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Added the WorldMagneticModel calculation module into the GCS utils.
git-svn-id: svn://svn.openpilot.org/OpenPilot/trunk@2515 ebee16cc-31ac-478f-84a7-5cbb03baadba
This commit is contained in:
pip
pip
parent
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commit
b1ed3c0381
@ -1,93 +1,95 @@
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TEMPLATE = lib
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TARGET = Utils
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QT += gui \
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network
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DEFINES += QTCREATOR_UTILS_LIB
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include(../../openpilotgcslibrary.pri)
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SOURCES += reloadpromptutils.cpp \
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settingsutils.cpp \
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filesearch.cpp \
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pathchooser.cpp \
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pathlisteditor.cpp \
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filewizardpage.cpp \
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filewizarddialog.cpp \
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projectintropage.cpp \
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basevalidatinglineedit.cpp \
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filenamevalidatinglineedit.cpp \
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projectnamevalidatinglineedit.cpp \
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codegeneration.cpp \
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newclasswidget.cpp \
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classnamevalidatinglineedit.cpp \
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linecolumnlabel.cpp \
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fancylineedit.cpp \
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qtcolorbutton.cpp \
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savedaction.cpp \
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submiteditorwidget.cpp \
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synchronousprocess.cpp \
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submitfieldwidget.cpp \
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consoleprocess.cpp \
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uncommentselection.cpp \
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parameteraction.cpp \
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treewidgetcolumnstretcher.cpp \
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checkablemessagebox.cpp \
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styledbar.cpp \
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stylehelper.cpp \
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welcomemodetreewidget.cpp \
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iwelcomepage.cpp \
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fancymainwindow.cpp \
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detailsbutton.cpp \
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detailswidget.cpp \
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coordinateconversions.cpp \
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pathutils.cpp
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win32 {
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SOURCES += abstractprocess_win.cpp \
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consoleprocess_win.cpp \
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winutils.cpp
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HEADERS += winutils.h
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}
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else:SOURCES += consoleprocess_unix.cpp
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HEADERS += utils_global.h \
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reloadpromptutils.h \
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settingsutils.h \
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filesearch.h \
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listutils.h \
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pathchooser.h \
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pathlisteditor.h \
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filewizardpage.h \
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filewizarddialog.h \
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projectintropage.h \
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basevalidatinglineedit.h \
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filenamevalidatinglineedit.h \
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projectnamevalidatinglineedit.h \
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codegeneration.h \
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newclasswidget.h \
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classnamevalidatinglineedit.h \
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linecolumnlabel.h \
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fancylineedit.h \
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qtcolorbutton.h \
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savedaction.h \
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submiteditorwidget.h \
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abstractprocess.h \
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consoleprocess.h \
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synchronousprocess.h \
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submitfieldwidget.h \
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uncommentselection.h \
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parameteraction.h \
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treewidgetcolumnstretcher.h \
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checkablemessagebox.h \
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qtcassert.h \
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styledbar.h \
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stylehelper.h \
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welcomemodetreewidget.h \
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iwelcomepage.h \
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fancymainwindow.h \
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detailsbutton.h \
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detailswidget.h \
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coordinateconversions.h \
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pathutils.h
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FORMS += filewizardpage.ui \
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projectintropage.ui \
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newclasswidget.ui \
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submiteditorwidget.ui \
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checkablemessagebox.ui
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RESOURCES += utils.qrc
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TEMPLATE = lib
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TARGET = Utils
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QT += gui \
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network
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DEFINES += QTCREATOR_UTILS_LIB
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include(../../openpilotgcslibrary.pri)
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SOURCES += reloadpromptutils.cpp \
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settingsutils.cpp \
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filesearch.cpp \
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pathchooser.cpp \
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pathlisteditor.cpp \
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filewizardpage.cpp \
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filewizarddialog.cpp \
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projectintropage.cpp \
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basevalidatinglineedit.cpp \
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filenamevalidatinglineedit.cpp \
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projectnamevalidatinglineedit.cpp \
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codegeneration.cpp \
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newclasswidget.cpp \
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classnamevalidatinglineedit.cpp \
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linecolumnlabel.cpp \
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fancylineedit.cpp \
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qtcolorbutton.cpp \
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savedaction.cpp \
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submiteditorwidget.cpp \
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synchronousprocess.cpp \
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submitfieldwidget.cpp \
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consoleprocess.cpp \
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uncommentselection.cpp \
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parameteraction.cpp \
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treewidgetcolumnstretcher.cpp \
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checkablemessagebox.cpp \
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styledbar.cpp \
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stylehelper.cpp \
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welcomemodetreewidget.cpp \
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iwelcomepage.cpp \
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fancymainwindow.cpp \
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detailsbutton.cpp \
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detailswidget.cpp \
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coordinateconversions.cpp \
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pathutils.cpp \
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worldmagmodel.cpp
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win32 {
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SOURCES += abstractprocess_win.cpp \
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consoleprocess_win.cpp \
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winutils.cpp
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HEADERS += winutils.h
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}
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else:SOURCES += consoleprocess_unix.cpp
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HEADERS += utils_global.h \
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reloadpromptutils.h \
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settingsutils.h \
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filesearch.h \
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listutils.h \
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pathchooser.h \
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pathlisteditor.h \
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filewizardpage.h \
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filewizarddialog.h \
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projectintropage.h \
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basevalidatinglineedit.h \
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filenamevalidatinglineedit.h \
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projectnamevalidatinglineedit.h \
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codegeneration.h \
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newclasswidget.h \
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classnamevalidatinglineedit.h \
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linecolumnlabel.h \
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fancylineedit.h \
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qtcolorbutton.h \
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savedaction.h \
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submiteditorwidget.h \
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abstractprocess.h \
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consoleprocess.h \
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synchronousprocess.h \
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submitfieldwidget.h \
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uncommentselection.h \
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parameteraction.h \
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treewidgetcolumnstretcher.h \
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checkablemessagebox.h \
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qtcassert.h \
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styledbar.h \
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stylehelper.h \
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welcomemodetreewidget.h \
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iwelcomepage.h \
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fancymainwindow.h \
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detailsbutton.h \
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detailswidget.h \
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coordinateconversions.h \
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pathutils.h \
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worldmagmodel.h
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FORMS += filewizardpage.ui \
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projectintropage.ui \
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newclasswidget.ui \
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submiteditorwidget.ui \
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checkablemessagebox.ui
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RESOURCES += utils.qrc
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1072
ground/src/libs/utils/worldmagmodel.cpp
Normal file
1072
ground/src/libs/utils/worldmagmodel.cpp
Normal file
@ -0,0 +1,1072 @@
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/**
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******************************************************************************
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*
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* @file worldmagmodel.cpp
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* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
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* @brief Utilities to find the location of openpilot GCS files:
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* - Plugins Share directory path
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*
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* @brief Source file for the World Magnetic Model
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* This is a port of code available from the US NOAA.
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*
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* The hard coded coefficients should be valid until 2015.
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*
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* Updated coeffs from ..
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* http://www.ngdc.noaa.gov/geomag/WMM/wmm_ddownload.shtml
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*
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* NASA C source code ..
