// SomeRelativityMath.cpp : Defines the entry point for the application.
// https://arxiv.org/pdf/2506.09946
#include "pch.h"
#include "framework.h"
#include "SomeRelativityMath.h"
#include <stdio.h>
#include <vector>
#define MAX_LOADSTRING 100
typedef struct tagPoint2d
{
double x, y;
} POINT2D, * PPOINT2D;
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
char text[8192];
std::vector<POINT2D> points1, points2;
std::vector<POINT2D> points3, points4;
// 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 DrawGraph(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_SOMERELATIVITYMATH, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_SOMERELATIVITYMATH));
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_SOMERELATIVITYMATH));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_SOMERELATIVITYMATH);
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;
}
static void FindMinMax(
double& xMin, double& xMax,
double& yMin, double& yMax)
{
// uses global 2D double points structure
xMin = yMin = DBL_MAX;
xMax = yMax = DBL_MIN;
for (size_t i = 0; i < points1.size(); i++)
{
POINT2D pt = points1[i];
double x = pt.x;
double y = pt.y;
if (x < xMin)
xMin = x;
if (x > xMax)
xMax = x;
if (y < yMin)
yMin = y;
if (y > yMax)
yMax = y;
}
for (size_t i = 0; i < points2.size(); i++)
{
POINT2D pt = points2[i];
double x = pt.x;
double y = pt.y;
if (x < xMin)
xMin = x;
if (x > xMax)
xMax = x;
if (y < yMin)
yMin = y;
if (y > yMax)
yMax = y;
}
for (size_t i = 0; i < points3.size(); i++)
{
POINT2D pt = points3[i];
double x = pt.x;
double y = pt.y;
if (x < xMin)
xMin = x;
if (x > xMax)
xMax = x;
if (y < yMin)
yMin = y;
if (y > yMax)
yMax = y;
}
for (size_t i = 0; i < points4.size(); i++)
{
POINT2D pt = points4[i];
double x = pt.x;
double y = pt.y;
if (x < xMin)
xMin = x;
if (x > xMax)
xMax = x;
if (y < yMin)
yMin = y;
if (y > yMax)
yMax = y;
}
}
static void DrawFormattedText(HDC hdc, char text[], RECT rect)
{
// Draw the text with formatting options
DrawTextA(hdc, text, -1, &rect, DT_SINGLELINE | DT_NOCLIP);
}
//
// 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_CREATE:
{
double P1 = 0, P2 = 0, P3 = 0, P4 = 0;
int numberPts = 1024;
double x0 = 1, h = 0.5 / numberPts, x = x0;
points1.resize(numberPts);
points2.resize(numberPts);
points3.resize(numberPts);
points4.resize(numberPts);
for (int i = 0; i < numberPts; i++)
{
P1 = x + 1.0;
P2 = 3.0 * x * x + 4.0 * x + 2.0;
P3 = 15.0 * x * x * x + 16.0 * x * x + 6.0 * x;
P4 = 105.0 * x * x * x * x + 156.0 * x * x * x +
94.0 * x * x + 24.0 * x;
POINT2D pt = { 0 };
pt.x = x;
pt.y = log(P1);
points1[i] = pt;
pt.y = log(P2);
points2[i] = pt;
pt.y = log(P3);
points3[i] = pt;
pt.y = log(P4);
points4[i] = pt;
x += h;
}
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 IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
break;
case WM_PAINT:
{
double h = 0, pi = 0, plm = 0, theta = 0;
double xMax = 0, xMin = 0, yMax = 0, yMin = 0;
FindMinMax(xMin, xMax, yMin, yMax);
float xSpan = (float)(xMax - xMin);
float ySpan = (float)(yMax - yMin);
RECT rect = { };
GetClientRect(hWnd, &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(hWnd, &ps);
int i = 0;
float x = (float)xMin;
float y = (float)yMax;
px = x;
py = y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
char buffer[128] = { };
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);
sprintf_s(buffer, "%3.2f", x);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
buffer,
strlen(buffer),
&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, buffer, 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)
{
sprintf_s(buffer, "%3.1f", y);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
buffer,
strlen(buffer),
&size);
RECT textRect = { };
textRect.left = (long)(sx0 - size.cx - size.cx / 5.0f);
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, buffer, textRect);
}
y += deltaY;
i++;
}
HGDIOBJ rPenNew = NULL;
HGDIOBJ hPenOld = NULL;
rPenNew = CreatePen(PS_SOLID, 2, RGB(255, 0, 0));
hPenOld = SelectObject(hdc, rPenNew);
px = (float)points1[0].x;
py = (float)points1[0].y;
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 < points1.size(); j++)
{
px = (float)points1[j].x;
py = (float)points1[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(rPenNew);
