Derivatives.txt Derivatives.wxmx Simplify.xml

desruisseaux Thu, 29 May 2025 16:23:08 -0700

Author: desruisseaux
Date: Thu May 29 23:21:44 2025
New Revision: 1925964

URL: http://svn.apache.org/viewvc?rev=1925964&view=rev
Log:
Add the tools that were used for deriving the formulas of the Jacobian of the 
"Geographic to spherical" conversion.
https://issues.apache.org/jira/browse/SIS-302


Added:
    sis/analysis/Geographic to spherical/
    sis/analysis/Geographic to spherical/Derivatives.txt
    sis/analysis/Geographic to spherical/Derivatives.wxmx   (with props)
    sis/analysis/Geographic to spherical/Simplify.xml

Added: sis/analysis/Geographic to spherical/Derivatives.txt
URL: 
http://svn.apache.org/viewvc/sis/analysis/Geographic%20to%20spherical/Derivatives.txt?rev=1925964&view=auto
==============================================================================
--- sis/analysis/Geographic to spherical/Derivatives.txt (added)
+++ sis/analysis/Geographic to spherical/Derivatives.txt Thu May 29 23:21:44 
2025
@@ -0,0 +1,20 @@
+#
+# Results copied from "Derivatives.wxmx" as plain text.
+# For each derivative, the first line is copied verbatim.
+# The second line is the result of `ant -f Simplify.xml`
+# together with manual editions.
+#
+
+âÎ©/âÏ: diff(L, Ï);
+((e^2*(1-e^2)*sin(Ï)^2)/((1-e^2*sin(Ï)^2)^(3/2)*(1/sqrt(1-e^2*sin(Ï)^2)+h))+(sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h))/(cos(Ï)^2*(1/sqrt(1-e^2*sin(Ï)^2)+h))+((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)/(1/sqrt(1-e^2*sin(Ï)^2)+h)-(e^2*sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h))/((1-e^2*sin(Ï)^2)^(3/2)*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2))/((sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)^2)/(cos(Ï)^2*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2)+1)
+
+âÎ©/âh: diff(L, h);
+(sin(Ï)/(cos(Ï)*(1/sqrt(1-e^2*sin(Ï)^2)+h))-(sin(Ï)*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h))/(cos(Ï)*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2))/((sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)^2)/(cos(Ï)^2*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2)+1)
+After simplification: cosÏ*(sinÏ*r - Z) / (R*R)
+
+âR/âÏ: diff(R, Ï);
+(2*cos(Ï)*sin(Ï)*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)^2-2*cos(Ï)*sin(Ï)*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2+(2*e^2*(1-e^2)*cos(Ï)*sin(Ï)^3*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h))/(1-e^2*sin(Ï)^2)^(3/2)+(2*e^2*cos(Ï)^3*sin(Ï)*(1/sqrt(1-e^2*sin(Ï)^2)+h))/(1-e^2*sin(Ï)^2)^(3/2))/(2*sqrt(sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)^2+cos(Ï)^2*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2))
+
+âR/âh: diff(R, h);
+(2*sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)+2*cos(Ï)^2*(1/sqrt(1-e^2*sin(Ï)^2)+h))/(2*sqrt(sin(Ï)^2*((1-e^2)/sqrt(1-e^2*sin(Ï)^2)+h)^2+cos(Ï)^2*(1/sqrt(1-e^2*sin(Ï)^2)+h)^2))
+After simplification: (Z*sinÏ + r*cosÏ*cosÏ) / R

Added: sis/analysis/Geographic to spherical/Derivatives.wxmx
URL: 
http://svn.apache.org/viewvc/sis/analysis/Geographic%20to%20spherical/Derivatives.wxmx?rev=1925964&view=auto
==============================================================================
Binary file - no diff available.

Propchange: sis/analysis/Geographic to spherical/Derivatives.wxmx
------------------------------------------------------------------------------
    svn:mime-type = application/zip

