Category: Astrophysics

Blog Input © Saturday, March 21, 2026, by James Pate Williams, Jr., Three Model Universes

Blog Entry Saturday March 21 2026Download
#pragma once

class UniversalModels
{
public:
	static void deSitterUniverse(
		double epsilon, double lambda, double ct,
		double A, double B, double& K);
	static void RadiationUniverse(
		double A, double epsilon,
		double deltaT, double& K);
	static void FriedmannUniverse(
		int epsilon, double M,
		double cT, double& K);
};


#include "UniversalModels.h"
#include <math.h>

void UniversalModels::deSitterUniverse(
	double epsilon, double lambda,
	double ct, double A, double B, double& K)
{
	if (lambda > 0)
	{
		if (epsilon == +1)
		{
			K = cosh(B * ct) / B;
		}

		else if (epsilon == -1)
		{
			K = sinh(B * ct) / B;
		}

		else
		{
			K = A * exp(B * ct);
		}
	}

	else if (lambda < 0)
	{
		if (epsilon == -1)
		{
			lambda = -3.0 * B * B;
			K = cos(B * ct) / B;
		}
	}
}

void UniversalModels::RadiationUniverse(
	double A, double epsilon,
	double deltaT, double& K)
{
	double c = 1.0, kappa = 1.0;

	if (epsilon == 0)
	{
		K = sqrt(2.0 * c * sqrt(kappa * A / 3.0) * deltaT);
	}

	else if (epsilon == -1)
	{
		K = sqrt(c * c * pow(deltaT, 2.0) + 2 * c *
			sqrt(kappa * A / 3.0) * deltaT);
	}

	else if (epsilon == +1)
	{
		K = sqrt(-c * c * pow(deltaT, 2.0) + 2 * c *
			sqrt(kappa * A / 3.0) * deltaT);
	}
}

void UniversalModels::FriedmannUniverse(
	int epsilon, double M, double cT, double& K)
{
	if (epsilon == 0)
	{
		K = M * cT * cT / 12.0;
	}

	else if (epsilon == -1)
	{
		K = M * (cosh(cT) - 1.0) / 6.0;
	}

	else if (epsilon == +1)
	{
		K = M * (1.0 - cos(cT)) / 6.0;
	}
}


// ModelUniverses.cpp (c) Thursday, March 19, 2026
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Reference: "General Relativity An Introduction
// to the theory of the gravitational field "
// (c) 1982 by Hans Stephani translated by Martin
// Pollack and John Stewart

#include "framework.h"
#include "ModelUniverses.h"
#include "UniversalModels.h"
#include <math.h>
#include <string>
#include <vector>

#define MAX_LOADSTRING 100

typedef struct tagPoint2dDeSitter
{
    double ct, K;
} Point2dDeSitter, * PPoint2dDeSitter;

typedef struct tagPoint2dRadiation
{
    double deltaT, K;
} Point2dRadiation, * PPoint2dRadiation;

typedef struct tagPoint2dFriedmann
{
    double cT, K;
} Point2dFriedmann, * PPoint2dFriedmann;


// Global Variables:
HINSTANCE hInst;                                // current instance
WCHAR szTitle[MAX_LOADSTRING];                  // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING];            // the main window class name
bool deSitter, radiation, friedmann;            // universal model type
std::wstring fTitle, xTitle, yTitle;            // graph titles
std::vector<Point2dDeSitter> pointsDeSitter;    // graph points
std::vector<Point2dRadiation> pointsRadiation;  // graph points
std::vector<Point2dFriedmann> pointsFriedmann;  // graph points

// 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_PTR CALLBACK    DataInputDialogDeSitter(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogDeSitter(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogRadiation(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogRadiation(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogFriedmann(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogFriedmann(HWND, UINT, WPARAM, LPARAM);

int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
                     _In_opt_ HINSTANCE hPrevInstance,
                     _In_ LPWSTR    lpCmdLine,
                     _In_ int       nCmdShow)
{
    UNREFERENCED_PARAMETER(hPrevInstance);
    UNREFERENCED_PARAMETER(lpCmdLine);

    // TODO: Place code here.

