Blog Entry © Friday, May 23, 2025, NASA Geopotential Altitude and the Variation of the Gravitational Acceleration by James Pate Williams, Jr., BA, BS, Master of Software Engineering, PhD Computer Science

More source code is available upon request.
Reference: 19770009539.pdf
Win32 C/C++ application output to a Win32 window:
H Z1 Z2 Z3 g
80000 79005.7 79005.7 79005.7 9.56735
80500 79493.3 79493.3 79493.3 9.56590
81000 79980.9 79980.9 79980.9 9.56446
81500 80468.3 80468.3 80468.3 9.56301
82000 80955.7 80955.7 80955.7 9.56156
82500 81443.0 81443.0 81443.0 9.56011
83000 81930.2 81930.2 81930.2 9.55867
83500 82417.4 82417.4 82417.4 9.55722
84000 82904.5 82904.5 82904.5 9.55577
84500 83391.5 83391.5 83391.5 9.55433
85000 83878.4 83878.4 83878.4 9.55288
85500 84365.3 84365.3 84365.3 9.55144
H Geopotential Altitude
Z1 Geopotential Gauss-Legendre 128 Steps
Z2 Geopotential Simpson's Rule 256 Steps
Z3 Geopotential Trapezoidal Rule 512 Steps
g gravitational acceleration in m/s/s
https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf
See Table 8. Page 9
// NASAGeopotentialAltitude.cpp : Defines the entry point for the application.
// Copyright (c) Friday, May 23, 2025 by James Pate Williams, Jr.
// BA, BS, MSWE, PhD All Applicable Rights Reserved

#include "stdafx.h"
#include "GeopotentialAltitude.h"
#include "Integration1d.h"
#include "NASAGeopotentialAltitude.h"
#include <math.h>
#include <stdio.h>
#include <tchar.h>
#include <string.h>
#include <vector>
using namespace std;

#define MAX_LOADSTRING 100

// Global Variables:
HINSTANCE hInst;								// current instance
TCHAR szTitle[MAX_LOADSTRING];					// The title bar text
TCHAR szWindowClass[MAX_LOADSTRING];			// the main window class name

// Forward declarations of functions included in this code module:
ATOM				MyRegisterClass(HINSTANCE hInstance);
BOOL				InitInstance(HINSTANCE, int);
LRESULT CALLBACK	WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK	About(HWND, UINT, WPARAM, LPARAM);

int APIENTRY _tWinMain(HINSTANCE hInstance,
                     HINSTANCE hPrevInstance,
                     LPTSTR    lpCmdLine,
                     int       nCmdShow)
{
	UNREFERENCED_PARAMETER(hPrevInstance);
	UNREFERENCED_PARAMETER(lpCmdLine);

 	// TODO: Place code here.
	MSG msg;
	HACCEL hAccelTable;

	// Initialize global strings
	LoadString(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
	LoadString(hInstance, IDC_NASAGEOPOTENTIALALTITUDE, szWindowClass, MAX_LOADSTRING);
	MyRegisterClass(hInstance);

	// Perform application initialization:
	if (!InitInstance (hInstance, nCmdShow))
	{
		return FALSE;
	}

	hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_NASAGEOPOTENTIALALTITUDE));

	// Main message loop:
	while (GetMessage(&msg, NULL, 0, 0))
	{
		if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
		{
			TranslateMessage(&msg);
			DispatchMessage(&msg);
		}
	}

	return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
//  COMMENTS:
//
//    This function and its usage are only necessary if you want this code
//    to be compatible with Win32 systems prior to the 'RegisterClassEx'
//    function that was added to Windows 95. It is important to call this function
//    so that the application will get 'well formed' small icons associated
//    with it.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
	WNDCLASSEX wcex;

	wcex.cbSize = sizeof(WNDCLASSEX);

	wcex.style			= CS_HREDRAW | CS_VREDRAW;
	wcex.lpfnWndProc	= WndProc;
	wcex.cbClsExtra		= 0;
	wcex.cbWndExtra		= 0;
	wcex.hInstance		= hInstance;
	wcex.hIcon			= LoadIcon(hInstance, MAKEINTRESOURCE(IDI_NASAGEOPOTENTIALALTITUDE));
	wcex.hCursor		= LoadCursor(NULL, IDC_ARROW);
	wcex.hbrBackground	= (HBRUSH)(COLOR_WINDOW+1);
	wcex.lpszMenuName	= MAKEINTRESOURCE(IDC_NASAGEOPOTENTIALALTITUDE);
	wcex.lpszClassName	= szWindowClass;
	wcex.hIconSm		= LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

	return RegisterClassEx(&wcex);
}

//
//   FUNCTION: InitInstance(HINSTANCE, int)
//
//   PURPOSE: Saves instance handle and creates main window
//
//   COMMENTS:
//
//        In this function, we save the instance handle in a global variable and
//        create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
   HWND hWnd;

   hInst = hInstance; // Store instance handle in our global variable

   hWnd = CreateWindow(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, NULL, NULL, hInstance, NULL);

   if (!hWnd)
   {
      return FALSE;
   }

   ShowWindow(hWnd, nCmdShow);
   UpdateWindow(hWnd);

   return TRUE;
}

//
//  FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  PURPOSE:  Processes messages for the main window.
//
//  WM_CREATE   - creates a multiple line edit control
//  WM_COMMAND	- process the application menu
//  WM_PAINT	- Paint the main window
//  WM_DESTROY	- post a quit message and return
//
//