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* http://www.ngdc.noaa.gov/geomag/WMM/wmm_wdownload.shtml
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*
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* Major changes include:
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* - No geoid model (altitude must be geodetic WGS-84)
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* - Floating point calculation (not double precision)
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* - Hard coded coefficients for model
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* - Elimination of user interface
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* - Elimination of dynamic memory allocation
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*
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* @see The GNU Public License (GPL) Version 3
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*
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*****************************************************************************/
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/*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*/
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#include "worldmagmodel.h"
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#include <stdint.h>
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#include <QDebug>
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#include <math.h>
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#define RAD2DEG(rad) ((rad) * (180.0 / M_PI))
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#define DEG2RAD(deg) ((deg) * (M_PI / 180.0))
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// updated coeffs available from http://www.ngdc.noaa.gov/geomag/WMM/wmm_ddownload.shtml
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const double CoeffFile[91][6] = {
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{0, 0, 0, 0, 0, 0},
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{1, 0, -29496.6, 0.0, 11.6, 0.0},
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{1, 1, -1586.3, 4944.4, 16.5, -25.9},
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{2, 0, -2396.6, 0.0, -12.1, 0.0},
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{2, 1, 3026.1, -2707.7, -4.4, -22.5},
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{2, 2, 1668.6, -576.1, 1.9, -11.8},
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{3, 0, 1340.1, 0.0, 0.4, 0.0},
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{3, 1, -2326.2, -160.2, -4.1, 7.3},
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{3, 2, 1231.9, 251.9, -2.9, -3.9},
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{3, 3, 634.0, -536.6, -7.7, -2.6},
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{4, 0, 912.6, 0.0, -1.8, 0.0},
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{4, 1, 808.9, 286.4, 2.3, 1.1},
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{4, 2, 166.7, -211.2, -8.7, 2.7},
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{4, 3, -357.1, 164.3, 4.6, 3.9},
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{4, 4, 89.4, -309.1, -2.1, -0.8},
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{5, 0, -230.9, 0.0, -1.0, 0.0},
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{5, 1, 357.2, 44.6, 0.6, 0.4},
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{5, 2, 200.3, 188.9, -1.8, 1.8},
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{5, 3, -141.1, -118.2, -1.0, 1.2},
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{5, 4, -163.0, 0.0, 0.9, 4.0},
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{5, 5, -7.8, 100.9, 1.0, -0.6},
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{6, 0, 72.8, 0.0, -0.2, 0.0},
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{6, 1, 68.6, -20.8, -0.2, -0.2},
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{6, 2, 76.0, 44.1, -0.1, -2.1},
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{6, 3, -141.4, 61.5, 2.0, -0.4},
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{6, 4, -22.8, -66.3, -1.7, -0.6},
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{6, 5, 13.2, 3.1, -0.3, 0.5},
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{6, 6, -77.9, 55.0, 1.7, 0.9},
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{7, 0, 80.5, 0.0, 0.1, 0.0},
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{7, 1, -75.1, -57.9, -0.1, 0.7},
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{7, 2, -4.7, -21.1, -0.6, 0.3},
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{7, 3, 45.3, 6.5, 1.3, -0.1},
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{7, 4, 13.9, 24.9, 0.4, -0.1},
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{7, 5, 10.4, 7.0, 0.3, -0.8},
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{7, 6, 1.7, -27.7, -0.7, -0.3},
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{7, 7, 4.9, -3.3, 0.6, 0.3},
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{8, 0, 24.4, 0.0, -0.1, 0.0},
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{8, 1, 8.1, 11.0, 0.1, -0.1},
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{8, 2, -14.5, -20.0, -0.6, 0.2},
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{8, 3, -5.6, 11.9, 0.2, 0.4},
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{8, 4, -19.3, -17.4, -0.2, 0.4},
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{8, 5, 11.5, 16.7, 0.3, 0.1},
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{8, 6, 10.9, 7.0, 0.3, -0.1},
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{8, 7, -14.1, -10.8, -0.6, 0.4},
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{8, 8, -3.7, 1.7, 0.2, 0.3},
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{9, 0, 5.4, 0.0, 0.0, 0.0},
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{9, 1, 9.4, -20.5, -0.1, 0.0},
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{9, 2, 3.4, 11.5, 0.0, -0.2},
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{9, 3, -5.2, 12.8, 0.3, 0.0},
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{9, 4, 3.1, -7.2, -0.4, -0.1},
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{9, 5, -12.4, -7.4, -0.3, 0.1},
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{9, 6, -0.7, 8.0, 0.1, 0.0},
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{9, 7, 8.4, 2.1, -0.1, -0.2},
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{9, 8, -8.5, -6.1, -0.4, 0.3},
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{9, 9, -10.1, 7.0, -0.2, 0.2},
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{10, 0, -2.0, 0.0, 0.0, 0.0},
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{10, 1, -6.3, 2.8, 0.0, 0.1},
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{10, 2, 0.9, -0.1, -0.1, -0.1},
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{10, 3, -1.1, 4.7, 0.2, 0.0},
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{10, 4, -0.2, 4.4, 0.0, -0.1},
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{10, 5, 2.5, -7.2, -0.1, -0.1},
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{10, 6, -0.3, -1.0, -0.2, 0.0},
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{10, 7, 2.2, -3.9, 0.0, -0.1},
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{10, 8, 3.1, -2.0, -0.1, -0.2},
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{10, 9, -1.0, -2.0, -0.2, 0.0},
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{10, 10, -2.8, -8.3, -0.2, -0.1},
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{11, 0, 3.0, 0.0, 0.0, 0.0},
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{11, 1, -1.5, 0.2, 0.0, 0.0},
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{11, 2, -2.1, 1.7, 0.0, 0.1},
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{11, 3, 1.7, -0.6, 0.1, 0.0},
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{11, 4, -0.5, -1.8, 0.0, 0.1},
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{11, 5, 0.5, 0.9, 0.0, 0.0},
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{11, 6, -0.8, -0.4, 0.0, 0.1},
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{11, 7, 0.4, -2.5, 0.0, 0.0},
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{11, 8, 1.8, -1.3, 0.0, -0.1},
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{11, 9, 0.1, -2.1, 0.0, -0.1},
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{11, 10, 0.7, -1.9, -0.1, 0.0},
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{11, 11, 3.8, -1.8, 0.0, -0.1},
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{12, 0, -2.2, 0.0, 0.0, 0.0},
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{12, 1, -0.2, -0.9, 0.0, 0.0},
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{12, 2, 0.3, 0.3, 0.1, 0.0},
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{12, 3, 1.0, 2.1, 0.1, 0.0},
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{12, 4, -0.6, -2.5, -0.1, 0.0},
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{12, 5, 0.9, 0.5, 0.0, 0.0},
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{12, 6, -0.1, 0.6, 0.0, 0.1},
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{12, 7, 0.5, 0.0, 0.0, 0.0},
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{12, 8, -0.4, 0.1, 0.0, 0.0},
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{12, 9, -0.4, 0.3, 0.0, 0.0},
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{12, 10, 0.2, -0.9, 0.0, 0.0},
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{12, 11, -0.8, -0.2, -0.1, 0.0},
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{12, 12, 0.0, 0.9, 0.1, 0.0}
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};
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namespace Utils {
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WorldMagModel::WorldMagModel()
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{
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Initialize();
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}
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int WorldMagModel::GetMagVector(double Lat, double Lon, double AltEllipsoid, int Month, int Day, int Year, double *X, double *Y, double *Z)
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{
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// ***********
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// range check supplied params
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if (Lat < -90) return -1; // error
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if (Lat > 90) return -2; // error
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if (Lon < -180) return -3; // error
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if (Lon > 180) return -4; // error
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// ***********
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WMMtype_CoordSpherical CoordSpherical;
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WMMtype_CoordGeodetic CoordGeodetic;
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WMMtype_GeoMagneticElements GeoMagneticElements;
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Initialize();
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CoordGeodetic.lambda = Lon;
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CoordGeodetic.phi = Lat;
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CoordGeodetic.HeightAboveEllipsoid = AltEllipsoid;
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// Convert from geodeitic to Spherical Equations: 17-18, WMM Technical report
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GeodeticToSpherical(&CoordGeodetic, &CoordSpherical);
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if (DateToYear(Month, Day, Year) < 0)
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return -5; // error
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// Compute the geoMagnetic field elements and their time change
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if (Geomag(&CoordSpherical, &CoordGeodetic, &GeoMagneticElements) < 0)
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return -6; // error
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// set the returned values
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*X = GeoMagneticElements.X;
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*Y = GeoMagneticElements.Y;
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*Z = GeoMagneticElements.Z;
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// ***********
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return 0; // OK
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}
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void WorldMagModel::Initialize()
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{ // Sets default values for WMM subroutines.
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// UPDATES : Ellip and MagneticModel
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// Sets WGS-84 parameters
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Ellip.a = 6378.137; // semi-major axis of the ellipsoid in km
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Ellip.b = 6356.7523142; // semi-minor axis of the ellipsoid in km
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Ellip.fla = 1 / 298.257223563; // flattening
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Ellip.eps = sqrt(1 - (Ellip.b * Ellip.b) / (Ellip.a * Ellip.a)); // first eccentricity
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Ellip.epssq = (Ellip.eps * Ellip.eps); // first eccentricity squared
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Ellip.re = 6371.2; // Earth's radius in km
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// Sets Magnetic Model parameters
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MagneticModel.nMax = WMM_MAX_MODEL_DEGREES;
|
||||
MagneticModel.nMaxSecVar = WMM_MAX_SECULAR_VARIATION_MODEL_DEGREES;
|
||||
MagneticModel.SecularVariationUsed = 0;
|
||||
|
||||
// Really, Really needs to be read from a file - out of date in 2015 at latest
|
||||
MagneticModel.EditionDate = 5.7863328170559505e-307;
|
||||
MagneticModel.epoch = 2010.0;
|
||||
sprintf(MagneticModel.ModelName, "WMM-2010");
|
||||
}
|
||||
|
||||
|
||||
int WorldMagModel::Geomag(WMMtype_CoordSpherical *CoordSpherical, WMMtype_CoordGeodetic *CoordGeodetic, WMMtype_GeoMagneticElements *GeoMagneticElements)
|
||||
/*
|
||||
The main subroutine that calls a sequence of WMM sub-functions to calculate the magnetic field elements for a single point.
|
||||
The function expects the model coefficients and point coordinates as input and returns the magnetic field elements and
|
||||
their rate of change. Though, this subroutine can be called successively to calculate a time series, profile or grid
|
||||
of magnetic field, these are better achieved by the subroutine WMM_Grid.
