[2,] 0.4508753  0.6528366  0.6528366  0.6528366  0.6528366  0.6528366 0.6528366
         [,95]     [,96]     [,97]     [,98]     [,99]     [,100]     [,101]
[1,] 0.1745329 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317
[2,] 0.6528366 0.6528366 0.6528366 0.6528366 0.6528366  0.8813736  0.8813736
         [,102]     [,103]     [,104]    [,105]    [,106]    [,107]    [,108]
[1,] -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988
[2,]  0.8813736  0.8813736  0.8813736 0.8813736 0.8813736 0.8813736 0.8813736
        [,109]    [,110]
[1,] 0.6981317 0.8726646
[2,] 0.8813736 0.8813736

$laue
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,]   NA   NA   NA   NA   NA   NA   NA   NA   NA    NA    NA    NA    NA    NA
[2,]   NA   NA   NA   NA   NA   NA   NA   NA   NA    NA    NA    NA    NA    NA
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
[1,]    NA     NA     NA     NA     NA     NA     NA     NA     NA     NA
[2,]    NA     NA     NA     NA     NA     NA     NA     NA     NA     NA
     [,109] [,110]
[1,]     NA     NA
[2,]     NA     NA

$lune
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,]   NA   NA   NA   NA   NA   NA   NA   NA   NA    NA    NA    NA    NA    NA
[2,]   NA   NA   NA   NA   NA   NA   NA   NA   NA    NA    NA    NA    NA    NA
     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
[1,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
[2,]    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
     [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
[1,]    NA    NA    NA    NA    NA     0     0     0     0     0     0     0
[2,]    NA    NA    NA    NA    NA     0     0     0     0     0     0     0
     [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
[1,]     0     0     0     0     0     0     0     0     0     0     0     0
[2,]     0     0     0     0     0     0     0     0     0     0     0     0
     [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,]     0     0     0     0     0     0     0     0     0     0     0     0
[2,]     0     0     0     0     0     0     0     0     0     0     0     0
     [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
[1,]     0     0     0     0     0     0     0     0     0     0     0     0
[2,]     0     0     0     0     0     0     0     0     0     0     0     0
     [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
[1,]     0      0      0      0      0      0      0      0      0      0
[2,]     0      0      0      0      0      0      0      0      0      0
     [,109] [,110]
[1,]      0      0
[2,]      0      0

$mercator
           [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329  0.0000000
[2,] -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.8813736
           [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.1745329  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646
[2,] -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.8813736 -0.6528366
          [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
[1,] -0.6981317 -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329
[2,] -0.6528366 -0.6528366 -0.6528366 -0.6528366 -0.6528366 -0.6528366
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.3490659  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317
[2,] -0.6528366 -0.6528366 -0.6528366 -0.6528366 -0.4508753 -0.4508753
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.5235988 -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659
[2,] -0.4508753 -0.4508753 -0.4508753 -0.4508753 -0.4508753 -0.4508753
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.5235988  0.6981317  0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] -0.4508753 -0.4508753 -0.4508753 -0.2648422 -0.2648422 -0.2648422
          [,37]      [,38]      [,39]      [,40]      [,41]      [,42]
[1,] -0.3490659 -0.1745329  0.0000000  0.1745329  0.3490659  0.5235988
[2,] -0.2648422 -0.2648422 -0.2648422 -0.2648422 -0.2648422 -0.2648422
          [,43]      [,44]       [,45]       [,46]       [,47]       [,48]
[1,]  0.6981317  0.8726646 -0.87266463 -0.69813170 -0.52359878 -0.34906585
[2,] -0.2648422 -0.2648422 -0.08737744 -0.08737744 -0.08737744 -0.08737744
           [,49]       [,50]       [,51]       [,52]       [,53]       [,54]
[1,] -0.17453293  0.00000000  0.17453293  0.34906585  0.52359878  0.69813170
[2,] -0.08737744 -0.08737744 -0.08737744 -0.08737744 -0.08737744 -0.08737744
           [,55]       [,56]       [,57]       [,58]       [,59]       [,60]
[1,]  0.87266463 -0.87266463 -0.69813170 -0.52359878 -0.34906585 -0.17453293
[2,] -0.08737744  0.08737744  0.08737744  0.08737744  0.08737744  0.08737744
          [,61]      [,62]      [,63]      [,64]      [,65]      [,66]
[1,] 0.00000000 0.17453293 0.34906585 0.52359878 0.69813170 0.87266463
[2,] 0.08737744 0.08737744 0.08737744 0.08737744 0.08737744 0.08737744
          [,67]      [,68]      [,69]      [,70]      [,71]     [,72]     [,73]
[1,] -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329
[2,]  0.2648422  0.2648422  0.2648422  0.2648422  0.2648422 0.2648422 0.2648422
         [,74]     [,75]     [,76]     [,77]      [,78]      [,79]      [,80]
[1,] 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317 -0.5235988
[2,] 0.2648422 0.2648422 0.2648422 0.2648422  0.4508753  0.4508753  0.4508753
          [,81]      [,82]     [,83]     [,84]     [,85]     [,86]     [,87]
[1,] -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988 0.6981317
[2,]  0.4508753  0.4508753 0.4508753 0.4508753 0.4508753 0.4508753 0.4508753
         [,88]      [,89]      [,90]      [,91]      [,92]      [,93]     [,94]
[1,] 0.8726646 -0.8726646 -0.6981317 -0.5235988 -0.3490659 -0.1745329 0.0000000
[2,] 0.4508753  0.6528366  0.6528366  0.6528366  0.6528366  0.6528366 0.6528366
         [,95]     [,96]     [,97]     [,98]     [,99]     [,100]     [,101]
[1,] 0.1745329 0.3490659 0.5235988 0.6981317 0.8726646 -0.8726646 -0.6981317
[2,] 0.6528366 0.6528366 0.6528366 0.6528366 0.6528366  0.8813736  0.8813736
         [,102]     [,103]     [,104]    [,105]    [,106]    [,107]    [,108]
[1,] -0.5235988 -0.3490659 -0.1745329 0.0000000 0.1745329 0.3490659 0.5235988
[2,]  0.8813736  0.8813736  0.8813736 0.8813736 0.8813736 0.8813736 0.8813736
        [,109]    [,110]
[1,] 0.6981317 0.8726646
[2,] 0.8813736 0.8813736