HGDIOBJ gPenNew = CreatePen(PS_SOLID, 2, RGB(0, 255, 0));
hPenOld = SelectObject(hdc, gPenNew);
px = (float)points2[0].x;
py = (float)points2[0].y;
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 < points2.size(); j++)
{
px = (float)points2[j].x;
py = (float)points2[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(gPenNew);
HGDIOBJ bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
hPenOld = SelectObject(hdc, bPenNew);
px = (float)points3[0].x;
py = (float)points3[0].y;
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 < points3.size(); j++)
{
px = (float)points3[j].x;
py = (float)points3[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(bPenNew);
HGDIOBJ pPenNew = CreatePen(PS_SOLID, 2, RGB(128, 0, 128));
hPenOld = SelectObject(hdc, pPenNew);
px = (float)points4[0].x;
py = (float)points4[0].y;
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 < points4.size(); j++)
{
px = (float)points4[j].x;
py = (float)points4[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(pPenNew);
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;
}
static INT_PTR CALLBACK DrawGraph(
HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
char line[256] = { };
switch (message)
{
case WM_INITDIALOG:
GetWindowTextA(hDlg, line, 256);
strcat_s(text, 8192, " ");
strcat_s(text, 8192, line);
SetWindowTextA(hDlg, text);
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 h = 0, pi = 0, plm = 0, theta = 0;
double xMax = 0, xMin = 0, yMax = 0, yMin = 0;
FindMinMax(xMin, xMax, yMin, yMax);
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;
px = x;
py = y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
char buffer[128] = { };
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);
sprintf_s(buffer, "%3.0f", x);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
buffer,
strlen(buffer),
&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, buffer, 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)
{
sprintf_s(buffer, "%3.0f", y);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
buffer,
strlen(buffer),
&size);
RECT textRect = { };
textRect.left = (long)(sx0 - size.cx - size.cx / 5.0f);
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, buffer, textRect);
}
y += deltaY;
i++;
}
HGDIOBJ rPenNew = NULL;
HGDIOBJ hPenOld = NULL;
rPenNew = CreatePen(PS_SOLID, 2, RGB(255, 0, 0));
hPenOld = SelectObject(hdc, rPenNew);
px = (float)points1[1].x;
py = (float)points1[1].y;
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 < points1.size(); j++)
{
px = (float)points1[j].x;
py = (float)points1[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(rPenNew);
px = (float)points2[1].x;
py = (float)points2[1].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)sx, (int)sy, &wPt);
HGDIOBJ gPenNew = CreatePen(PS_SOLID, 2, RGB(0, 255, 0));
hPenOld = SelectObject(hdc, gPenNew);
px = (float)points2[1].x;
py = (float)points2[1].y;
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 < points2.size(); j++)
{
px = (float)points2[j].x;
py = (float)points2[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(gPenNew);
px = (float)points3[1].x;
py = (float)points3[1].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)sx, (int)sy, &wPt);
HGDIOBJ bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
hPenOld = SelectObject(hdc, bPenNew);
px = (float)points3[1].x;
py = (float)points3[1].y;
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 < points3.size(); j++)
{
px = (float)points3[j].x;
py = (float)points3[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(bPenNew);
px = (float)points4[1].x;
py = (float)points4[1].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)sx, (int)sy, &wPt);
HGDIOBJ tPenNew = CreatePen(PS_SOLID, 2, RGB(128, 0, 128));
hPenOld = SelectObject(hdc, tPenNew);
px = (float)points4[1].x;
py = (float)points4[1].y;
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 < points4.size(); j++)
{
px = (float)points4[j].x;
py = (float)points4[j].y;
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
SelectObject(hdc, hPenOld);
DeleteObject(tPenNew);
EndPaint(hDlg, &ps);
return (INT_PTR)FALSE;
break;
}
return (INT_PTR)FALSE;
}
Numerical Explorations 