|
||||
|
||||
INPUT: Ellip
|
||||
CoordSpherical
|
||||
CoordGeodetic
|
||||
TimedMagneticModel
|
||||
|
||||
OUTPUT : GeoMagneticElements
|
||||
*/
|
||||
{
|
||||
WMMtype_MagneticResults MagneticResultsSph;
|
||||
WMMtype_MagneticResults MagneticResultsGeo;
|
||||
WMMtype_MagneticResults MagneticResultsSphVar;
|
||||
WMMtype_MagneticResults MagneticResultsGeoVar;
|
||||
WMMtype_LegendreFunction LegendreFunction;
|
||||
WMMtype_SphericalHarmonicVariables SphVariables;
|
||||
|
||||
// Compute Spherical Harmonic variables
|
||||
ComputeSphericalHarmonicVariables(CoordSpherical, MagneticModel.nMax, &SphVariables);
|
||||
|
||||
// Compute ALF
|
||||
if (AssociatedLegendreFunction(CoordSpherical, MagneticModel.nMax, &LegendreFunction) < 0)
|
||||
return -1; // error
|
||||
|
||||
// Accumulate the spherical harmonic coefficients
|
||||
Summation(&LegendreFunction, &SphVariables, CoordSpherical, &MagneticResultsSph);
|
||||
|
||||
// Sum the Secular Variation Coefficients
|
||||
SecVarSummation(&LegendreFunction, &SphVariables, CoordSpherical, &MagneticResultsSphVar);
|
||||
|
||||
// Map the computed Magnetic fields to Geodeitic coordinates
|
||||
RotateMagneticVector(CoordSpherical, CoordGeodetic, &MagneticResultsSph, &MagneticResultsGeo);
|
||||
|
||||
// Map the secular variation field components to Geodetic coordinates
|
||||
RotateMagneticVector(CoordSpherical, CoordGeodetic, &MagneticResultsSphVar, &MagneticResultsGeoVar);
|
||||
|
||||
// Calculate the Geomagnetic elements, Equation 18 , WMM Technical report
|
||||
CalculateGeoMagneticElements(&MagneticResultsGeo, GeoMagneticElements);
|
||||
|
||||
// Calculate the secular variation of each of the Geomagnetic elements
|
||||
CalculateSecularVariation(&MagneticResultsGeoVar, GeoMagneticElements);
|
||||
|
||||
return 0; // OK
|
||||
}
|
||||
|
||||
void WorldMagModel::ComputeSphericalHarmonicVariables(WMMtype_CoordSpherical *CoordSpherical, int nMax, WMMtype_SphericalHarmonicVariables *SphVariables)
|
||||
{
|
||||
/* Computes Spherical variables
|
||||
Variables computed are (a/r)^(n+2), cos_m(lamda) and sin_m(lambda) for spherical harmonic
|
||||
summations. (Equations 10-12 in the WMM Technical Report)
|
||||
INPUT Ellip data structure with the following elements
|
||||
float a; semi-major axis of the ellipsoid
|
||||
float b; semi-minor axis of the ellipsoid
|
||||
float fla; flattening
|
||||
float epssq; first eccentricity squared
|
||||
float eps; first eccentricity
|
||||
float re; mean radius of ellipsoid
|
||||
CoordSpherical A data structure with the following elements
|
||||
float lambda; ( longitude)
|
||||
float phig; ( geocentric latitude )
|
||||
float r; ( distance from the center of the ellipsoid)
|
||||
nMax integer ( Maxumum degree of spherical harmonic secular model)\
|
||||
|
||||
OUTPUT SphVariables Pointer to the data structure with the following elements
|
||||
float RelativeRadiusPower[WMM_MAX_MODEL_DEGREES+1]; [earth_reference_radius_km sph. radius ]^n
|
||||
float cos_mlambda[WMM_MAX_MODEL_DEGREES+1]; cp(m) - cosine of (mspherical coord. longitude)
|
||||
float sin_mlambda[WMM_MAX_MODEL_DEGREES+1]; sp(m) - sine of (mspherical coord. longitude)
|
||||
*/
|
||||
double cos_lambda = cos(DEG2RAD(CoordSpherical->lambda));
|
||||
double sin_lambda = sin(DEG2RAD(CoordSpherical->lambda));
|
||||
|
||||
/* for n = 0 ... model_order, compute (Radius of Earth / Spherica radius r)^(n+2)
|
||||
for n 1..nMax-1 (this is much faster than calling pow MAX_N+1 times). */
|
||||
|
||||
SphVariables->RelativeRadiusPower[0] = (Ellip.re / CoordSpherical->r) * (Ellip.re / CoordSpherical->r);
|
||||
for (int n = 1; n <= nMax; n++)
|
||||
SphVariables->RelativeRadiusPower[n] = SphVariables->RelativeRadiusPower[n - 1] * (Ellip.re / CoordSpherical->r);
|
||||
|
||||
/*
|
||||
Compute cos(m*lambda), sin(m*lambda) for m = 0 ... nMax
|
||||
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
|
||||
sin(a + b) = cos(a)*sin(b) + sin(a)*cos(b)
|
||||
*/
|
||||
SphVariables->cos_mlambda[0] = 1.0;
|
||||
SphVariables->sin_mlambda[0] = 0.0;
|
||||
|
||||
SphVariables->cos_mlambda[1] = cos_lambda;
|
||||
SphVariables->sin_mlambda[1] = sin_lambda;
|
||||
for (int m = 2; m <= nMax; m++)
|
||||
{
|
||||
SphVariables->cos_mlambda[m] = SphVariables->cos_mlambda[m - 1] * cos_lambda - SphVariables->sin_mlambda[m - 1] * sin_lambda;
|
||||
SphVariables->sin_mlambda[m] = SphVariables->cos_mlambda[m - 1] * sin_lambda + SphVariables->sin_mlambda[m - 1] * cos_lambda;
|
||||
}
|
||||
}
|
||||
|
||||
int WorldMagModel::AssociatedLegendreFunction(WMMtype_CoordSpherical *CoordSpherical, int nMax, WMMtype_LegendreFunction *LegendreFunction)
|
||||
{
|
||||
/* Computes all of the Schmidt-semi normalized associated Legendre
|
||||
functions up to degree nMax. If nMax <= 16, function WMM_PcupLow is used.
|
||||
Otherwise WMM_PcupHigh is called.
|
||||
INPUT CoordSpherical A data structure with the following elements
|
||||
float lambda; ( longitude)
|
||||
float phig; ( geocentric latitude )
|
||||
float r; ( distance from the center of the ellipsoid)
|
||||
nMax integer ( Maxumum degree of spherical harmonic secular model)
|
||||
LegendreFunction Pointer to data structure with the following elements
|
||||
float *Pcup; ( pointer to store Legendre Function )
|
||||
float *dPcup; ( pointer to store Derivative of Lagendre function )
|
||||
|
||||
OUTPUT LegendreFunction Calculated Legendre variables in the data structure
|
||||
*/
|
||||
|
||||
double sin_phi = sin(DEG2RAD(CoordSpherical->phig)); // sin (geocentric latitude)
|
||||
|
||||
if (nMax <= 16 || (1 - fabs(sin_phi)) < 1.0e-10) /* If nMax is less tha 16 or at the poles */
|
||||
PcupLow(LegendreFunction->Pcup, LegendreFunction->dPcup, sin_phi, nMax);
|
||||
else
|
||||
{
|
||||
if (PcupHigh(LegendreFunction->Pcup, LegendreFunction->dPcup, sin_phi, nMax) < 0)
|
||||
return -1; // error
|
||||
}
|
||||
|
||||
return 0; // OK
|
||||
}
|
||||
|
||||
void WorldMagModel::Summation( WMMtype_LegendreFunction *LegendreFunction,
|
||||
WMMtype_SphericalHarmonicVariables *SphVariables,
|
||||
WMMtype_CoordSpherical *CoordSpherical,
|
||||
WMMtype_MagneticResults *MagneticResults)
|
||||
{
|
||||
/* Computes Geomagnetic Field Elements X, Y and Z in Spherical coordinate system using spherical harmonic summation.
