outdated: 39.Introduction to Physical Simulations

这一节说明了三种运动，直线运动，弹性运动和万有引力下运动。本节对三种运动在每个点上力做了分析。

Physics.h文件中定义了四个类，Vector3D类重载了基本的操作运算符和求解法向量函数。Mass类有基本的质量m、位置position、速率velocity和力force，及牛顿第一定律。Simulation类为模拟类，ConstantVelocity类、MotionUnderGravitation类和MassConnectedWithSpring类都继承自Simulation类。

下面为代码，

#ifndef GL_FRAMEWORK_INCLUDED
#define GL_FRAMEWORK_INCLUDED

#include <windows.h>

typedef struct {                                   // Structure for keyboard stuff
    BOOL keyDown[256];
} Keys;

typedef struct {                                   // Contains information vital to applications 
    HMODULE hInstance;                             // Application Instance
    const char* className;
} Application;

typedef struct {                                   // Window creation info
    Application* application;
    char* title;
    int width;
    int height;
    int bitsPerPixel;
    BOOL isFullScreen;
} GL_WindowInit;

typedef struct {                                   // Contains information vital to a window
    Keys* keys;
    HWND hWnd;                                     // Windows handle
    HDC hDC;                                       // Device context
    HGLRC hRC;                                     // Rendering context
    GL_WindowInit init;
    BOOL isVisible;                                // Window visiable?
    DWORD lastTickCount;                           // Tick counter
} GL_Window;

void TerminateApplication(GL_Window* window);      // Terminate the application

void ToggleFullscreen(GL_Window* window);          // Toggle fullscreen / Windowed mode

BOOL Initialize(GL_Window* window, Keys* keys);

void Deinitialize(void);

void Update(DWORD milliseconds);

void Draw(void);

#endif

#include <Windows.h>
#include <GL\glew.h>
#include <GL\glut.h>
#include "Previous.h"

#define WM_TOGGLEFULLSCREEN (WM_USER+1)                   // Application define message for toggling 
// between fulscreen / windowed mode
static BOOL g_isProgramLooping;                           // Window creation loop, for fullscreen / windowed mode
static BOOL g_createFullScreen;                           // If true, then create window

void TerminateApplication(GL_Window* window)              // Terminate the application
{
    PostMessage(window->hWnd, WM_QUIT, 0, 0);             // Send a WM_QUIT message
    g_isProgramLooping = FALSE;                           // Stop looping of the program
}

void ToggleFullscreen(GL_Window* window)                  // Toggle fullscreen /windowed mode
{
    PostMessage(window->hWnd, WM_TOGGLEFULLSCREEN, 0, 0); // Send a WM_TOGGLEFULLSCREEN message
}

void ReshapeGL(int width, int height)                     // Reshape the window  when it's moved or resized
{
    glViewport(0, 0, (GLsizei)(width), (GLsizei)(height)); // Reset the current viewport
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    // Calcutate the aspect ratio of the window
    gluPerspective(45.0f, (GLfloat)(width) / (GLfloat)(height), 1.0, 100.0f);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
}

BOOL ChangeScreenResolution(int width, int height, int bitsPerPixel)     // Change the screen resolution
{
    DEVMODE dmScreenSettings;                              // Device mode
    ZeroMemory(&dmScreenSettings, sizeof(DEVMODE));        // Make sure memory is cleared
    dmScreenSettings.dmSize = sizeof(DEVMODE);             // Size of the devmode structure
    dmScreenSettings.dmPelsWidth = width;
    dmScreenSettings.dmPelsHeight = height;
    dmScreenSettings.dmBitsPerPel = bitsPerPixel;
    dmScreenSettings.dmFields = DM_BITSPERPEL | DM_PELSWIDTH | DM_PELSHEIGHT;
    if (ChangeDisplaySettings(&dmScreenSettings, CDS_FULLSCREEN) != DISP_CHANGE_SUCCESSFUL) {
        return FALSE;                                      // Display change failed
    }
    return TRUE;
}

BOOL CreateWindowGL(GL_Window* window)
{
    DWORD windowStyle = WS_OVERLAPPEDWINDOW;                // Define window style
    DWORD windowExtendedStyle = WS_EX_APPWINDOW;            // Define the window's extended style