    // Initialize global strings
    LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
    LoadStringW(hInstance, IDC_MODELUNIVERSES, szWindowClass, MAX_LOADSTRING);
    MyRegisterClass(hInstance);

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

    HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_MODELUNIVERSES));

    MSG msg;

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

    return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
    WNDCLASSEXW wcex = { 0 };

    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_MODELUNIVERSES));
    wcex.hCursor        = LoadCursor(nullptr, IDC_ARROW);
    wcex.hbrBackground  = (HBRUSH)(COLOR_WINDOW+1);
    wcex.lpszMenuName   = MAKEINTRESOURCEW(IDC_MODELUNIVERSES);
    wcex.lpszClassName  = szWindowClass;
    wcex.hIconSm        = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

    return RegisterClassExW(&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)
{
   hInst = hInstance; // Store instance handle in our global variable

   HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);

   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_COMMAND  - process the application menu
//  WM_PAINT    - Paint the main window
//  WM_DESTROY  - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    switch (message)
    {
    case WM_COMMAND:
        {
            int wmId = LOWORD(wParam);
            // Parse the menu selections:
            switch (wmId)
            {
            case IDM_ABOUT:
                DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
                break;
            case IDM_DE_SITTER:
                deSitter = true;
                fTitle = L"de Sitter Universe";
                xTitle = L"Bct";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_DE_SITTER), 
                    hWnd, DataInputDialogDeSitter);
                break;
            case IDM_RADIATION:
                radiation = true;
                fTitle = L"Radiation Universe";
                xTitle = L"t - t0";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_RADIATION), hWnd,
                    DataInputDialogRadiation);
                break;
            case IDM_FRIEDMANN:
                friedmann = true;
                fTitle = L"Friedmann Universe";
                xTitle = L"cT";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_FRIEDMANN), hWnd,
                    DataInputDialogFriedmann);
                break;
            case IDM_EXIT:
                DestroyWindow(hWnd);
                break;
            default:
                return DefWindowProc(hWnd, message, wParam, lParam);
            }
        }
        break;
    case WM_PAINT:
        {
            PAINTSTRUCT ps;
            HDC hdc = BeginPaint(hWnd, &ps);
            // TODO: Add any drawing code that uses hdc here...
            EndPaint(hWnd, &ps);
        }
        break;
    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;
}

INT_PTR CALLBACK DataInputDialogDeSitter(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_A = GetDlgItem(hDlg, IDC_COMBO_A_1);
    static HWND hCombo_B = GetDlgItem(hDlg, IDC_COMBO_B);
    static HWND hCombo_ct = GetDlgItem(hDlg, IDC_COMBO_CT);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_1);
    static HWND hCombo_lambda = GetDlgItem(hDlg, IDC_COMBO_LAMBDA);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-5");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-4");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-3");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-2");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_DE_SITTER)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_A_1, line, 128);
            double A = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_B, line, 128);
            double B = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_CT, line, 128);
            double CT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_1, FALSE, TRUE);
            GetDlgItemTextA(hDlg, IDC_COMBO_LAMBDA, line, 128);
            double lambda = atof(line);
			double ct = 0.0, K = 0.0;
			double delta_ct = CT / 256.0;
			int index = 0;

            pointsDeSitter.clear();

			while (ct <= CT)
			{
                UniversalModels::deSitterUniverse(
                    epsilon, lambda, ct, A, B, K);
				Point2dDeSitter pt = { 0 };
				pt.ct = ct;
				pt.K = K;
				ct += delta_ct;
                pointsDeSitter.push_back(pt);
			}

			DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_DE_SITTER),
				hDlg, DrawGraphDialogDeSitter);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxDeSitter(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsDeSitter[0].ct;
    xmax = pointsDeSitter[0].ct;
    ymin = pointsDeSitter[0].K;
    ymax = pointsDeSitter[0].K;

    for (int i = 1; i < pointsDeSitter.size(); i++)
    {
        Point2dDeSitter pt = pointsDeSitter[i];

        if (pt.ct < xmin)
            xmin = pt.ct;
        if (pt.ct > xmax)
            xmax = pt.ct;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static void DrawTitles(
    HDC hdc, RECT clientRect,
    const std::wstring& fTitle,
    const std::wstring& xTitle,
    const std::wstring& yTitle,
    int sx0, int sx1, int sy0, int sy1)
{
    HFONT hCustomFont = CreateFont(
        -MulDiv(10, GetDeviceCaps(hdc, LOGPIXELSY), 72), // Height in logical units
        0,                      // Width (0 = default)
        0,                      // Escapement
        0,                      // Orientation
        FW_BOLD,                // Weight (700 = bold)
        FALSE,                  // Italic
        FALSE,                  // Underline
        FALSE,                  // StrikeOut
        DEFAULT_CHARSET,        // Charset
        OUT_DEFAULT_PRECIS,     // Output precision
        CLIP_DEFAULT_PRECIS,    // Clipping precision
        DEFAULT_QUALITY,        // Quality
        FIXED_PITCH | FF_MODERN,// Pitch and family
        L"Courier New"          // Typeface name
    );