Added: sis/analysis/Geographic to spherical/Simplify.xml
URL: 
http://svn.apache.org/viewvc/sis/analysis/Geographic%20to%20spherical/Simplify.xml?rev=1925964&view=auto
==============================================================================
--- sis/analysis/Geographic to spherical/Simplify.xml (added)
+++ sis/analysis/Geographic to spherical/Simplify.xml Thu May 29 23:21:44 2025
@@ -0,0 +1,61 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+  Simplification of the derivatives. The target values are names of variables
+  used in the `EllipsoidToCentricTransform` Java class. For running, copy the
+  formula to simplify in a temporary file named "formula.txt" then execute on
+  the command line: `ant -f Simplify.xml`.
+
+  Note that this file alone is not sufficient. Manual editions are needed.
+  It can be done by adding parenthesis and executing the Ant script again.
+  For example, if `1*Î½` has not been simplified, replace by `(1*Î½)`, then
+  re-execute Ant. `1*Î½` is a trivial example, but with larger expressions,
+  adding the missing parenthesis is safer than manual simplifications.
+-->
+<project name="Replace" default="replace">
+  <target name="replace">
+    <replace dir="." summary="yes">
+      <include name="formula.txt"/>
+      <replacefilter token="cos(Ï)" value="cosÏ"/>
+      <replacefilter token="sin(Ï)" value="sinÏ"/>
+      <replacefilter token="sinÏ^2" value="(sinÏ*sinÏ)"/>
+      <replacefilter token="cosÏ^2" value="(cosÏ*cosÏ)"/>
+      <replacefilter token="sinÏ^3" value="(sinÏ*sinÏ*sinÏ)"/>
+      <replacefilter token="cosÏ^3" value="(cosÏ*cosÏ*cosÏ)"/>
+
+      <replacefilter token=  "(1/(1-e^2*(sinÏ*sinÏ)))" value= "Î½2"/>
+      <replacefilter token=    "/(1-e^2*(sinÏ*sinÏ))"  value="*Î½2"/>
+      <replacefilter token=    "*(1-e^2*(sinÏ*sinÏ))"  value="/Î½2"/>
+      <replacefilter token="*sqrt(1-e^2*(sinÏ*sinÏ))"  value= "/Î½"/>
+      <replacefilter token="/sqrt(1-e^2*(sinÏ*sinÏ))"  value= "*Î½"/>
+      <replacefilter token=     "(1-e^2*(sinÏ*sinÏ))"  value= "(1/Î½2)"/>
+      <replacefilter token="sqrt(Î½2)"                  value= "Î½"/>
+      <replacefilter token="Î½2^(3/2)"                  value="(Î½2*Î½)"/>
+      <replacefilter token="(1/Î½2)^(3/2)"              value="(1/(Î½2*Î½))"/>
+      <replacefilter token="(Î½*(1-e^2))"               value= "Î½â¯"/>
+      <replacefilter token="((1-e^2)*Î½)"               value= "Î½â¯"/>
+      <replacefilter token="((1-e^2)*Î½+h)"             value= "(Î½â¯+h)"/>
+      <replacefilter token="(1*Î½+h)"                   value= "(Î½+h)"/>
+      <replacefilter token="(1*Î½)"                     value= "Î½"/>
+
+      <replacefilter token="(Î½+h)"                  value= "r"/>
+      <replacefilter token="((Î½â¯+h)*sinÏ)"          value= "Z"/>
+      <replacefilter token="(sinÏ*(Î½â¯+h))"          value= "Z"/>
+      <replacefilter token="((Î½â¯+h)^2*(sinÏ*sinÏ))" value="(Z*Z)"/>
+      <replacefilter token="((sinÏ*sinÏ)*(Î½â¯+h)^2)" value="(Z*Z)"/>
+      <replacefilter token="((sinÏ*sinÏ)*(Î½â¯+h))"   value="(sinÏ*Z)"/>
+      <replacefilter token="(sinÏ^3*(Î½â¯+h))"        
value="(sinÏ*sinÏ*Z)"/>
+      <replacefilter token="(sinÏ*(Î½â¯+h)^2)"        value="(Z*Z/sinÏ)"/>
+      <replacefilter token="Z^2"                    value="(Z*Z)"/>
+
+      <replacefilter token="(r*cosÏ)"           value="rcosÏ"/>
+      <replacefilter token="((cosÏ*cosÏ)*r^2)"  value="(rcosÏ*rcosÏ)"/>
+      <replacefilter token="(r^2*(cosÏ*cosÏ))"  value="(rcosÏ*rcosÏ)"/>
+      <replacefilter token="(r^2*cosÏ*cosÏ)"    value="(rcosÏ*rcosÏ)"/>
+      <replacefilter token="((cosÏ*cosÏ)*r)"    value="(cosÏ*rcosÏ)"/>
+
+      <replacefilter token="((Z*Z)/(rcosÏ*rcosÏ)+1)" 
value="(((Z*Z)+(rcosÏ*rcosÏ))/(rcosÏ*rcosÏ))"/>
+      <replacefilter token="sqrt((Z*Z)+rcosÏ*rcosÏ)" value="R"/>
+      <replacefilter token="((Z*Z)+(rcosÏ*rcosÏ))"   value="(R*R)"/>
+    </replace>
+  </target>
+</project>

svn commit: r1925964 - in /sis/analysis/Geographic to spherical: ./ Derivatives.txt Derivatives.wxmx Simplify.xml

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