    PIXELFORMATDESCRIPTOR pdf = {
        sizeof(PIXELFORMATDESCRIPTOR),                      // Size of this pixel format descriptor
        1,                                                  // Version Number
        PFD_DRAW_TO_WINDOW |                                // Format must support window
        PFD_SUPPORT_OPENGL |                                // Format must support openGL
        PFD_DOUBLEBUFFER,                                   // Must support double buffering
        PFD_TYPE_RGBA,                                      // Request an RGBA format
        window->init.bitsPerPixel,                          // Select color depth
        0, 0, 0, 0, 0, 0,                                   // Color bits ignored
        0,                                                  // No alpha buffer
        0,                                                  // Shift bit ignored
        0,                                                  // No accumulation buffer
        0, 0, 0, 0,                                         // Accumulation bits ignored
        16,                                                 // 16bits Z-buffer (depth buffer)
        0,                                                  // No stencil buffer
        0,                                                  // No auxiliary buffer
        PFD_MAIN_PLANE,                                     // Main drawing layer
        0,                                                  // Reserved
        0, 0, 0                                             // Layer masks ignored
    };
    RECT windowRect = { 0, 0, window->init.width, window->init.height };   // Window coordiantes

    GLuint PixelFormat;

    if (window->init.isFullScreen == TRUE) {
        if (ChangeScreenResolution(window->init.width, window->init.height, window->init.bitsPerPixel) == FALSE)
        {
            // Fullscreen mode failed, run in windowed mode instead
            MessageBox(HWND_DESKTOP, "Mode Switch Failed.\nRuning In Windowed Mode.",
                "Error", MB_OK | MB_ICONEXCLAMATION);
            window->init.isFullScreen = FALSE;
        }
        else {
            ShowCursor(FALSE);
            windowStyle = WS_POPUP;                         // Popup window
            windowExtendedStyle |= WS_EX_TOPMOST;
        }
    }
    else {
        // Adjust window, account for window borders
        AdjustWindowRectEx(&windowRect, windowStyle, 0, windowExtendedStyle);
    }
    // Create Opengl window
    window->hWnd = CreateWindowEx(windowExtendedStyle,      // Extended style
        window->init.application->className,                // Class name
        window->init.title,                                 // Window title
        windowStyle,                                        // Window style
        0, 0,                                               // Window X,Y position
        windowRect.right - windowRect.left,                 // Window width
        windowRect.bottom - windowRect.top,                 // Window height
        HWND_DESKTOP,                                       // Desktop is window's parent
        0,                                                  // No menu
        window->init.application->hInstance,                // Pass the window instance
        window);

    if (window->hWnd == 0) {                                // Was window creation a success?
        return FALSE;
    }
    window->hDC = GetDC(window->hWnd);
    if (window->hDC == 0) {
        DestroyWindow(window->hWnd);
        window->hWnd = 0;
        return FALSE;
    }
    PixelFormat = ChoosePixelFormat(window->hDC, &pdf);     // Find a compatible pixel format
    if (PixelFormat == 0) {
        ReleaseDC(window->hWnd, window->hDC);               // Release device context
        window->hDC = 0;
        DestroyWindow(window->hWnd);
        window->hWnd = 0;
        return FALSE;
    }
    if (SetPixelFormat(window->hDC, PixelFormat, &pdf) == FALSE) {   // Try to set the pixel format
        ReleaseDC(window->hWnd, window->hDC);
        window->hDC = 0;
        DestroyWindow(window->hWnd);
        window->hWnd = 0;
        return FALSE;
    }
    window->hRC = wglCreateContext(window->hDC);            // Try to get a rendering context
    if (window->hRC == 0) {
        ReleaseDC(window->hWnd, window->hDC);
        window->hDC = 0;
        DestroyWindow(window->hWnd);
        window->hWnd = 0;
        return FALSE;
    }
    // Make the rendering context our current rendering context
    if (wglMakeCurrent(window->hDC, window->hRC) == FALSE) {
        wglDeleteContext(window->hRC);                      //  Delete the rendering context
        window->hRC = 0;
        ReleaseDC(window->hWnd, window->hDC);
        window->hDC = 0;
        DestroyWindow(window->hWnd);
        window->hWnd = 0;
        return FALSE;
    }
    ShowWindow(window->hWnd, SW_NORMAL);                    // Make the window visiable
    window->isVisible = TRUE;
    ReshapeGL(window->init.width, window->init.height);     // Reshape our GL window
    ZeroMemory(window->keys, sizeof(Keys));                 // Clear all keys
    window->lastTickCount = GetTickCount();
    return TRUE;
}