    HFONT hOldFont = (HFONT)SelectObject(hdc, hCustomFont);

    SIZE sz;
    int width = clientRect.right - clientRect.left;

    // Title: fTitle
    GetTextExtentPoint32W(hdc, fTitle.c_str(), (int)fTitle.length(), &sz);
    int w = sz.cx;
    int h = sz.cy;
    TextOutW(hdc, (width - w) / 2, h, fTitle.c_str(), (int)fTitle.length());
    // draw x-axis title
    GetTextExtentPoint32W(hdc, xTitle.c_str(), (int)xTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx0 + (sx1 - sx0 - w) / 2, sy1 + 2 * h, 
        xTitle.c_str(), (int)xTitle.length());
    // draw y-axis title
    GetTextExtentPoint32W(hdc, yTitle.c_str(), (int)yTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx1 + w / 5, sy0 + (sy1 - sy0) / 2 - h / 2, 
        yTitle.c_str(), (int)yTitle.length());
    SelectObject(hdc, hOldFont); // Restore original font
}

static void DrawFormattedText(HDC hdc, char loctext[], RECT rect)
{
    // Draw the text with formatting options
    DrawTextA(hdc, loctext, (int)strlen(loctext), &rect, DT_SINGLELINE | DT_NOCLIP);
}

static INT_PTR CALLBACK DrawGraphDialogDeSitter(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog deSitter Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxDeSitter(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsDeSitter[0].ct;
        py = (float)pointsDeSitter[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsDeSitter[0].ct;
        py = (float)pointsDeSitter[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsDeSitter.size(); j++)
        {
            px = (float)pointsDeSitter[j].ct;
            py = (float)pointsDeSitter[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogRadiation(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_B = GetDlgItem(hDlg, IDC_COMBO_B);
    static HWND hCombo_ct = GetDlgItem(hDlg, IDC_COMBO_DELTA_T);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_2);
    static HWND hCombo_lambda = GetDlgItem(hDlg, IDC_COMBO_LAMBDA);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e1");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e2");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e3");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e4");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e5");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-5");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-4");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-3");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-2");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+0");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+2");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+3");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+4");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+5");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_RADIATION)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_A_2, line, 128);
            double A = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_DELTA_T, line, 128);
            double deltaT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_2, FALSE, TRUE);
            double step = deltaT / 256.0, t = 0.0, K = 0.0;
            int index = 0;

            pointsRadiation.clear();

            while (t <= deltaT)
            {
                UniversalModels::RadiationUniverse(
                    A, epsilon, t, K);
                Point2dRadiation pt = { 0 };
                pt.deltaT = t;
                pt.K = K;
                t += step;
                pointsRadiation.push_back(pt);
            }

            DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_RADIATION),
                hDlg, DrawGraphDialogRadiation);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxRadiation(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsRadiation[0].deltaT;
    xmax = pointsRadiation[0].deltaT;
    ymin = pointsRadiation[0].K;
    ymax = pointsRadiation[0].K;

    for (int i = 1; i < pointsRadiation.size(); i++)
    {
        Point2dRadiation pt = pointsRadiation[i];

        if (pt.deltaT < xmin)
            xmin = pt.deltaT;
        if (pt.deltaT > xmax)
            xmax = pt.deltaT;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static INT_PTR CALLBACK DrawGraphDialogRadiation(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog Radiation Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxRadiation(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsRadiation[0].deltaT;
        py = (float)pointsRadiation[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsRadiation[0].deltaT;
        py = (float)pointsRadiation[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsRadiation.size(); j++)
        {
            px = (float)pointsRadiation[j].deltaT;
            py = (float)pointsRadiation[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogFriedmann(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_M = GetDlgItem(hDlg, IDC_COMBO_M);
    static HWND hCombo_CT1 = GetDlgItem(hDlg, IDC_COMBO_CT1);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_3);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_FRIEDMANN)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_M, line, 128);
            double M = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_CT1, line, 128);
            double cT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_3, FALSE, TRUE);
            double step = cT / 256.0, t = 0.0, K = 0.0;
            int index = 0;

            pointsFriedmann.clear();

            while (t <= cT)
            {
                UniversalModels::FriedmannUniverse(
                    epsilon, M, t, K);
                Point2dFriedmann pt = { 0 };
                pt.cT = t;
                pt.K = K;
                t += step;
                pointsFriedmann.push_back(pt);
            }

            DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_FRIEDMANN),
                hDlg, DrawGraphDialogFriedmann);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxFriedmann(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsFriedmann[0].cT;
    xmax = pointsFriedmann[0].cT;
    ymin = pointsFriedmann[0].K;
    ymax = pointsFriedmann[0].K;

    for (int i = 1; i < pointsFriedmann.size(); i++)
    {
        Point2dFriedmann pt = pointsFriedmann[i];

        if (pt.cT < xmin)
            xmin = pt.cT;
        if (pt.cT > xmax)
            xmax = pt.cT;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static INT_PTR CALLBACK DrawGraphDialogFriedmann(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog Friedmann Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxFriedmann(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsFriedmann[0].cT;
        py = (float)pointsFriedmann[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsFriedmann[0].cT;
        py = (float)pointsFriedmann[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsFriedmann.size(); j++)
        {
            px = (float)pointsFriedmann[j].cT;
            py = (float)pointsFriedmann[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}


//Microsoft Visual C++ generated resource script.
//
#include "resource.h"

#define APSTUDIO_READONLY_SYMBOLS
/////////////////////////////////////////////////////////////////////////////
//
// Generated from the TEXTINCLUDE resource.
//
#ifndef APSTUDIO_INVOKED
#include "targetver.h"
#endif
#define APSTUDIO_HIDDEN_SYMBOLS
#include "windows.h"
#undef APSTUDIO_HIDDEN_SYMBOLS
/////////////////////////////////////////////////////////////////////////////
#undef APSTUDIO_READONLY_SYMBOLS

#if !defined(AFX_RESOURCE_DLL) || defined(AFX_TARG_ENU)
LANGUAGE 9, 1

/////////////////////////////////////////////////////////////////////////////
//
// Icon
//

// Icon with lowest ID value placed first to ensure application icon
// remains consistent on all systems.

IDI_MODELUNIVERSES       ICON         "ModelUniverses.ico"
IDI_SMALL               ICON         "small.ico"

/////////////////////////////////////////////////////////////////////////////
//
// Menu
//

IDC_MODELUNIVERSES MENU
BEGIN
    POPUP "&Begin"
    BEGIN
        MENUITEM "&de Sitter Universe", IDM_DE_SITTER
        MENUITEM "&Radiation Universe", IDM_RADIATION
        MENUITEM "&Friedmann Universe", IDM_FRIEDMANN
        MENUITEM SEPARATOR
        MENUITEM "E&xit",               IDM_EXIT
    END
    POPUP "&Help"
    BEGIN
        MENUITEM "&About ...",          IDM_ABOUT
    END
END


/////////////////////////////////////////////////////////////////////////////
//
// Accelerator
//

IDC_MODELUNIVERSES ACCELERATORS
BEGIN
    "?",            IDM_ABOUT,              ASCII,  ALT
    "/",            IDM_ABOUT,              ASCII,  ALT
END


/////////////////////////////////////////////////////////////////////////////
//
// Dialog
//

IDD_ABOUTBOX DIALOGEX 0, 0, 170, 62
STYLE DS_SETFONT | DS_MODALFRAME | DS_FIXEDSYS | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "About ModelUniverses"
FONT 8, "MS Shell Dlg"
BEGIN
    ICON            IDI_MODELUNIVERSES,IDC_STATIC,14,14,21,20
    LTEXT           "ModelUniverses, Version 1.0",IDC_STATIC,42,14,114,8,SS_NOPREFIX
    LTEXT           "Copyright (c) 2026",IDC_STATIC,42,26,114,8
    DEFPUSHBUTTON   "OK",IDOK,113,41,50,14,WS_GROUP
END

IDD_DATA_INPUT_DIALOG_DE_SITTER DIALOGEX 0, 0, 280, 200
STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "Data Input Dialog de Sitter Universe"
FONT 10, "Courier New", 700
BEGIN
LTEXT       "A:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_A_1, 120, 10, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "B:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_B, 120, 40, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "ct:", IDC_STATIC, 10, 70, 100, 10
COMBOBOX    IDC_COMBO_CT, 120, 70, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "epsilon:",
IDC_STATIC, 10, 100, 50, 60
COMBOBOX    IDC_COMBO_EPSILON_1, 120, 100, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "Lambda:",
IDC_STATIC, 10, 130, 50, 60
COMBOBOX    IDC_COMBO_LAMBDA, 120, 130, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_DE_SITTER, 10, 160, 50, 16
PUSHBUTTON  "Cancel", IDCANCEL, 210, 160, 50, 16
END

