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From: "Martin Desruisseaux (JIRA)"
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Subject: [jira] [Updated] (SIS-465) Referencing on celestial bodies with
high flattening factor
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[ https://issues.apache.org/jira/browse/SIS-465?page=3Dcom.atlassian.j=
ira.plugin.system.issuetabpanels:all-tabpanel ]
Martin Desruisseaux updated SIS-465:
------------------------------------
Description:=20
Some map projections or geodesic calculations use series expansions as appr=
oximations of integrals. Those series expansions are published in books lik=
e _Map Projections - A Working Manual_ (John P. Snyder, U.S. Geological Sur=
vey Professional Paper 1395, 1987) or _Coordinate Conversions and Transform=
ations including Formulas_ (EPSG Geomatics Guidance Note Number 7, part 2).=
But the number of terms in those series expansions is chosen for planets w=
ith a flattening factor like Earth. For celestial bodies with higher flatte=
ning factor, the number of terms may be insufficient. This JIRA issue lists=
some work that needs to be done if we want Apache SIS to support higher fl=
attening factors. There is two strategies: increase the number of terms, or=
use iterative methods.
h2. Mercator, Lambert conic, Polar stereographic
{{ConformalProjection}} is the base class of {{LambertConicConformal}}, {{M=
ercator}} and {{PolarStereographic}} projections and provides the algorithm=
described here. Apache SIS starts with series expansion. Then if the ellip=
soid eccentricity is greater than 0.16 (determined empirically for centimet=
ric precision), it continues with iterative method. For comparison, Earth e=
ccentricity is about 0.082.
*Status:* {color:green}done{color}, but does not converge for very high ecc=
entricity.
h2. Albers equal area, Cylindrical equal area
{{EqualAreaProjection}} is the base class of {{AlbersEqualArea}} and {{Cyli=
ndricalEqualArea}} projections and provides the algorithm described here. A=
pache SIS starts with series expansion. Then if the ellipsoid eccentricity =
is greater than 0.1 (determined empirically for centimetric precision), it =
continues with iterative method. For comparison, Earth eccentricity is abou=
t 0.082.
*Status:* {color:green}done{color}, but does not converge for very high ecc=
entricity.
h2. Polyconic, Sinusoidal=20
{{MeridianArcBased}} is the base class of {{Polyconic}} and {{Sinusoidal}} =
projections and provides the algorithm described here. Apache SIS uses seri=
es expansion only. We can increase the amount of terms by at least one by u=
ncommenting the {{cf5}} term, but it requires updating the {{dM_d=CF=86}} m=
ethod too.
*Status:* {color:red}*to do:* increase the number of terms at least with {{=
cf5}}.{color} We still have to determine at which eccentricity threshold we=
lost centrimetric accuracy for a planet the size of Earth.
h2. Transverse Mercator
There is currently no check of eccentricity limits. Note that Transverse Me=
rcator projection is approximate anyway (even on Earth) for coordinates far=
from central meridian. The effect of high flattening factor may be that th=
e area validity become smaller, but it needs to be verified.
*Status:* {color:red}*to do:* determine how area of validity varies with fl=
attening factor.{color}
h2. Geodesics on ellipsoid
Formulas currently implemented in {{GeodesicsOnEllipsoid}} class are derive=
d from [Karney 2013, Algorithms for geodesics|https://doi.org/10.1007/s0019=
0-012-0578-z]. A slightly older publication, [Karney 2011, Geodesics on an =
ellipsoid of revolution|https://arxiv.org/pdf/1102.1215.pdf], gives more te=
rms. Those additional terms were omitted in more recent publication because=
they are smaller than IEEE 754 double-precision when the flattening factor=
is Earth's one, but they can be useful for other celestial bodies. Incorpo=
rating those additional terms in Apache SIS requires that we update the Cle=
nshaw summation formulas that we use. [Multiple-Angle formulas|http://mathw=
orld.wolfram.com/Multiple-AngleFormulas.html] for 7=CE=B8 and 8=CE=B8 can b=
e determined by [Chebyshev polynomial of the second kind|http://mathworld.w=
olfram.com/ChebyshevPolynomialoftheSecondKind.html]. Another way to find th=
e Clenshaw summation formulas is to use the iterative algorithm given by Ka=
rney 2011 equation 59.