BOOL DestoryWindowGL(GL_Window* window)
{
    if (window->hWnd != 0) {
        if (window->hDC != 0) {
            wglMakeCurrent(window->hDC, 0);                 // Setting current active rendering context to zero
            if (window->hRC != 0) {
                wglDeleteContext(window->hRC);
                window->hRC = 0;
            }
            ReleaseDC(window->hWnd, window->hDC);
            window->hDC = 0;
        }
        DestroyWindow(window->hWnd);
        window->hWnd = 0;
    }
    if (window->init.isFullScreen) {
        ChangeDisplaySettings(NULL, 0);                     // Switch back to desktop resolution
        ShowCursor(TRUE);
    }
    return TRUE;
}

// Process window message callback
LRESULT CALLBACK WindowProc(HWND hWnd, UINT uMsg, WPARAM wParam, LPARAM lParam)
{
    // Get the window context
    GL_Window* window = (GL_Window*)(GetWindowLong(hWnd, GWL_USERDATA));
    switch (uMsg) {                                         // Evaluate window message
    case WM_SYSCOMMAND:                                     // Intercept system commands
    {
        switch (wParam) {                                   // Check system calls
        case SC_SCREENSAVE:                                 // Screensaver trying to start?
        case SC_MONITORPOWER:                               // Mointer trying to enter powersave?
            return 0;                                           // Prevent form happening
        }
        break;
    }
    return 0;
    case WM_CREATE:
    {
        CREATESTRUCT* creation = (CREATESTRUCT*)(lParam);   // Store window structure pointer
        window = (GL_Window*)(creation->lpCreateParams);
        SetWindowLong(hWnd, GWL_USERDATA, (LONG)(window));
    }
    return 0;

    case WM_CLOSE:
        TerminateApplication(window);
        return 0;

    case WM_SIZE:
        switch (wParam) {
        case SIZE_MINIMIZED:                                 // Was window minimized?
            window->isVisible = FALSE;
            return 0;
        case SIZE_MAXIMIZED:
            window->isVisible = TRUE;
            ReshapeGL(LOWORD(lParam), HIWORD(lParam));
            return 0;
        case SIZE_RESTORED:
            window->isVisible = TRUE;
            ReshapeGL(LOWORD(lParam), HIWORD(lParam));
            return 0;
        }
        break;

    case WM_KEYDOWN:
        if ((wParam >= 0) && (wParam <= 255)) {
            window->keys->keyDown[wParam] = TRUE;            // Set the selected key(wParam) to true
            return 0;
        }
        break;

    case WM_KEYUP:
        if ((wParam >= 0) && (wParam <= 255)) {
            window->keys->keyDown[wParam] = FALSE;
            return 0;
        }
        break;

    case WM_TOGGLEFULLSCREEN:
        g_createFullScreen = (g_createFullScreen == TRUE) ? FALSE : TRUE;
        PostMessage(hWnd, WM_QUIT, 0, 0);
        break;
    }
    return DefWindowProc(hWnd, uMsg, wParam, lParam);        // Pass unhandle message to DefWindowProc
}

BOOL RegisterWindowClass(Application* application)
{
    WNDCLASSEX windowClass;
    ZeroMemory(&windowClass, sizeof(WNDCLASSEX));            // Make sure memory is cleared
    windowClass.cbSize = sizeof(WNDCLASSEX);                 // Size of the windowClass structure
    windowClass.style = CS_HREDRAW | CS_VREDRAW | CS_OWNDC;  // Redraws the window for any movement / resizing
    windowClass.lpfnWndProc = (WNDPROC)(WindowProc);         // WindowProc handles message
    windowClass.hInstance = application->hInstance;          // Set the instance
    windowClass.hbrBackground = (HBRUSH)(COLOR_APPWORKSPACE);// Class background brush color
    windowClass.hCursor = LoadCursor(NULL, IDC_ARROW);       // Load the arrow pointer
    windowClass.lpszClassName = application->className;      // Sets the application className
    if (RegisterClassEx(&windowClass) == 0) {
        MessageBox(HWND_DESKTOP, "RegisterClassEx Failed!", "Error", MB_OK | MB_ICONEXCLAMATION);
        return FALSE;
    }
    return TRUE;
}

int WINAPI WinMain(HINSTANCE hIstance, HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nCmdShow)
{
    Application application;
    GL_Window window;
    Keys keys;
    BOOL isMessagePumpActive;
    MSG msg;
    DWORD tickCount;

    application.className = "OpenGL";
    application.hInstance = hIstance;