IDD_DRAW_GRAPH_DIALOG_DE_SITTER DIALOGEX 0, 0, 600, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog de Sitter Universe"
FONT 10, "Courier New", 700
BEGIN
END

IDD_DATA_INPUT_DIALOG_RADIATION DIALOGEX 0, 0, 280, 170
STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "Data Input Dialog Radiation Universe"
FONT 10, "Courier New", 700
BEGIN
LTEXT       "A:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_A_2, 120, 10, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "t - t0:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_DELTA_T, 120, 40, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "epsilon:",
IDC_STATIC, 10, 70, 50, 60
COMBOBOX    IDC_COMBO_EPSILON_2, 120, 70, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_RADIATION, 10, 100, 50, 16
PUSHBUTTON  "Cancel", IDCANCEL, 210, 100, 50, 16
END

IDD_DRAW_GRAPH_DIALOG_RADIATION DIALOGEX 0, 0, 600, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog Radiation Universe"
FONT 10, "Courier New", 700
BEGIN
END

IDD_DATA_INPUT_DIALOG_FRIEDMANN DIALOGEX 0, 0, 280, 170
STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "Data Input Dialog Friedmann Universe"
FONT 10, "Courier New", 700
BEGIN
LTEXT       "M:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_M, 120, 10, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "cT:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_CT1, 120, 40, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "epsilon:",
IDC_STATIC, 10, 70, 50, 60
COMBOBOX    IDC_COMBO_EPSILON_3, 120, 70, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_FRIEDMANN, 10, 100, 50, 16
PUSHBUTTON  "Cancel", IDCANCEL, 210, 100, 50, 16
END

IDD_DRAW_GRAPH_DIALOG_FRIEDMANN DIALOGEX 0, 0, 600, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog Friedmann Universe"
FONT 10, "Courier New", 700
BEGIN
END

/////////////////////////////////////////////////////////////////////////////
//
// DESIGNINFO
//

#ifdef APSTUDIO_INVOKED
GUIDELINES DESIGNINFO
BEGIN
    IDD_ABOUTBOX, DIALOG
    BEGIN
        LEFTMARGIN, 7
        RIGHTMARGIN, 163
        TOPMARGIN, 7
        BOTTOMMARGIN, 55
    END
END
#endif    // APSTUDIO_INVOKED

#ifdef APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// TEXTINCLUDE
//
1 TEXTINCLUDE
BEGIN
    "resource.h\0"
END

2 TEXTINCLUDE
BEGIN
    "#ifndef APSTUDIO_INVOKED\r\n"
    "#include ""targetver.h""\r\n"
    "#endif\r\n"
    "#define APSTUDIO_HIDDEN_SYMBOLS\r\n"
    "#include ""windows.h""\r\n"
    "#undef APSTUDIO_HIDDEN_SYMBOLS\r\n"
    "\0"
END

3 TEXTINCLUDE
BEGIN
    "\r\n"
    "\0"
END

#endif    // APSTUDIO_INVOKED

/////////////////////////////////////////////////////////////////////////////
//
// String Table
//

STRINGTABLE
BEGIN
   IDC_MODELUNIVERSES   "MODELUNIVERSES"
   IDS_APP_TITLE       "ModelUniverses"
END

#endif
/////////////////////////////////////////////////////////////////////////////



#ifndef APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// Generated from the TEXTINCLUDE resource.
//

/////////////////////////////////////////////////////////////////////////////
#endif    // not APSTUDIO_INVOKED


//{{NO_DEPENDENCIES}}
// Microsoft Visual C++ generated include file.
// Used by ModelUniverses.rc

#define IDS_APP_TITLE			103

#define IDR_MAINFRAME			128
#define IDD_MODELUNIVERSES_DIALOG	102
#define IDD_ABOUTBOX			103
#define IDM_ABOUT				104
#define IDM_EXIT				105
#define IDI_MODELUNIVERSES		107
#define IDI_SMALL				108
#define IDC_MODELUNIVERSES		109
#define IDC_MYICON				2
#ifndef IDC_STATIC
#define IDC_STATIC				-1
#endif
// Next default values for new objects
//
#ifdef APSTUDIO_INVOKED
#ifndef APSTUDIO_READONLY_SYMBOLS