*Status:* {color:red}*to do:* add more terms in series expansions from Karn=
ey (2011).{color} We will still have to determine at which eccentricity thr=
eshold we lost centimetric precision for a planet of the size of Earth. The=
domain given by Karney 2013 (_f_ =E2=89=A4 1/150, equivalent to an eccentr=
icity of about 0.12) is for finer accuracy than centimetric.
was:
Some map projections or geodesic calculations use series expansions as appr=
oximations of integrals. Those series expansions are published in books lik=
e _Map Projections - A Working Manual_ (John P. Snyder, U.S. Geological Sur=
vey Professional Paper 1395, 1987) or _Coordinate Conversions and Transform=
ations including Formulas_ (EPSG Geomatics Guidance Note Number 7, part 2).=
But the number of terms in those series expansions is chosen for planets w=
ith a flattening factor like Earth. For celestial bodies with higher flatte=
ning factor, the number of terms may be insufficient. This JIRA issue lists=
some work that needs to be done if we want Apache SIS to support higher fl=
attening factors. There is two strategies: increase the number of terms, or=
use iterative methods.
h2. Mercator, Lambert conic, Polar stereographic
{{ConformalProjection}} is the base class of {{LambertConicConformal}}, {{M=
ercator}} and {{PolarStereographic}} projections and provides the algorithm=
described here. Apache SIS starts with series expansion. Then if the ellip=
soid eccentricity is greater than 0.16 (determined empirically for centimet=
ric precision), it continues with iterative method. For comparison, Earth e=
ccentricity is about 0.082.
*Status:* {color:green}done{color}, but does not converge for very high ecc=
entricity.
h2. Albers equal area, Cylindrical equal area
{{EqualAreaProjection}} is the base class of {{AlbersEqualArea}} and {{Cyli=
ndricalEqualArea}} projections and provides the algorithm described here. A=
pache SIS starts with series expansion. Then if the ellipsoid eccentricity =
is greater than 0.1 (determined empirically for centimetric precision), it =
continues with iterative method. For comparison, Earth eccentricity is abou=
t 0.082.
*Status:* {color:green}done{color}, but does not converge for very high ecc=
entricity.
h2. Polyconic, Sinusoidal=20
{{MeridianArcBased}} is the base class of {{Polyconic}} and {{Sinusoidal}} =
projections and provides the algorithm described here. Apache SIS uses seri=
es expansion only. We can increase the amount of terms by at least one by u=
ncommenting the {{cf5}} term, but it requires updating the {{dM_d=CF=86}} m=
ethod too.
*Status:* {color:red}*to do:* increase the number of terms at least with {{=
cf5}}.{color} We still have to determine at which eccentricity threshold we=
lost centrimetric accuracy for a planet the size of Earth.
h2. Transverse Mercator
There is currently no check of eccentricity limits. Note that Transverse Me=
rcator projection is approximate anyway (even on Earth) for coordinates far=
from central meridian. The effect of high flattening factor may be that th=
e area validity become smaller, but it needs to be verified.
*Status:* {color:red}*to do:* determine how area of validity varies with fl=
attening factor.{color}
h2. Geodesics on ellipsoid
Formulas currently implemented in {{GeodesicsOnEllipsoid}} class are derive=
d from [Karney 2013, Algorithms for geodesics|https://link.springer.com/con=
tent/pdf/10.1007%2Fs00190-012-0578-z.pdf]. A slightly older publication, [K=
arney 2011, Geodesics on an ellipsoid of revolution|https://arxiv.org/pdf/1=
102.1215.pdf], gives more terms. Those additional terms were omitted in mor=
e recent publication because they are smaller than IEEE 754 double-precisio=
n when the flattening factor is Earth's one, but they can be useful for oth=
er celestial bodies. Incorporating those additional terms in Apache SIS req=
uires that we update the Clenshaw summation formulas that we use. [Multiple=
-Angle formulas|http://mathworld.wolfram.com/Multiple-AngleFormulas.html] f=
or 7=CE=B8 and 8=CE=B8 can be determined by [Chebyshev polynomial of the se=
cond kind|http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.h=
tml]. Another way to find the Clenshaw summation formulas is to use the ite=
rative algorithm given by Karney 2011 equation 59.
*Status:* {color:red}*to do:* add more terms in series expansions from Karn=
ey (2011).{color} We will still have to determine at which eccentricity thr=
eshold we lost centimetric precision for a planet of the size of Earth. The=
domain given by Karney 2013 (_f_ =E2=89=A4 1/150, equivalent to an eccentr=
icity of about 0.12) is for finer accuracy than centimetric.