|
||||
|
||||
The vector Magnetic field is given by -grad V, where V is Geomagnetic scalar potential
|
||||
The gradient in spherical coordinates is given by:
|
||||
|
||||
dV ^ 1 dV ^ 1 dV ^
|
||||
grad V = -- r + - -- t + -------- -- p
|
||||
dr r dt r sin(t) dp
|
||||
|
||||
INPUT : LegendreFunction
|
||||
MagneticModel
|
||||
SphVariables
|
||||
CoordSpherical
|
||||
OUTPUT : MagneticResults
|
||||
|
||||
Manoj Nair, June, 2009 Manoj.C.Nair@Noaa.Gov
|
||||
*/
|
||||
|
||||
MagneticResults->Bz = 0.0;
|
||||
MagneticResults->By = 0.0;
|
||||
MagneticResults->Bx = 0.0;
|
||||
|
||||
for (int n = 1; n <= MagneticModel.nMax; n++)
|
||||
{
|
||||
for (int m = 0; m <= n; m++)
|
||||
{
|
||||
int index = (n * (n + 1) / 2 + m);
|
||||
|
||||
/* nMax (n+2) n m m m
|
||||
Bz = -SUM (a/r) (n+1) SUM [g cos(m p) + h sin(m p)] P (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Equation 12 in the WMM Technical report. Derivative with respect to radius.*/
|
||||
MagneticResults->Bz -=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_main_field_coeff_g(index) *
|
||||
SphVariables->cos_mlambda[m] + get_main_field_coeff_h(index) * SphVariables->sin_mlambda[m])
|
||||
* (double)(n + 1) * LegendreFunction->Pcup[index];
|
||||
|
||||
/* 1 nMax (n+2) n m m m
|
||||
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Equation 11 in the WMM Technical report. Derivative with respect to longitude, divided by radius. */
|
||||
MagneticResults->By +=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_main_field_coeff_g(index) *
|
||||
SphVariables->sin_mlambda[m] - get_main_field_coeff_h(index) * SphVariables->cos_mlambda[m])
|
||||
* (double)(m) * LegendreFunction->Pcup[index];
|
||||
/* nMax (n+2) n m m m
|
||||
Bx = - SUM (a/r) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Equation 10 in the WMM Technical report. Derivative with respect to latitude, divided by radius. */
|
||||
|
||||
MagneticResults->Bx -=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_main_field_coeff_g(index) *
|
||||
SphVariables->cos_mlambda[m] + get_main_field_coeff_h(index) * SphVariables->sin_mlambda[m])
|
||||
* LegendreFunction->dPcup[index];
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
double cos_phi = cos(DEG2RAD(CoordSpherical->phig));
|
||||
if (fabs(cos_phi) > 1.0e-10)
|
||||
{
|
||||
MagneticResults->By = MagneticResults->By / cos_phi;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* Special calculation for component - By - at Geographic poles.
|
||||
* If the user wants to avoid using this function, please make sure that
|
||||
* the latitude is not exactly +/-90. An option is to make use the function
|
||||
* WMM_CheckGeographicPoles.
|
||||
*/
|
||||
SummationSpecial(SphVariables, CoordSpherical, MagneticResults);
|
||||
}
|
||||
}
|
||||
|
||||
void WorldMagModel::SecVarSummation( WMMtype_LegendreFunction *LegendreFunction,
|
||||
WMMtype_SphericalHarmonicVariables *SphVariables,
|
||||
WMMtype_CoordSpherical *CoordSpherical,
|
||||
WMMtype_MagneticResults *MagneticResults)
|
||||
{
|
||||
/*This Function sums the secular variation coefficients to get the secular variation of the Magnetic vector.
|
||||
INPUT : LegendreFunction
|
||||
MagneticModel
|
||||
SphVariables
|
||||
CoordSpherical
|
||||
OUTPUT : MagneticResults
|
||||
*/
|
||||
|
||||
MagneticModel.SecularVariationUsed = true;
|
||||
|
||||
MagneticResults->Bz = 0.0;
|
||||
MagneticResults->By = 0.0;
|
||||
MagneticResults->Bx = 0.0;
|
||||
|
||||
for (int n = 1; n <= MagneticModel.nMaxSecVar; n++)
|
||||
{
|
||||
for (int m = 0; m <= n; m++)
|
||||
{
|
||||
int index = (n * (n + 1) / 2 + m);
|
||||
|
||||
/* nMax (n+2) n m m m
|
||||
Bz = -SUM (a/r) (n+1) SUM [g cos(m p) + h sin(m p)] P (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Derivative with respect to radius.*/
|
||||
MagneticResults->Bz -=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_secular_var_coeff_g(index) *
|
||||
SphVariables->cos_mlambda[m] + get_secular_var_coeff_h(index) * SphVariables->sin_mlambda[m])
|
||||
* (double)(n + 1) * LegendreFunction->Pcup[index];
|
||||
|
||||
/* 1 nMax (n+2) n m m m
|
||||
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Derivative with respect to longitude, divided by radius. */
|
||||
MagneticResults->By +=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_secular_var_coeff_g(index) *
|
||||
SphVariables->sin_mlambda[m] - get_secular_var_coeff_h(index) * SphVariables->cos_mlambda[m])
|
||||
* (double)(m) * LegendreFunction->Pcup[index];
|
||||
/* nMax (n+2) n m m m
|
||||
Bx = - SUM (a/r) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Derivative with respect to latitude, divided by radius. */
|
||||
|
||||
MagneticResults->Bx -=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_secular_var_coeff_g(index) *
|
||||
SphVariables->cos_mlambda[m] + get_secular_var_coeff_h(index) * SphVariables->sin_mlambda[m])
|
||||
* LegendreFunction->dPcup[index];
|
||||
}
|
||||
}
|
||||
|
||||
double cos_phi = cos(DEG2RAD(CoordSpherical->phig));
|
||||
if (fabs(cos_phi) > 1.0e-10)
|
||||
{
|
||||
MagneticResults->By = MagneticResults->By / cos_phi;
|
||||
}
|
||||
else
|
||||
{ /* Special calculation for component By at Geographic poles */
|
||||
SecVarSummationSpecial(SphVariables, CoordSpherical, MagneticResults);
|
||||
}
|
||||
}
|
||||
|
||||
void WorldMagModel::RotateMagneticVector( WMMtype_CoordSpherical *CoordSpherical,
|
||||
WMMtype_CoordGeodetic *CoordGeodetic,
|
||||
WMMtype_MagneticResults *MagneticResultsSph,
|
||||
WMMtype_MagneticResults *MagneticResultsGeo)
|
||||
{
|
||||
/* Rotate the Magnetic Vectors to Geodetic Coordinates
|
||||
Manoj Nair, June, 2009 Manoj.C.Nair@Noaa.Gov
|
||||
Equation 16, WMM Technical report
|
||||
|
||||
INPUT : CoordSpherical : Data structure WMMtype_CoordSpherical with the following elements
|
||||
float lambda; ( longitude)
|
||||
float phig; ( geocentric latitude )
|
||||
float r; ( distance from the center of the ellipsoid)
|
||||
|
||||
CoordGeodetic : Data structure WMMtype_CoordGeodetic with the following elements
|
||||
float lambda; (longitude)
|
||||
float phi; ( geodetic latitude)
|
||||
float HeightAboveEllipsoid; (height above the ellipsoid (HaE) )
|
||||
float HeightAboveGeoid;(height above the Geoid )
|
||||
|
||||
MagneticResultsSph : Data structure WMMtype_MagneticResults with the following elements
|
||||
float Bx; North
|
||||
float By; East
|
||||
float Bz; Down
|
||||
|
||||
OUTPUT: MagneticResultsGeo Pointer to the data structure WMMtype_MagneticResults, with the following elements
|
||||
float Bx; North
|
||||
float By; East
|
||||
float Bz; Down
|
||||
*/
|
||||
|
||||
/* Difference between the spherical and Geodetic latitudes */
|
||||
double Psi = DEG2RAD(CoordSpherical->phig - CoordGeodetic->phi);
|
||||
|
||||
/* Rotate spherical field components to the Geodeitic system */
|
||||
MagneticResultsGeo->Bz = MagneticResultsSph->Bx * sin(Psi) + MagneticResultsSph->Bz * cos(Psi);
|
||||
MagneticResultsGeo->Bx = MagneticResultsSph->Bx * cos(Psi) - MagneticResultsSph->Bz * sin(Psi);
|
||||
MagneticResultsGeo->By = MagneticResultsSph->By;
|
||||
}
|
||||
|
||||
void WorldMagModel::CalculateGeoMagneticElements(WMMtype_MagneticResults *MagneticResultsGeo, WMMtype_GeoMagneticElements *GeoMagneticElements)
|
||||
{
|
||||
/* Calculate all the Geomagnetic elements from X,Y and Z components
|
||||
INPUT MagneticResultsGeo Pointer to data structure with the following elements
|
||||
float Bx; ( North )
|
||||
float By; ( East )
|
||||
float Bz; ( Down )
|
||||
OUTPUT GeoMagneticElements Pointer to data structure with the following elements
|
||||
float Decl; (Angle between the magnetic field vector and true north, positive east)
|
||||
float Incl; Angle between the magnetic field vector and the horizontal plane, positive down
|
||||
float F; Magnetic Field Strength
|
||||
float H; Horizontal Magnetic Field Strength
|
||||
float X; Northern component of the magnetic field vector
|
||||
float Y; Eastern component of the magnetic field vector
|
||||
float Z; Downward component of the magnetic field vector
|
||||
*/
|
||||
|
||||
GeoMagneticElements->X = MagneticResultsGeo->Bx;
|
||||
GeoMagneticElements->Y = MagneticResultsGeo->By;
|
||||
GeoMagneticElements->Z = MagneticResultsGeo->Bz;
|
||||
|
||||
GeoMagneticElements->H = sqrt(MagneticResultsGeo->Bx * MagneticResultsGeo->Bx + MagneticResultsGeo->By * MagneticResultsGeo->By);
|
||||
GeoMagneticElements->F = sqrt(GeoMagneticElements->H * GeoMagneticElements->H + MagneticResultsGeo->Bz * MagneticResultsGeo->Bz);
|
||||
GeoMagneticElements->Decl = RAD2DEG(atan2(GeoMagneticElements->Y, GeoMagneticElements->X));
|
||||
GeoMagneticElements->Incl = RAD2DEG(atan2(GeoMagneticElements->Z, GeoMagneticElements->H));
|
||||
}
|
||||
|
||||
void WorldMagModel::CalculateSecularVariation(WMMtype_MagneticResults *MagneticVariation, WMMtype_GeoMagneticElements *MagneticElements)
|
||||
{
|
||||
/* This takes the Magnetic Variation in x, y, and z and uses it to calculate the secular variation of each of the Geomagnetic elements.