#define _APS_NO_MFC					130
#define _APS_NEXT_RESOURCE_VALUE	129
#define _APS_NEXT_COMMAND_VALUE		32771
#define _APS_NEXT_CONTROL_VALUE		1000
#define _APS_NEXT_SYMED_VALUE		110
#endif
#endif

#define IDD_DATA_INPUT_DIALOG_DE_SITTER	1000
#define IDC_COMBO_A_1				1010
#define IDC_COMBO_B					1020
#define IDC_COMBO_CT				1030
#define IDC_COMBO_EPSILON_1			1040
#define IDC_COMBO_LAMBDA			1050
#define IDC_BUTTON_DRAW_DE_SITTER	1060
#define IDD_DRAW_GRAPH_DIALOG_DE_SITTER	2000
#define IDD_DATA_INPUT_DIALOG_RADIATION	3000
#define IDC_COMBO_A_2				3010
#define IDC_COMBO_DELTA_T			3020
#define IDC_COMBO_EPSILON_2			3030
#define IDC_BUTTON_DRAW_RADIATION	3040
#define IDD_DRAW_GRAPH_DIALOG_RADIATION	4000
#define IDD_DATA_INPUT_DIALOG_FRIEDMANN 5000
#define IDC_COMBO_M					5010
#define IDC_COMBO_CT1				5020
#define IDC_COMBO_EPSILON_3			5030
#define IDC_BUTTON_DRAW_FRIEDMANN	5040
#define IDD_DRAW_GRAPH_DIALOG_FRIEDMANN	6000
#define IDM_DE_SITTER				32771
#define IDM_RADIATION				32772
#define IDM_FRIEDMANN				32773

Blog Entry © Sunday, January 25, 2026, by James Pate Williams, Jr., Schwarzschild Solution of Einstein’s General Relativity Gravitational Field Equation

Blog Entry Sunday January 25 2026Download

Blog Entry © Wednesday, October 29, 2025, by James Pate Williams, Jr. Hydrogenic Atomic Spectral Lines

Blog Entry Wednesday October 29 2025Download
// HydrogenSpectralLines.cpp : Defines the entry point for the application.
//

#include "pch.h"
#include "framework.h"
#include "HydrogenSpectralLines.h"

#define MAX_LOADSTRING 100

// Global Variables:
HINSTANCE hInst;                                // current instance
WCHAR szTitle[MAX_LOADSTRING];                  // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING];            // the main window class name
WCHAR buffer[32768], line[128], line1[128], line2[512];
double c = 299792458;
double h = 4.135667696e-15;

// 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 wWinMain(_In_ HINSTANCE hInstance,
                     _In_opt_ HINSTANCE hPrevInstance,
                     _In_ LPWSTR    lpCmdLine,
                     _In_ int       nCmdShow)
{
    UNREFERENCED_PARAMETER(hPrevInstance);
    UNREFERENCED_PARAMETER(lpCmdLine);

    // TODO: Place code here.

    // Initialize global strings
    LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
    LoadStringW(hInstance, IDC_HYDROGENSPECTRALLINES, szWindowClass, MAX_LOADSTRING);
    MyRegisterClass(hInstance);

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

    HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_HYDROGENSPECTRALLINES));

    MSG msg;

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

    return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
    WNDCLASSEXW 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_HYDROGENSPECTRALLINES));
    wcex.hCursor        = LoadCursor(nullptr, IDC_ARROW);
    wcex.hbrBackground  = (HBRUSH)(COLOR_WINDOW+1);
    wcex.lpszMenuName   = MAKEINTRESOURCEW(IDC_HYDROGENSPECTRALLINES);
    wcex.lpszClassName  = szWindowClass;
    wcex.hIconSm        = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

    return RegisterClassExW(&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)
{
   hInst = hInstance; // Store instance handle in our global variable

   HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);

   if (!hWnd)
   {
      return FALSE;
   }

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

   return TRUE;
}

#define IDC_COMPUTE_BUTTON  1010
#define IDC_CANCEL_BUTTON   1020
#define IDC_CLEAR_BUTTON    1030
#define IDC_EDIT_MULTILINE  1040