> Referencing on celestial bodies with high flattening factor
> -----------------------------------------------------------
>
> Key: SIS-465
> URL: https://issues.apache.org/jira/browse/SIS-465
> Project: Spatial Information Systems
> Issue Type: Improvement
> Components: Referencing
> Affects Versions: 0.6, 0.7, 0.8, 1.0
> Reporter: Martin Desruisseaux
> Priority: Major
>
> Some map projections or geodesic calculations use series expansions as ap=
proximations of integrals. Those series expansions are published in books l=
ike _Map Projections - A Working Manual_ (John P. Snyder, U.S. Geological S=
urvey Professional Paper 1395, 1987) or _Coordinate Conversions and Transfo=
rmations including Formulas_ (EPSG Geomatics Guidance Note Number 7, part 2=
). But the number of terms in those series expansions is chosen for planets=
with a flattening factor like Earth. For celestial bodies with higher flat=
tening factor, the number of terms may be insufficient. This JIRA issue lis=
ts some work that needs to be done if we want Apache SIS to support higher =
flattening factors. There is two strategies: increase the number of terms, =
or use iterative methods.
> h2. Mercator, Lambert conic, Polar stereographic
> {{ConformalProjection}} is the base class of {{LambertConicConformal}}, {=
{Mercator}} and {{PolarStereographic}} projections and provides the algorit=
hm described here. Apache SIS starts with series expansion. Then if the ell=
ipsoid eccentricity is greater than 0.16 (determined empirically for centim=
etric precision), it continues with iterative method. For comparison, Earth=
eccentricity is about 0.082.
> *Status:* {color:green}done{color}, but does not converge for very high e=
ccentricity.
> h2. Albers equal area, Cylindrical equal area
> {{EqualAreaProjection}} is the base class of {{AlbersEqualArea}} and {{Cy=
lindricalEqualArea}} projections and provides the algorithm described here.=
Apache SIS starts with series expansion. Then if the ellipsoid eccentricit=
y is greater than 0.1 (determined empirically for centimetric precision), i=
t continues with iterative method. For comparison, Earth eccentricity is ab=
out 0.082.
> *Status:* {color:green}done{color}, but does not converge for very high e=
ccentricity.
> h2. Polyconic, Sinusoidal=20
> {{MeridianArcBased}} is the base class of {{Polyconic}} and {{Sinusoidal}=
} projections and provides the algorithm described here. Apache SIS uses se=
ries expansion only. We can increase the amount of terms by at least one by=
uncommenting the {{cf5}} term, but it requires updating the {{dM_d=CF=86}}=
method too.
> *Status:* {color:red}*to do:* increase the number of terms at least with =
{{cf5}}.{color} We still have to determine at which eccentricity threshold =
we lost centrimetric accuracy for a planet the size of Earth.
> h2. Transverse Mercator
> There is currently no check of eccentricity limits. Note that Transverse =
Mercator projection is approximate anyway (even on Earth) for coordinates f=
ar from central meridian. The effect of high flattening factor may be that =
the area validity become smaller, but it needs to be verified.
> *Status:* {color:red}*to do:* determine how area of validity varies with =
flattening factor.{color}
> h2. Geodesics on ellipsoid
> Formulas currently implemented in {{GeodesicsOnEllipsoid}} class are deri=
ved from [Karney 2013, Algorithms for geodesics|https://doi.org/10.1007/s00=
190-012-0578-z]. A slightly older publication, [Karney 2011, Geodesics on a=
n ellipsoid of revolution|https://arxiv.org/pdf/1102.1215.pdf], gives more =
terms. Those additional terms were omitted in more recent publication becau=
se they are smaller than IEEE 754 double-precision when the flattening fact=
or is Earth's one, but they can be useful for other celestial bodies. Incor=
porating those additional terms in Apache SIS requires that we update the C=
lenshaw summation formulas that we use. [Multiple-Angle formulas|http://mat=
hworld.wolfram.com/Multiple-AngleFormulas.html] for 7=CE=B8 and 8=CE=B8 can=
be determined by [Chebyshev polynomial of the second kind|http://mathworld=
.wolfram.com/ChebyshevPolynomialoftheSecondKind.html]. Another way to find =
the Clenshaw summation formulas is to use the iterative algorithm given by =
Karney 2011 equation 59.
> *Status:* {color:red}*to do:* add more terms in series expansions from Ka=
rney (2011).{color} We will still have to determine at which eccentricity t=
hreshold we lost centimetric precision for a planet of the size of Earth. T=
he domain given by Karney 2013 (_f_ =E2=89=A4 1/150, equivalent to an eccen=
tricity of about 0.12) is for finer accuracy than centimetric.
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