$mollweide
           [,1]       [,2]       [,3]       [,4]        [,5]       [,6]
[1,] -0.4477263 -0.3581810 -0.2686358 -0.1790905 -0.08954525  0.0000000
[2,] -0.5920417 -0.5920417 -0.5920417 -0.5920417 -0.59204175 -0.5920417
            [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
[1,]  0.08954525  0.1790905  0.2686358  0.3581810  0.4477263 -0.4909002
[2,] -0.59204175 -0.5920417 -0.5920417 -0.5920417 -0.5920417 -0.4682040
          [,13]      [,14]      [,15]       [,16]     [,17]       [,18]
[1,] -0.3927202 -0.2945401 -0.1963601 -0.09818004  0.000000  0.09818004
[2,] -0.4682040 -0.4682040 -0.4682040 -0.46820401 -0.468204 -0.46820401
          [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
[1,]  0.1963601  0.2945401  0.3927202  0.4909002 -0.5227583 -0.4182066
[2,] -0.4682040 -0.4682040 -0.4682040 -0.4682040 -0.3385041 -0.3385041
          [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
[1,] -0.3136550 -0.2091033 -0.1045517  0.0000000  0.1045517  0.2091033
[2,] -0.3385041 -0.3385041 -0.3385041 -0.3385041 -0.3385041 -0.3385041
          [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
[1,]  0.3136550  0.4182066  0.5227583 -0.5437898 -0.4350318 -0.3262739
[2,] -0.3385041 -0.3385041 -0.3385041 -0.2047150 -0.2047150 -0.2047150
          [,37]     [,38]     [,39]     [,40]      [,41]      [,42]      [,43]
[1,] -0.2175159 -0.108758  0.000000  0.108758  0.2175159  0.3262739  0.4350318
[2,] -0.2047150 -0.204715 -0.204715 -0.204715 -0.2047150 -0.2047150 -0.2047150
          [,44]       [,45]       [,46]       [,47]       [,48]       [,49]
[1,]  0.5437898 -0.55425041 -0.44340033 -0.33255024 -0.22170016 -0.11085008
[2,] -0.2047150 -0.06850558 -0.06850558 -0.06850558 -0.06850558 -0.06850558
           [,50]       [,51]       [,52]       [,53]       [,54]       [,55]
[1,]  0.00000000  0.11085008  0.22170016  0.33255024  0.44340033  0.55425041
[2,] -0.06850558 -0.06850558 -0.06850558 -0.06850558 -0.06850558 -0.06850558
           [,56]       [,57]       [,58]       [,59]       [,60]      [,61]
[1,] -0.55425041 -0.44340033 -0.33255024 -0.22170016 -0.11085008 0.00000000
[2,]  0.06850558  0.06850558  0.06850558  0.06850558  0.06850558 0.06850558
          [,62]      [,63]      [,64]      [,65]      [,66]      [,67]
[1,] 0.11085008 0.22170016 0.33255024 0.44340033 0.55425041 -0.5437898
[2,] 0.06850558 0.06850558 0.06850558 0.06850558 0.06850558  0.2047150
          [,68]      [,69]      [,70]     [,71]    [,72]    [,73]     [,74]
[1,] -0.4350318 -0.3262739 -0.2175159 -0.108758 0.000000 0.108758 0.2175159
[2,]  0.2047150  0.2047150  0.2047150  0.204715 0.204715 0.204715 0.2047150
         [,75]     [,76]     [,77]      [,78]      [,79]      [,80]      [,81]
[1,] 0.3262739 0.4350318 0.5437898 -0.5227583 -0.4182066 -0.3136550 -0.2091033
[2,] 0.2047150 0.2047150 0.2047150  0.3385041  0.3385041  0.3385041  0.3385041
          [,82]     [,83]     [,84]     [,85]     [,86]     [,87]     [,88]
[1,] -0.1045517 0.0000000 0.1045517 0.2091033 0.3136550 0.4182066 0.5227583
[2,]  0.3385041 0.3385041 0.3385041 0.3385041 0.3385041 0.3385041 0.3385041
          [,89]      [,90]      [,91]      [,92]       [,93]    [,94]
[1,] -0.4909002 -0.3927202 -0.2945401 -0.1963601 -0.09818004 0.000000
[2,]  0.4682040  0.4682040  0.4682040  0.4682040  0.46820401 0.468204
          [,95]     [,96]     [,97]     [,98]     [,99]     [,100]     [,101]
[1,] 0.09818004 0.1963601 0.2945401 0.3927202 0.4909002 -0.4477263 -0.3581810
[2,] 0.46820401 0.4682040 0.4682040 0.4682040 0.4682040  0.5920417  0.5920417
         [,102]     [,103]      [,104]    [,105]     [,106]    [,107]    [,108]
[1,] -0.2686358 -0.1790905 -0.08954525 0.0000000 0.08954525 0.1790905 0.2686358
[2,]  0.5920417  0.5920417  0.59204175 0.5920417 0.59204175 0.5920417 0.5920417
        [,109]    [,110]
[1,] 0.3581810 0.4477263
[2,] 0.5920417 0.5920417

$newyorker
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10<