#define ID_EDITCHILD 100
char asciiData[16384];
char asciiLine[16384];
TCHAR textData[16384];

void ConvertCharToTChar(const char* charArray, TCHAR* tcharArray, size_t tcharSize) {
#ifdef _UNICODE
	MultiByteToWideChar(CP_ACP, 0, charArray, -1, tcharArray, (int)tcharSize);
#else
    strncpy(tcharArray, charArray, tcharSize - 1);
    tcharArray[tcharSize - 1] = '\0'; // Ensure null-termination
#endif
}

LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
	int wmId, wmEvent;
	PAINTSTRUCT ps;
	HDC hdc;
	static HWND hwndEdit;
	static double zArray[] = {
		80000, 80500, 81000, 81500, 82000, 82500,
		83000, 83500, 84000, 84500, 85000, 85500 };
	static vector<double> z(12);
	static vector<double> potential1(12);
	static vector<double> potential2(12);
	static vector<double> potential3(12);
	static vector<double> potential4(12);
	size_t numberPoints = z.size();

	for (size_t i = 0; i < z.size(); i++)
	{
		z[i] = zArray[i];
	}

	switch (message)
	{
	case WM_CREATE:
	GeopotentialAltitude::GaussianLegendre(
		numberPoints, z, potential1);
	GeopotentialAltitude::SimpsonsRule(
		numberPoints, z, potential2);
	GeopotentialAltitude::TrapezoidalRule(
		numberPoints, z, potential3);

	strcpy_s(asciiData, 16384, "H\tZ1\tZ2\tZ3\tg\r\n");

	for (size_t i = 0; i < z.size(); i++)
	{
		double zi = z[i];
		double p1 = potential1[i];
		double p2 = potential2[i];
		double p3 = potential3[i];
		double g = g0 * pow(r0 / (r0 + p1), 2.0);

		sprintf_s(
			asciiLine, 16384,
			"%5.0lf\t%5.1lf\t%5.1lf\t%5.1lf\t%7.5lf\r\n",
			zi, p1, p2, p3, g);
		strcat_s(asciiData, 16384, asciiLine);
	}

	strcat_s(asciiData, "H Geopotential Altitude\r\n");
	strcat_s(asciiData, "Z1 Geopotential Gauss-Legendre 128 Steps\r\n");
	strcat_s(asciiData, "Z2 Geopotential Simpson's Rule 256 Steps\r\n");
	strcat_s(asciiData, "Z3 Geopotential Trapezoidal Rule 512 Steps\r\n");
	strcat_s(asciiData, "g gravitational acceleration in m/s/s\r\n");
	strcat_s(asciiData, "https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf\r\n");
	strcat_s(asciiData, "See Table 8. Page 9\r\n");

	ConvertCharToTChar(asciiData, textData, sizeof(textData));

	// https://learn.microsoft.com/en-us/windows/win32/controls/use-a-multiline-edit-control

	hwndEdit = CreateWindowEx(
		0, L"EDIT",   // predefined class 
        NULL,         // no window title 
        WS_CHILD | WS_VISIBLE | WS_VSCROLL | 
        ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL, 
        0, 0, 0, 0,   // set size in WM_SIZE message 
        hWnd,         // parent window 
        (HMENU) ID_EDITCHILD,   // edit control ID 
		hInst,
        /*(HINSTANCE) GetWindowLongPtr(hWnd, GWLP_HINSTANCE),*/ 
		NULL);        // pointer not needed 
    // Add text to the window. 
	SendMessage(hwndEdit, WM_SETTEXT, 0, (LPARAM) textData); 
    return 0; 
	case WM_COMMAND:
		wmId    = LOWORD(wParam);
		wmEvent = HIWORD(wParam);
		// Parse the menu selections:
		switch (wmId)
		{
		case IDM_ABOUT:
			DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
			break;
		case IDM_EXIT:
			DestroyWindow(hWnd);
			break;
		default:
			return DefWindowProc(hWnd, message, wParam, lParam);
		}
		break;
	case WM_PAINT:
		hdc = BeginPaint(hWnd, &ps);
		// TODO: Add any drawing code here...
		EndPaint(hWnd, &ps);
		break;
	case WM_SIZE: 
            // Make the edit control the size of the window's client area. 
		MoveWindow(hwndEdit, 
			0, 0,                  // starting x- and y-coordinates 
            LOWORD(lParam),        // width of client area 
            HIWORD(lParam),        // height of client area 
            TRUE);                 // repaint window 
        return 0; 
	case WM_DESTROY:
		PostQuitMessage(0);
		break;
	default:
		return DefWindowProc(hWnd, message, wParam, lParam);
	}
	return 0;
}

// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
	UNREFERENCED_PARAMETER(lParam);
	switch (message)
	{
	case WM_INITDIALOG:
		return (INT_PTR)TRUE;

	case WM_COMMAND:
		if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
		{
			EndDialog(hDlg, LOWORD(wParam));
			return (INT_PTR)TRUE;
		}
		break;
	}
	return (INT_PTR)FALSE;
}

Unknown's avatar

Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

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