|
||||
INPUT MagneticVariation Data structure with the following elements
|
||||
float Bx; ( North )
|
||||
float By; ( East )
|
||||
float Bz; ( Down )
|
||||
OUTPUT MagneticElements Pointer to the data structure with the following elements updated
|
||||
float Decldot; Yearly Rate of change in declination
|
||||
float Incldot; Yearly Rate of change in inclination
|
||||
float Fdot; Yearly rate of change in Magnetic field strength
|
||||
float Hdot; Yearly rate of change in horizontal field strength
|
||||
float Xdot; Yearly rate of change in the northern component
|
||||
float Ydot; Yearly rate of change in the eastern component
|
||||
float Zdot; Yearly rate of change in the downward component
|
||||
float GVdot;Yearly rate of chnage in grid variation
|
||||
*/
|
||||
|
||||
MagneticElements->Xdot = MagneticVariation->Bx;
|
||||
MagneticElements->Ydot = MagneticVariation->By;
|
||||
MagneticElements->Zdot = MagneticVariation->Bz;
|
||||
MagneticElements->Hdot = (MagneticElements->X * MagneticElements->Xdot + MagneticElements->Y * MagneticElements->Ydot) / MagneticElements->H; //See equation 19 in the WMM technical report
|
||||
MagneticElements->Fdot =
|
||||
(MagneticElements->X * MagneticElements->Xdot +
|
||||
MagneticElements->Y * MagneticElements->Ydot + MagneticElements->Z * MagneticElements->Zdot) / MagneticElements->F;
|
||||
MagneticElements->Decldot =
|
||||
180.0 / M_PI * (MagneticElements->X * MagneticElements->Ydot -
|
||||
MagneticElements->Y * MagneticElements->Xdot) / (MagneticElements->H * MagneticElements->H);
|
||||
MagneticElements->Incldot =
|
||||
180.0 / M_PI * (MagneticElements->H * MagneticElements->Zdot -
|
||||
MagneticElements->Z * MagneticElements->Hdot) / (MagneticElements->F * MagneticElements->F);
|
||||
MagneticElements->GVdot = MagneticElements->Decldot;
|
||||
}
|
||||
|
||||
int WorldMagModel::PcupHigh(double *Pcup, double *dPcup, double x, int nMax)
|
||||
{
|
||||
/* This function evaluates all of the Schmidt-semi normalized associated Legendre
|
||||
functions up to degree nMax. The functions are initially scaled by
|
||||
10^280 sin^m in order to minimize the effects of underflow at large m
|
||||
near the poles (see Holmes and Featherstone 2002, J. Geodesy, 76, 279-299).
|
||||
Note that this function performs the same operation as WMM_PcupLow.
|
||||
However this function also can be used for high degree (large nMax) models.
|
||||
|
||||
Calling Parameters:
|
||||
INPUT
|
||||
nMax: Maximum spherical harmonic degree to compute.
|
||||
x: cos(colatitude) or sin(latitude).
|
||||
|
||||
OUTPUT
|
||||
Pcup: A vector of all associated Legendgre polynomials evaluated at
|
||||
x up to nMax. The lenght must by greater or equal to (nMax+1)*(nMax+2)/2.
|
||||
dPcup: Derivative of Pcup(x) with respect to latitude
|
||||
Notes:
|
||||
|
||||
Adopted from the FORTRAN code written by Mark Wieczorek September 25, 2005.
|
||||
|
||||
Manoj Nair, Nov, 2009 Manoj.C.Nair@Noaa.Gov
|
||||
|
||||
Change from the previous version
|
||||
The prevous version computes the derivatives as
|
||||
dP(n,m)(x)/dx, where x = sin(latitude) (or cos(colatitude) ).
|
||||
However, the WMM Geomagnetic routines requires dP(n,m)(x)/dlatitude.
|
||||
Hence the derivatives are multiplied by sin(latitude).
|
||||
Removed the options for CS phase and normalizations.
|
||||
|
||||
Note: In geomagnetism, the derivatives of ALF are usually found with
|
||||
respect to the colatitudes. Here the derivatives are found with respect
|
||||
to the latitude. The difference is a sign reversal for the derivative of
|
||||
the Associated Legendre Functions.
|
||||
|
||||
The derivates can't be computed for latitude = |90| degrees.
|
||||
*/
|
||||
double f1[WMM_NUMPCUP];
|
||||
double f2[WMM_NUMPCUP];
|
||||
double PreSqr[WMM_NUMPCUP];
|
||||
int m;
|
||||
|
||||
if (fabs(x) == 1.0)
|
||||
{
|
||||
// printf("Error in PcupHigh: derivative cannot be calculated at poles\n");
|
||||
return -2;
|
||||
}
|
||||
|
||||
double scalef = 1.0e-280;
|
||||
|
||||
for (int n = 0; n <= 2 * nMax + 1; ++n)
|
||||
PreSqr[n] = sqrt((double)(n));
|
||||
|
||||
int k = 2;
|
||||
|
||||
for (int n = 2; n <= nMax; n++)
|
||||
{
|
||||
k = k + 1;
|
||||
f1[k] = (double)(2 * n - 1) / n;
|
||||
f2[k] = (double)(n - 1) / n;
|
||||
for (int m = 1; m <= n - 2; m++)
|
||||
{
|
||||
k = k + 1;
|
||||
f1[k] = (double)(2 * n - 1) / PreSqr[n + m] / PreSqr[n - m];
|
||||
f2[k] = PreSqr[n - m - 1] * PreSqr[n + m - 1] / PreSqr[n + m] / PreSqr[n - m];
|
||||
}
|
||||
k = k + 2;
|
||||
}
|
||||
|
||||
/*z = sin (geocentric latitude) */
|
||||
double z = sqrt((1.0 - x) * (1.0 + x));
|
||||
double pm2 = 1.0;
|
||||
Pcup[0] = 1.0;
|
||||
dPcup[0] = 0.0;
|
||||
if (nMax == 0)
|
||||
return -3;
|
||||
double pm1 = x;
|
||||
Pcup[1] = pm1;
|
||||
dPcup[1] = z;
|
||||
k = 1;
|
||||
|
||||
for (int n = 2; n <= nMax; n++)
|
||||
{
|
||||
k = k + n;
|
||||
double plm = f1[k] * x * pm1 - f2[k] * pm2;
|
||||
Pcup[k] = plm;
|
||||
dPcup[k] = (double)(n) * (pm1 - x * plm) / z;
|
||||
pm2 = pm1;
|
||||
pm1 = plm;
|
||||
}
|
||||
|
||||
double pmm = PreSqr[2] * scalef;
|
||||
double rescalem = 1.0 / scalef;
|
||||
int kstart = 0;
|
||||
|
||||
for (m = 1; m <= nMax - 1; ++m)
|
||||
{
|
||||
rescalem = rescalem * z;
|
||||
|
||||
/* Calculate Pcup(m,m) */
|
||||
kstart = kstart + m + 1;
|
||||
pmm = pmm * PreSqr[2 * m + 1] / PreSqr[2 * m];
|
||||
Pcup[kstart] = pmm * rescalem / PreSqr[2 * m + 1];
|
||||
dPcup[kstart] = -((double)(m) * x * Pcup[kstart] / z);
|
||||
pm2 = pmm / PreSqr[2 * m + 1];
|
||||
/* Calculate Pcup(m+1,m) */
|
||||
k = kstart + m + 1;
|
||||
pm1 = x * PreSqr[2 * m + 1] * pm2;
|
||||
Pcup[k] = pm1 * rescalem;
|
||||
dPcup[k] = ((pm2 * rescalem) * PreSqr[2 * m + 1] - x * (double)(m + 1) * Pcup[k]) / z;
|
||||
/* Calculate Pcup(n,m) */
|
||||
for (int n = m + 2; n <= nMax; ++n)
|
||||
{
|
||||
k = k + n;
|
||||
double plm = x * f1[k] * pm1 - f2[k] * pm2;
|
||||
Pcup[k] = plm * rescalem;
|
||||
dPcup[k] = (PreSqr[n + m] * PreSqr[n - m] * (pm1 * rescalem) - (double)(n) * x * Pcup[k]) / z;
|
||||
pm2 = pm1;
|
||||
pm1 = plm;
|
||||
}
|
||||
}
|
||||
|
||||
/* Calculate Pcup(nMax,nMax) */
|
||||
rescalem = rescalem * z;
|
||||
kstart = kstart + m + 1;
|
||||
pmm = pmm / PreSqr[2 * nMax];
|
||||
Pcup[kstart] = pmm * rescalem;
|
||||
dPcup[kstart] = -(double)(nMax) * x * Pcup[kstart] / z;
|
||||
|
||||
// *********
|
||||
|
||||
return 0; // OK
|
||||
}
|
||||
|
||||
void WorldMagModel::PcupLow(double *Pcup, double *dPcup, double x, int nMax)
|
||||
{
|
||||
/* This function evaluates all of the Schmidt-semi normalized associated Legendre functions up to degree nMax.