    ZeroMemory(&window, sizeof(GL_Window));
    window.keys = &keys;                                     // Window key structure
    window.init.application = &application;                  // Window application
    window.init.title = "Resource File";                       // Window title
    window.init.width = 640;                                 // Window width
    window.init.height = 480;                                // Window height
    window.init.bitsPerPixel = 16;                           // Bits per pixel
    window.init.isFullScreen = TRUE;                         // Fullscreen? (set to TRUE)

    ZeroMemory(&keys, sizeof(Keys));
    if (MessageBox(HWND_DESKTOP, "Would You Like To Run In Fullscreen Mode?", "Start FullScreen?",
        MB_YESNO | MB_ICONQUESTION) == IDNO)
    {
        window.init.isFullScreen = FALSE;
    }
    if (RegisterWindowClass(&application) == FALSE)
    {
        MessageBox(HWND_DESKTOP, "Error Registering Window Class!", "Error", MB_OK | MB_ICONEXCLAMATION);
        return -1;
    }
    g_isProgramLooping = TRUE;
    g_createFullScreen = window.init.isFullScreen;
    while (g_isProgramLooping) {                             // Loop until WM_QUIT is received
        window.init.isFullScreen = g_createFullScreen;       // Set init param of window creation to fullscreen?
        if (CreateWindowGL(&window) == TRUE) {               // Was window creation successful?
                                                             // At this point we should have a window that is setup to render OpenGL
            if (Initialize(&window, &keys) == FALSE) {
                TerminateApplication(&window);               // Close window, this will handle the shutdown
            }
            else {
                isMessagePumpActive = TRUE;
                while (isMessagePumpActive == TRUE) {
                    // Success creating window. Check for window messages
                    if (PeekMessage(&msg, window.hWnd, 0, 0, PM_REMOVE) != 0) {
                        if (msg.message != WM_QUIT) {
                            DispatchMessage(&msg);
                        }
                        else {
                            isMessagePumpActive = FALSE;     // Terminate the message pump
                        }
                    }
                    else {
                        if (window.isVisible == FALSE) {
                            WaitMessage();                   // Application is minimized wait for a message
                        }
                        else {
                            // Process application loop
                            tickCount = GetTickCount();      // Get the tick count
                            Update(tickCount - window.lastTickCount); // Update the counter
                            window.lastTickCount = tickCount;// Set last count to current count
                            Draw();                          // Draw screen
                            SwapBuffers(window.hDC);
                        }
                    }
                }
            }
            // Application is finished
            Deinitialize();
            DestoryWindowGL(&window);
        }
        else {
            MessageBox(HWND_DESKTOP, "Error Creating OpenGL Window", "Error", MB_OK | MB_ICONEXCLAMATION);
            g_isProgramLooping = FALSE;
        }
    }
    UnregisterClass(application.className, application.hInstance);    // UnRegister window class
    return 0;
}

#include <math.h>

class Vector3D {
public:
    float x, y, z;

    Vector3D(): x(0), y(0), z(0) {}
    Vector3D(float x, float y, float z)
    {
        this->x = x;
        this->y = y;
        this->z = z;
    }

    Vector3D& operator= (Vector3D v)
    {
        x = v.x;
        y = v.y;
        z = v.z;
        return *this;
    }

    Vector3D operator+ (Vector3D v)
    {
        return Vector3D(x + v.x, y + v.y, z + v.z);
    }

    Vector3D operator- (Vector3D v)
    {
        return Vector3D(x - v.x, y - v.y, z - v.z);
    }

    Vector3D operator* (float value)
    {
        return Vector3D(x * value, y * value, z * value);
    }

    Vector3D operator/ (float value)
    {
        return Vector3D(x / value, y / value, z / value);
    }

    Vector3D& operator+= (Vector3D v)
    {
        x += v.x;
        y += v.y;
        z += v.z;
        return *this;
    }

    Vector3D& operator-= (Vector3D v)
    {
        x -= v.x;
        y -= v.y;
        z -= v.z;
        return *this;
    }