//
//  FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  PURPOSE: Processes messages for the main window.
//
//  WM_COMMAND  - process the application menu
//  WM_PAINT    - Paint the main window
//  WM_DESTROY  - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    static HFONT hFont = nullptr;
    static HWND hCombo1 = nullptr;
    static HWND hCombo2 = nullptr;
    static HWND hCombo3 = nullptr;
    static HWND hCombo4 = nullptr;
    static HWND hEditMultiline = nullptr;

    switch (message)
    {
    case WM_CREATE:
        CreateWindowEx(0, L"STATIC", L"Series:", WS_CHILD | WS_VISIBLE,
            10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
        hCombo1 = CreateWindowEx(0, L"COMBOBOX", nullptr,
            WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
            ES_AUTOVSCROLL, 120, 10, 200, 100, hWnd, nullptr, hInst, nullptr);
        CreateWindowEx(0, L"STATIC", L"n2:", WS_CHILD | WS_VISIBLE,
            10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
        hCombo2 = CreateWindowEx(0, L"COMBOBOX", nullptr,
            WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
            ES_AUTOVSCROLL, 120, 40, 120, 150, hWnd, nullptr, hInst, nullptr);
        CreateWindowEx(0, L"STATIC", L"atom:", WS_CHILD | WS_VISIBLE,
            10, 70, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
        hCombo3 = CreateWindowEx(0, L"COMBOBOX", nullptr,
            WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
            ES_AUTOVSCROLL, 120, 70, 120, 150, hWnd, nullptr, hInst, nullptr);
        CreateWindowEx(0, L"STATIC", L"formula:", WS_CHILD | WS_VISIBLE,
            10, 100, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
        hCombo4 = CreateWindowEx(0, L"COMBOBOX", nullptr,
            WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
            ES_AUTOVSCROLL, 120, 100, 120, 150, hWnd, nullptr, hInst, nullptr);
        CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
            10, 140, 80, 30, hWnd, (HMENU)IDC_COMPUTE_BUTTON, hInst, NULL);
        CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
            10, 180, 80, 30, hWnd, (HMENU)IDC_CANCEL_BUTTON, hInst, NULL);
        CreateWindowEx(0, L"BUTTON", L"Clear", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
            10, 220, 80, 30, hWnd, (HMENU)IDC_CLEAR_BUTTON, hInst, NULL);
        hFont = CreateFont(16, 0, 0, 0, FW_BOLD, FALSE, FALSE, FALSE,
            UNICODE, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
            DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New");
        hEditMultiline = CreateWindowEx(
            WS_EX_CLIENTEDGE,                       // Extended style for sunken border
            TEXT("EDIT"),                           // Class name
            TEXT(""),                               // Initial text (can be blank)
            WS_CHILD | WS_VISIBLE | WS_VSCROLL | ES_AUTOHSCROLL |
            ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL | WS_HSCROLL | WS_VSCROLL,
            340, 10, 640, 400,                      // Position and size
            hWnd,                                   // Parent window handle
            (HMENU)IDC_EDIT_MULTILINE,              // Unique control ID
            hInst,                                  // Application instance
            NULL                                    // Extra parameter
        );
        SendMessage(hCombo1, WM_SETFONT, (WPARAM)hFont, 0);
        SendMessage(hCombo2, WM_SETFONT, (WPARAM)hFont, 0);
        SendMessage(hCombo3, WM_SETFONT, (WPARAM)hFont, 0);
        SendMessage(hCombo4, WM_SETFONT, (WPARAM)hFont, 0);
        SendMessage(hEditMultiline, WM_SETFONT, (WPARAM)hFont, 0);
        SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Lyman    n1 = 1 n2 >= 2");
        SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Balmer   n1 = 2 n2 >= 3");
        SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Paschen  n1 = 3 n2 >= 4");
        SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Brackett n1 = 4 n2 >= 5");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"11");
        SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"12");
        SendMessage(hCombo1, CB_SETCURSEL, 0, 0);
        SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"hydrogen");
        SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"helium+");
        SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"lithium++");
        SendMessage(hCombo4, CB_ADDSTRING, 0, (LPARAM)L"energy eV");
        SendMessage(hCombo4, CB_ADDSTRING, 0, (LPARAM)L"frequency Hz");
        SendMessage(hCombo4, CB_ADDSTRING, 0, (LPARAM)L"wavelength A");
        SendMessage(hCombo1, CB_SETCURSEL, 0, 0);
        SendMessage(hCombo2, CB_SETCURSEL, 0, 0);
        SendMessage(hCombo3, CB_SETCURSEL, 0, 0);
        SendMessage(hCombo4, CB_SETCURSEL, 0, 0);
        buffer[0] = L'\0';
        break;
    case WM_COMMAND:
        {
            int wmId = LOWORD(wParam);
            // Parse the menu selections:
            switch (wmId)
            {
            case IDM_ABOUT:
                DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
                break;
            case IDC_COMPUTE_BUTTON:
            {
                int n1 = 0, n2 = 0;
                WCHAR series[16] = { 0 };