|
||||
|
||||
Calling Parameters:
|
||||
INPUT
|
||||
nMax: Maximum spherical harmonic degree to compute.
|
||||
x: cos(colatitude) or sin(latitude).
|
||||
|
||||
OUTPUT
|
||||
Pcup: A vector of all associated Legendgre polynomials evaluated at
|
||||
x up to nMax.
|
||||
dPcup: Derivative of Pcup(x) with respect to latitude
|
||||
|
||||
Notes: Overflow may occur if nMax > 20 , especially for high-latitudes.
|
||||
Use WMM_PcupHigh for large nMax.
|
||||
|
||||
Writted by Manoj Nair, June, 2009 . Manoj.C.Nair@Noaa.Gov.
|
||||
|
||||
Note: In geomagnetism, the derivatives of ALF are usually found with
|
||||
respect to the colatitudes. Here the derivatives are found with respect
|
||||
to the latitude. The difference is a sign reversal for the derivative of
|
||||
the Associated Legendre Functions.
|
||||
*/
|
||||
|
||||
double schmidtQuasiNorm[WMM_NUMPCUP];
|
||||
|
||||
Pcup[0] = 1.0;
|
||||
dPcup[0] = 0.0;
|
||||
|
||||
/*sin (geocentric latitude) - sin_phi */
|
||||
double z = sqrt((1.0 - x) * (1.0 + x));
|
||||
|
||||
/* First, Compute the Gauss-normalized associated Legendre functions */
|
||||
for (int n = 1; n <= nMax; n++)
|
||||
{
|
||||
for (int m = 0; m <= n; m++)
|
||||
{
|
||||
int index = (n * (n + 1) / 2 + m);
|
||||
if (n == m)
|
||||
{
|
||||
int index1 = (n - 1) * n / 2 + m - 1;
|
||||
Pcup[index] = z * Pcup[index1];
|
||||
dPcup[index] = z * dPcup[index1] + x * Pcup[index1];
|
||||
}
|
||||
else
|
||||
if (n == 1 && m == 0)
|
||||
{
|
||||
int index1 = (n - 1) * n / 2 + m;
|
||||
Pcup[index] = x * Pcup[index1];
|
||||
dPcup[index] = x * dPcup[index1] - z * Pcup[index1];
|
||||
}
|
||||
else
|
||||
if (n > 1 && n != m)
|
||||
{
|
||||
int index1 = (n - 2) * (n - 1) / 2 + m;
|
||||
int index2 = (n - 1) * n / 2 + m;
|
||||
if (m > n - 2)
|
||||
{
|
||||
Pcup[index] = x * Pcup[index2];
|
||||
dPcup[index] = x * dPcup[index2] - z * Pcup[index2];
|
||||
}
|
||||
else
|
||||
{
|
||||
double k = (double)(((n - 1) * (n - 1)) - (m * m)) / (double)((2 * n - 1) * (2 * n - 3));
|
||||
Pcup[index] = x * Pcup[index2] - k * Pcup[index1];
|
||||
dPcup[index] = x * dPcup[index2] - z * Pcup[index2] - k * dPcup[index1];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/*Compute the ration between the Gauss-normalized associated Legendre
|
||||
functions and the Schmidt quasi-normalized version. This is equivalent to
|
||||
sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)! */
|
||||
|
||||
schmidtQuasiNorm[0] = 1.0;
|
||||
for (int n = 1; n <= nMax; n++)
|
||||
{
|
||||
int index = (n * (n + 1) / 2);
|
||||
int index1 = (n - 1) * n / 2;
|
||||
/* for m = 0 */
|
||||
schmidtQuasiNorm[index] = schmidtQuasiNorm[index1] * (double)(2 * n - 1) / (double)n;
|
||||
|
||||
for (int m = 1; m <= n; m++)
|
||||
{
|
||||
index = (n * (n + 1) / 2 + m);
|
||||
index1 = (n * (n + 1) / 2 + m - 1);
|
||||
schmidtQuasiNorm[index] = schmidtQuasiNorm[index1] * sqrt((double)((n - m + 1) * (m == 1 ? 2 : 1)) / (double)(n + m));
|
||||
}
|
||||
}
|
||||
|
||||
/* Converts the Gauss-normalized associated Legendre
|
||||
functions to the Schmidt quasi-normalized version using pre-computed
|
||||
relation stored in the variable schmidtQuasiNorm */
|
||||
|
||||
for (int n = 1; n <= nMax; n++)
|
||||
{
|
||||
for (int m = 0; m <= n; m++)
|
||||
{
|
||||
int index = (n * (n + 1) / 2 + m);
|
||||
Pcup[index] = Pcup[index] * schmidtQuasiNorm[index];
|
||||
dPcup[index] = -dPcup[index] * schmidtQuasiNorm[index];
|
||||
/* The sign is changed since the new WMM routines use derivative with respect to latitude insted of co-latitude */
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void WorldMagModel::SummationSpecial(WMMtype_SphericalHarmonicVariables *SphVariables, WMMtype_CoordSpherical *CoordSpherical, WMMtype_MagneticResults *MagneticResults)
|
||||
{
|
||||
/* Special calculation for the component By at Geographic poles.
|
||||
Manoj Nair, June, 2009 manoj.c.nair@noaa.gov
|
||||
INPUT: MagneticModel
|
||||
SphVariables
|
||||
CoordSpherical
|
||||
OUTPUT: MagneticResults
|
||||
CALLS : none
|
||||
See Section 1.4, "SINGULARITIES AT THE GEOGRAPHIC POLES", WMM Technical report
|
||||
*/
|
||||
|
||||
double PcupS[WMM_NUMPCUPS];
|
||||
|
||||
PcupS[0] = 1;
|
||||
double schmidtQuasiNorm1 = 1.0;
|
||||
|
||||
MagneticResults->By = 0.0;
|
||||
double sin_phi = sin(DEG2RAD(CoordSpherical->phig));
|
||||
|
||||
for (int n = 1; n <= MagneticModel.nMax; n++)
|
||||
{
|
||||
/*Compute the ration between the Gauss-normalized associated Legendre
|
||||
functions and the Schmidt quasi-normalized version. This is equivalent to
|
||||
sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)! */
|
||||
|
||||
int index = (n * (n + 1) / 2 + 1);
|
||||
double schmidtQuasiNorm2 = schmidtQuasiNorm1 * (double)(2 * n - 1) / (double)n;
|
||||
double schmidtQuasiNorm3 = schmidtQuasiNorm2 * sqrt((double)(n * 2) / (double)(n + 1));
|
||||
schmidtQuasiNorm1 = schmidtQuasiNorm2;
|
||||
if (n == 1)
|
||||
{
|
||||
PcupS[n] = PcupS[n - 1];
|
||||
}
|
||||
else
|
||||
{
|
||||
double k = (double)(((n - 1) * (n - 1)) - 1) / (double)((2 * n - 1) * (2 * n - 3));
|
||||
PcupS[n] = sin_phi * PcupS[n - 1] - k * PcupS[n - 2];
|
||||
}
|
||||
|
||||
/* 1 nMax (n+2) n m m m
|
||||
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Equation 11 in the WMM Technical report. Derivative with respect to longitude, divided by radius. */
|
||||
|
||||
MagneticResults->By +=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_main_field_coeff_g(index) *
|
||||
SphVariables->sin_mlambda[1] - get_main_field_coeff_h(index) * SphVariables->cos_mlambda[1])
|
||||
* PcupS[n] * schmidtQuasiNorm3;
|
||||
}
|
||||
}
|
||||
|
||||
void WorldMagModel::SecVarSummationSpecial(WMMtype_SphericalHarmonicVariables *SphVariables, WMMtype_CoordSpherical *CoordSpherical, WMMtype_MagneticResults *MagneticResults)
|
||||
{
|
||||
/*Special calculation for the secular variation summation at the poles.