    Vector3D& operator*= (Vector3D v)
    {
        x *= v.x;
        y *= v.y;
        z *= v.z;
        return *this;
    }

    Vector3D& operator/= (Vector3D v)
    {
        x /= v.x;
        y /= v.y;
        z /= v.z;
        return *this;
    }

    Vector3D operator- ()
    {
        return Vector3D(-x, -y, -z);
    }

    float length()
    {
        return sqrtf(x*x + y*y + z*z);
    }

    void unitize()                            // Normalizes
    {
        float length = this->length();
        if (length == 0) return;

        x /= length;
        y /= length;
        z /= length;
    }

    Vector3D unit()                        // Normalizes return a new Vector3D
    {
        float length = this->length();
        if (length == 0)
            return *this;
        return Vector3D(x / length, y / length, z / length);
    }
};

class Mass {
public:
    float m;                 // The mass value
    Vector3D pos;            // Position
    Vector3D vel;            // Velocity
    Vector3D force;          // Force

    Mass(float m): m(m) {}

    void applyForce(Vector3D force)
    {
        this->force += force;
    }

    void init()
    {
        force.x = 0;
        force.y = 0;
        force.z = 0;
    }

    void simulate(float dt)                 // New velocity and position
    {
        vel += (force / m) * dt;
        pos += vel * dt;
    }
};

class Simulation {
public:
    int    numOfMasses;
    Mass** masses;

    Simulation(int numOfMasses, float m)                 // Constructor
    {
        this->numOfMasses = numOfMasses;
        masses = new Mass*[numOfMasses];
        for (int i = 0; i < numOfMasses; ++i) {
            masses[i] = new Mass(m);
        }
    }

    virtual void release()                      // Delete
    {
        for (int i = 0; i < numOfMasses; ++i) {
            delete(masses[i]);
            masses[i] = NULL;
        }
        delete(masses);
        masses = NULL;
    }

    Mass* getMass(int index)
    {
        if (index < 0 || index >= numOfMasses) {
            return NULL;
        }
        return masses[index];
    }

    virtual void init()
    {
        for (int i = 0; i < numOfMasses; ++i) {
            masses[i]->init();
        }
    }
    // No implementation because no forces are wanted in this basic container
    // in advanced containers, this method will be overrided and some forces will act on masses
    virtual void solve() {}

    virtual void simulate(float dt)
    {
        for (int i = 0; i < numOfMasses; ++i) {
            masses[i]->simulate(dt);
        }
    }

    virtual void operate(float dt)                     // The complete produce of simulation
    {
        init();
        solve();
        simulate(dt);
    }
};

class ConstantVelocity : public Simulation {
public:
    ConstantVelocity() : Simulation(1, 1.0f)
    {
        masses[0]->pos = Vector3D(0.0f, 0.0f, 0.0f);
        masses[0]->vel = Vector3D(1.0f, 0.0f, 0.0f);
    }
};

class MotionUnderGravitation : public Simulation {
public:
    Vector3D gravitation;
    MotionUnderGravitation(Vector3D gravitation) : Simulation(1, 1.0f)
    {
        this->gravitation = gravitation;
        masses[0]->pos = Vector3D(-10.0f, 0.0f, 0.0f);
        masses[0]->vel = Vector3D(10.0f, 15.0f, 0.0f);
    }

    virtual void solve()
    {
        for (int i = 0; i < numOfMasses; ++i) {
            masses[i]->applyForce(gravitation * masses[i]->m);
        }
    }
};

class MassConnectedWithSpring : public Simulation {
public:
    float springConstant;                      // More the springConstant, stiffer the spring force
    Vector3D connectionPos;                    // The arbitrary constant point that the mass is connected

    MassConnectedWithSpring(float springConstant) :Simulation(1, 1.0f)
    {
        this->springConstant = springConstant;
        connectionPos = Vector3D(0.0f, -5.0f, 0.0f);
        masses[0]->pos = connectionPos + Vector3D(10.0f, 0.0f, 0.0f);
        masses[0]->vel = Vector3D(0.0f, 0.0f, 0.0f);
    }

    virtual void solve()
    {
        for (int i = 0; i < numOfMasses; ++i) {
            Vector3D springVector = masses[i]->pos - connectionPos;
            masses[i]->applyForce(-springVector * springConstant);
        }
    }
};