                if (hCombo1)
                {
                    GetWindowText(hCombo1, line, 128);
                }

                if (std::wcsstr(line, L"Lyman"))
                {
                    wcscpy_s(series, L"Lyman");
                    n1 = 1;
                }
                
                else if (std::wcsstr(line, L"Balmer"))
                {
                    wcscpy_s(series, L"Balmer");
                    n1 = 2;
                }

                else if (std::wcsstr(line, L"Paschen"))
                {
                    wcscpy_s(series, L"Paschen");
                    n1 = 3;
                }

                else if (std::wcsstr(line, L"Brackett"))
                {
                    wcscpy_s(series, L"Brackett");
                    n1 = 4;
                }

                if (hCombo2)
                {
                    GetWindowText(hCombo2, line, 128);
                    std::wstring n2Str(line);
                    n2 = stoi(n2Str);
                }

                if (n2 < n1 + 1)
                {
                    MessageBox(hWnd, L"n2 must be greater than equal n1 + 1",
                        L"Warning", MB_OK | MB_ICONWARNING);
                    break;
                }

                double Z = 1.0;
                GetWindowText(hCombo3, line, 128);

                if (wcscmp(line, L"hydrogen") == 0)
                {
                    Z = 1.0;
                }

                else if (wcscmp(line, L"helium+") == 0)
                {
                    Z = 2.0;
                }

                else if (wcscmp(line, L"lithium++") == 0)
                {
                    Z = 3.0;
                }

                double deltaE = -13.6 * Z * Z * (1.0 / (n1 * n1) - 1.0 / (n2 * n2));
                double nu = deltaE / h;
                double lambda = c / nu / 1.0e-10;
                double number = deltaE;
    
                GetWindowText(hCombo4, line1, 128);

                if (wcscmp(line1, L"energy eV") == 0)
                {
                    number = deltaE;
                }

                else if (wcscmp(line1, L"frequency Hz") == 0)
                {
                    number = nu;
                }

                else if (wcscmp(line1, L"wavelength A") == 0)
                {
                    number = lambda;
                }

                swprintf_s(line2, L"%s\t%s\t%s\t%d\t%d\t%lf\r\n",
                    series, line, line1, n1, n2, number);
                wcscat_s(buffer, line2);

                if (hEditMultiline)
                {
                    SetWindowText(hEditMultiline, buffer);
                }

                break;
            }
            case IDC_CLEAR_BUTTON:
                buffer[0] = '\0';
                SetWindowText(hEditMultiline, buffer);
                break;
            case IDC_CANCEL_BUTTON:
            case IDM_EXIT:
                DestroyWindow(hWnd);
                break;
            default:
                return DefWindowProc(hWnd, message, wParam, lParam);
            }
        }
        break;
    case WM_PAINT:
        {
            PAINTSTRUCT ps;
            HDC hdc = BeginPaint(hWnd, &ps);
            // TODO: Add any drawing code that uses hdc here...
            EndPaint(hWnd, &ps);
        }
        break;
    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;
}

Blog Entry © Thursday, September 11, 2025, by James Pate Wiliams, Jr. Modeling the Friedmann Equation in the Early Universe

Blog Entry Thursday September 11 2025Download

Blog Entry © Sunday, August 24, 2025, by James Pate Williams, Jr. Corrections to New Quantum Chemical Total Molecular Ground-State Energies for the Helium Hydride Cation (a Hetero Nuclear molecule) and the Hydrogen Molecule (a Homo Nuclear Molecule)

Blog Entry Sunday August 24 2024Download

Blog Entry © Friday, August 22, 2025, by James Pate Williams, Jr. New Quantum Chemical Total Molecular Ground-State Energies for the Helium Hydride Cation (a Hetero Nuclear molecule) and the Hydrogen Molecule (a Homo Nuclear Molecule)

Blog Entry Friday August 22 2025Download

Blog Entry © Monday, August 18, 2025, by James Pate Williams, Jr. Curve Fitting Contracted Gaussian Type 1s Orbitals (CGTO-1s) to a Slater Type 1s Orbital

Blog Entry Monday August 18 2025Download

Blog Entry © Saturday, August 16, 2025, by James Pate Williams, Jr. Some More Elementary Quantum Chemistry

Blog Entry Saturday August 16 2025Download

Newtonian Gravity and Cosmology © Friday, July 18, 2025, by James Pate Williams, Jr. in Conjunction with the Microsoft Copilot AI

Newtonian Gravity and CosmologyDownload