|
||||
|
||||
INPUT: MagneticModel
|
||||
SphVariables
|
||||
CoordSpherical
|
||||
OUTPUT: MagneticResults
|
||||
*/
|
||||
|
||||
double PcupS[WMM_NUMPCUPS];
|
||||
|
||||
PcupS[0] = 1;
|
||||
double schmidtQuasiNorm1 = 1.0;
|
||||
|
||||
MagneticResults->By = 0.0;
|
||||
double sin_phi = sin(DEG2RAD(CoordSpherical->phig));
|
||||
|
||||
for (int n = 1; n <= MagneticModel.nMaxSecVar; n++)
|
||||
{
|
||||
int index = (n * (n + 1) / 2 + 1);
|
||||
double schmidtQuasiNorm2 = schmidtQuasiNorm1 * (double)(2 * n - 1) / (double)n;
|
||||
double schmidtQuasiNorm3 = schmidtQuasiNorm2 * sqrt((double)(n * 2) / (double)(n + 1));
|
||||
schmidtQuasiNorm1 = schmidtQuasiNorm2;
|
||||
if (n == 1)
|
||||
{
|
||||
PcupS[n] = PcupS[n - 1];
|
||||
}
|
||||
else
|
||||
{
|
||||
double k = (double)(((n - 1) * (n - 1)) - 1) / (double)((2 * n - 1) * (2 * n - 3));
|
||||
PcupS[n] = sin_phi * PcupS[n - 1] - k * PcupS[n - 2];
|
||||
}
|
||||
|
||||
/* 1 nMax (n+2) n m m m
|
||||
By = SUM (a/r) (m) SUM [g cos(m p) + h sin(m p)] dP (sin(phi))
|
||||
n=1 m=0 n n n */
|
||||
/* Derivative with respect to longitude, divided by radius. */
|
||||
|
||||
MagneticResults->By +=
|
||||
SphVariables->RelativeRadiusPower[n] *
|
||||
(get_secular_var_coeff_g(index) *
|
||||
SphVariables->sin_mlambda[1] - get_secular_var_coeff_h(index) * SphVariables->cos_mlambda[1])
|
||||
* PcupS[n] * schmidtQuasiNorm3;
|
||||
}
|
||||
}
|
||||
|
||||
// brief Comput the MainFieldCoeffH accounting for the date
|
||||
double WorldMagModel::get_main_field_coeff_g(int index)
|
||||
{
|
||||
if (index >= WMM_NUMTERMS)
|
||||
return 0;
|
||||
|
||||
double coeff = CoeffFile[index][2];
|
||||
|
||||
int a = MagneticModel.nMaxSecVar;
|
||||
int b = (a * (a + 1) / 2 + a);
|
||||
for (int n = 1; n <= MagneticModel.nMax; n++)
|
||||
{
|
||||
for (int m = 0; m <= n; m++)
|
||||
{
|
||||
int sum_index = (n * (n + 1) / 2 + m);
|
||||
|
||||
/* Hacky for now, will solve for which conditions need summing analytically */
|
||||
if (sum_index != index)
|
||||
continue;
|
||||
|
||||
if (index <= b)
|
||||
coeff += (decimal_date - MagneticModel.epoch) * get_secular_var_coeff_g(sum_index);
|
||||
}
|
||||
}
|
||||
|
||||
return coeff;
|
||||
}
|
||||
|
||||
double WorldMagModel::get_main_field_coeff_h(int index)
|
||||
{
|
||||
if (index >= WMM_NUMTERMS)
|
||||
return 0;
|
||||
|
||||
double coeff = CoeffFile[index][3];
|
||||
|
||||
int a = MagneticModel.nMaxSecVar;
|
||||
int b = (a * (a + 1) / 2 + a);
|
||||
for (int n = 1; n <= MagneticModel.nMax; n++)
|
||||
{
|
||||
for (int m = 0; m <= n; m++)
|
||||
{
|
||||
int sum_index = (n * (n + 1) / 2 + m);
|
||||
|
||||
/* Hacky for now, will solve for which conditions need summing analytically */
|
||||
if (sum_index != index)
|
||||
continue;
|
||||
|
||||
if (index <= b)
|
||||
coeff += (decimal_date - MagneticModel.epoch) * get_secular_var_coeff_h(sum_index);
|
||||
}
|
||||
}
|
||||
|
||||
return coeff;
|
||||
}
|
||||
|
||||
double WorldMagModel::get_secular_var_coeff_g(int index)
|
||||
{
|
||||
if (index >= WMM_NUMTERMS)
|
||||
return 0;
|
||||
|
||||
return CoeffFile[index][4];
|
||||
}
|
||||
|
||||
double WorldMagModel::get_secular_var_coeff_h(int index)
|
||||
{
|
||||
if (index >= WMM_NUMTERMS)
|
||||
return 0;
|
||||
|
||||
return CoeffFile[index][5];
|
||||
}
|
||||
|
||||
int WorldMagModel::DateToYear(int month, int day, int year)
|
||||
{
|
||||
// Converts a given calendar date into a decimal year
|
||||
|
||||
int temp = 0; // Total number of days
|
||||
int MonthDays[13] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
|
||||
int ExtraDay = 0;
|
||||
|
||||
if ((year % 4 == 0 && year % 100 != 0) || (year % 400 == 0))
|
||||
ExtraDay = 1;
|
||||
MonthDays[2] += ExtraDay;
|
||||
|
||||
/******************Validation********************************/
|
||||
|
||||
if (month <= 0 || month > 12)
|
||||
return -1; // error
|
||||
|
||||
if (day <= 0 || day > MonthDays[month])
|
||||
return -2; // error
|
||||
|
||||
/****************Calculation of t***************************/
|
||||
for (int i = 1; i <= month; i++)
|
||||
temp += MonthDays[i - 1];
|
||||
temp += day;
|
||||
|
||||
decimal_date = year + (temp - 1) / (365.0 + ExtraDay);
|
||||
|
||||
return 0; // OK
|
||||
}
|
||||
|
||||
void WorldMagModel::GeodeticToSpherical(WMMtype_CoordGeodetic *CoordGeodetic, WMMtype_CoordSpherical *CoordSpherical)
|
||||
{
|
||||
// Converts Geodetic coordinates to Spherical coordinates
|
||||
// Convert geodetic coordinates, (defined by the WGS-84
|
||||
// reference ellipsoid), to Earth Centered Earth Fixed Cartesian
|
||||
// coordinates, and then to spherical coordinates.
|
||||
|
||||
double CosLat = cos(DEG2RAD(CoordGeodetic->phi));
|
||||
double SinLat = sin(DEG2RAD(CoordGeodetic->phi));
|
||||
|
||||
// compute the local radius of curvature on the WGS-84 reference ellipsoid
|
||||
double rc = Ellip.a / sqrt(1.0 - Ellip.epssq * SinLat * SinLat);
|
||||
|
||||
// compute ECEF Cartesian coordinates of specified point (for longitude=0)
|
||||
double xp = (rc + CoordGeodetic->HeightAboveEllipsoid) * CosLat;
|
||||
double zp = (rc * (1.0 - Ellip.epssq) + CoordGeodetic->HeightAboveEllipsoid) * SinLat;
|
||||
|
||||
// compute spherical radius and angle lambda and phi of specified point
|
||||
CoordSpherical->r = sqrt(xp * xp + zp * zp);
|
||||
CoordSpherical->phig = RAD2DEG(asin(zp / CoordSpherical->r)); // geocentric latitude
|
||||
CoordSpherical->lambda = CoordGeodetic->lambda; // longitude
|
||||
}
|
||||
|
||||
}
|
||||
179
ground/src/libs/utils/worldmagmodel.h
Normal file
179
ground/src/libs/utils/worldmagmodel.h
Normal file
@ -0,0 +1,179 @@
|
||||
/**
|
||||
******************************************************************************
|
||||
*
|
||||
* @file worldmagmodel.h
|
||||
* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
|
||||
* Parts by Nokia Corporation (qt-info@nokia.com) Copyright (C) 2009.
|
||||
* @brief
|
||||
* @see The GNU Public License (GPL) Version 3
|
||||
* @defgroup
|
||||
* @{
|
||||
*
|
||||
*****************************************************************************/
|
||||
/*
|
||||
* This program is free software; you can redistribute it and/or modify
|
||||
* it under the terms of the GNU General Public License as published by
|
||||
* the Free Software Foundation; either version 3 of the License, or
|
||||
* (at your option) any later version.
|
||||
*
|
||||
* This program is distributed in the hope that it will be useful, but
|
||||
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
||||
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||
* for more details.
|
||||
*
|
||||
* You should have received a copy of the GNU General Public License along
|
||||
* with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
|
||||
*/
|
||||
|
||||
#ifndef WORLDMAGMODEL_H
|
||||
#define WORLDMAGMODEL_H
|
||||
|
||||
#include "utils_global.h"
|
||||
|
||||
// ******************************
|
||||
// internal structure definitions
|
||||
|
||||
#define WMM_MAX_MODEL_DEGREES 12
|
||||
#define WMM_MAX_SECULAR_VARIATION_MODEL_DEGREES 12
|
||||
#define WMM_NUMTERMS 91 // ((WMM_MAX_MODEL_DEGREES + 1) * (WMM_MAX_MODEL_DEGREES + 2) / 2);
|
||||
#define WMM_NUMPCUP 92 // NUMTERMS + 1
|
||||
#define WMM_NUMPCUPS 13 // WMM_MAX_MODEL_DEGREES + 1
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double EditionDate;
|
||||
double epoch; //Base time of Geomagnetic model epoch (yrs)
|
||||
char ModelName[20];
|
||||
// double Main_Field_Coeff_G[WMM_NUMTERMS]; // C - Gauss coefficients of main geomagnetic model (nT)
|
||||
// double Main_Field_Coeff_H[WMM_NUMTERMS]; // C - Gauss coefficients of main geomagnetic model (nT)
|
||||
// double Secular_Var_Coeff_G[WMM_NUMTERMS]; // CD - Gauss coefficients of secular geomagnetic model (nT/yr)
|
||||
// double Secular_Var_Coeff_H[WMM_NUMTERMS]; // CD - Gauss coefficients of secular geomagnetic model (nT/yr)
|
||||
int nMax; // Maximum degree of spherical harmonic model
|
||||
int nMaxSecVar; // Maxumum degree of spherical harmonic secular model
|
||||
int SecularVariationUsed; // Whether or not the magnetic secular variation vector will be needed by program
|
||||
} WMMtype_MagneticModel;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double a; // semi-major axis of the ellipsoid
|
||||
double b; // semi-minor axis of the ellipsoid
|
||||
double fla; // flattening
|
||||
double epssq; // first eccentricity squared
|
||||
double eps; // first eccentricity
|
||||
double re; // mean radius of ellipsoid
|
||||
} WMMtype_Ellipsoid;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double lambda; // longitude
|
||||
double phi; // geodetic latitude
|
||||
double HeightAboveEllipsoid; // height above the ellipsoid (HaE)
|
||||
} WMMtype_CoordGeodetic;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double lambda; // longitude
|
||||
double phig; // geocentric latitude
|
||||
double r; // distance from the center of the ellipsoid
|
||||
} WMMtype_CoordSpherical;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
int Year;
|
||||
int Month;
|
||||
int Day;
|
||||
double DecimalYear;
|
||||
} WMMtype_Date;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double Pcup[WMM_NUMPCUP]; // Legendre Function
|
||||
double dPcup[WMM_NUMPCUP]; // Derivative of Lagendre fn
|
||||
} WMMtype_LegendreFunction;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double Bx; // North
|
||||
double By; // East
|
||||
double Bz; // Down
|
||||
} WMMtype_MagneticResults;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double RelativeRadiusPower[WMM_MAX_MODEL_DEGREES + 1]; // [earth_reference_radius_km / sph. radius ]^n
|
||||
double cos_mlambda[WMM_MAX_MODEL_DEGREES + 1]; // cp(m) - cosine of (m*spherical coord. longitude
|
||||
double sin_mlambda[WMM_MAX_MODEL_DEGREES + 1]; // sp(m) - sine of (m*spherical coord. longitude)
|
||||
} WMMtype_SphericalHarmonicVariables;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
double Decl; /*1. Angle between the magnetic field vector and true north, positive east */
|
||||
double Incl; /*2. Angle between the magnetic field vector and the horizontal plane, positive down */
|
||||
double F; /*3. Magnetic Field Strength */
|
||||
double H; /*4. Horizontal Magnetic Field Strength */
|
||||
double X; /*5. Northern component of the magnetic field vector */
|
||||
double Y; /*6. Eastern component of the magnetic field vector */
|
||||
double Z; /*7. Downward component of the magnetic field vector */
|
||||
double GV; /*8. The Grid Variation */
|
||||
double Decldot; /*9. Yearly Rate of change in declination */
|
||||
double Incldot; /*10. Yearly Rate of change in inclination */
|
||||
double Fdot; /*11. Yearly rate of change in Magnetic field strength */
|
||||
double Hdot; /*12. Yearly rate of change in horizontal field strength */
|
||||
double Xdot; /*13. Yearly rate of change in the northern component */
|
||||
double Ydot; /*14. Yearly rate of change in the eastern component */
|
||||
double Zdot; /*15. Yearly rate of change in the downward component */
|
||||
double GVdot; /*16. Yearly rate of chnage in grid variation */
|
||||
} WMMtype_GeoMagneticElements;
|
||||
|
||||
// ******************************
|
||||
|
||||
namespace Utils {
|
||||
|
||||
class QTCREATOR_UTILS_EXPORT WorldMagModel
|
||||
{
|
||||
public:
|
||||
WorldMagModel();
|
||||
int GetMagVector(double Lat, double Lon, double AltEllipsoid, int Month, int Day, int Year, double *X, double *Y, double *Z);
|
||||
|
||||
private:
|
||||
WMMtype_Ellipsoid Ellip;
|
||||
WMMtype_MagneticModel MagneticModel;
|
||||
|
||||
double decimal_date;
|
||||
|
||||
void Initialize();
|
||||
int Geomag(WMMtype_CoordSpherical *CoordSpherical, WMMtype_CoordGeodetic *CoordGeodetic, WMMtype_GeoMagneticElements *GeoMagneticElements);
|
||||
void ComputeSphericalHarmonicVariables(WMMtype_CoordSpherical *CoordSpherical, int nMax, WMMtype_SphericalHarmonicVariables *SphVariables);
|
||||
int AssociatedLegendreFunction(WMMtype_CoordSpherical *CoordSpherical, int nMax, WMMtype_LegendreFunction *LegendreFunction);
|
||||
void Summation( WMMtype_LegendreFunction *LegendreFunction,
|
||||
WMMtype_SphericalHarmonicVariables *SphVariables,
|
||||
WMMtype_CoordSpherical *CoordSpherical,
|
||||
WMMtype_MagneticResults *MagneticResults);
|
||||
void SecVarSummation( WMMtype_LegendreFunction *LegendreFunction,
|
||||
WMMtype_SphericalHarmonicVariables *SphVariables,
|
||||
WMMtype_CoordSpherical *CoordSpherical,
|
||||
WMMtype_MagneticResults *MagneticResults);
|
||||
void RotateMagneticVector( WMMtype_CoordSpherical *CoordSpherical,
|
||||
WMMtype_CoordGeodetic *CoordGeodetic,
|
||||
WMMtype_MagneticResults *MagneticResultsSph,
|
||||
WMMtype_MagneticResults *MagneticResultsGeo);
|
||||
void CalculateGeoMagneticElements(WMMtype_MagneticResults *MagneticResultsGeo, WMMtype_GeoMagneticElements *GeoMagneticElements);
|
||||
void CalculateSecularVariation(WMMtype_MagneticResults *MagneticVariation, WMMtype_GeoMagneticElements *MagneticElements);
|
||||
int PcupHigh(double *Pcup, double *dPcup, double x, int nMax);
|
||||
void PcupLow(double *Pcup, double *dPcup, double x, int nMax);
|
||||
void SummationSpecial(WMMtype_SphericalHarmonicVariables *SphVariables, WMMtype_CoordSpherical *CoordSpherical, WMMtype_MagneticResults *MagneticResults);
|
||||
void SecVarSummationSpecial(WMMtype_SphericalHarmonicVariables *SphVariables, WMMtype_CoordSpherical *CoordSpherical, WMMtype_MagneticResults *MagneticResults);
|
||||
double get_main_field_coeff_g(int index);
|
||||
double get_main_field_coeff_h(int index);
|
||||
double get_secular_var_coeff_g(int index);
|
||||
double get_secular_var_coeff_h(int index);
|
||||
int DateToYear(int month, int day, int year);
|
||||
void GeodeticToSpherical(WMMtype_CoordGeodetic *CoordGeodetic, WMMtype_CoordSpherical *CoordSpherical);
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
// ******************************
|
||||
|
||||
#endif
|
||||
Loading…
Reference in New Issue
Block a user