#include <Windows.h>
#include <GL/glew.h>
#include <GL/glut.h>
#include <GL/GLUAX.H>
#include <math.h>
#include <stdio.h>
#include "Previous.h"
#include "Physics.h"

// Introduction to Physical Simulations
#pragma comment(lib, "legacy_stdio_definitions.lib")

#ifndef CDS_FULLSCREEN
#define CDS_FULLSCREEN 4
#endif

GL_Window* g_window;
Keys* g_keys;

ConstantVelocity* constantVelocity = new ConstantVelocity();

MotionUnderGravitation* motionUnderGravitation = new MotionUnderGravitation(Vector3D(0.0f, -9.81f, 0.0f));

MassConnectedWithSpring* massConnectedWithSpring = new MassConnectedWithSpring(2.0f);

float slowMotionRatio = 10.0f;               // Slow down the simulation
float timeElapsed = 0;                       // Not equal to real world's time unless slowMotionRatio Is 1
GLuint base;                 // Display

GLYPHMETRICSFLOAT gmf[256];         // Storage font characters

GLvoid BuildFont(GL_Window* window)           // Build bitmap font
{
    HFONT font;
    base = glGenLists(256);
    font = CreateFont(-12, 0, 0, 0, FW_BOLD, FALSE, FALSE, FALSE, ANSI_CHARSET, OUT_TT_PRECIS,
        CLIP_DEFAULT_PRECIS, ANTIALIASED_QUALITY, FF_DONTCARE | DEFAULT_PITCH, NULL);
    
    HDC hDC = window->hDC;
    SelectObject(hDC, font);

    wglUseFontOutlines(hDC,                    // Select the current DC
        0,                                       // Starting character
        255,                                   // Number of display lists to build
        base,                                  // Starting display lists
        0.0f,                                  // Deviation from the true outlines
        0.0f,                                  // Font thickness in the Z direction
        WGL_FONT_POLYGONS,                     // Use polygons, not lines
        gmf);                                  // Address of buffer to recieve data
}

GLvoid KillFont(GLvoid)
{
    glDeleteLists(base, 256);
}

GLvoid glPrint(float x, float y, float z, const char* fmt, ...)
{
    float length = 0;                         // The length of text
    char text[256];                           // String
    va_list ap;                               // Pointer to list of arguments

    if (fmt == NULL) {
        return;
    }

    va_start(ap, fmt);
        vsprintf(text, fmt, ap);
    va_end(ap);

    for (unsigned int loop = 0; loop < (strlen(text)); ++loop) {
        length += gmf[text[loop]].gmfCellIncX;             // Increase length by each characters width
    }
    glTranslatef(x - length, y, z);
    glPushAttrib(GL_LIST_BIT);
    glListBase(base);
    glCallLists(strlen(text), GL_UNSIGNED_BYTE, text);
    glPopAttrib();

    glTranslatef(-x, -y, -z);
}

BOOL Initialize(GL_Window* window, Keys* keys)
{
    g_window = window;
    g_keys = keys;

    glClearColor(0.0f, 0.0f, 0.0f, 0.5f);
    glShadeModel(GL_SMOOTH);
    glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);

    BuildFont(window);
    return TRUE;
}

void Deinitialize(void)
{
    KillFont();

    constantVelocity->release();
    delete(constantVelocity);
    constantVelocity = NULL;

    motionUnderGravitation->release();
    delete(motionUnderGravitation);
    motionUnderGravitation = NULL;

    massConnectedWithSpring->release();
    delete(massConnectedWithSpring);
    massConnectedWithSpring = NULL;
}

void Update(DWORD milliseconds)
{
    if (g_keys->keyDown[VK_ESCAPE] == TRUE) {
        TerminateApplication(g_window);
    }

    if (g_keys->keyDown[VK_F1] == TRUE) {
        ToggleFullscreen(g_window);
    }
    if (g_keys->keyDown[VK_F2] == TRUE) {
        slowMotionRatio = 1.0f;
    }
    if (g_keys->keyDown[VK_F3] == TRUE) {
        slowMotionRatio = 10.0f;
    }

    float dt = milliseconds / 1000.0f;
    dt /= slowMotionRatio;
    timeElapsed += dt;

    float maxPossible_dt = 0.1f;               //The maximum possible dt is 0.1 seconds
    int numOfIterations = (int)(dt / maxPossible_dt) + 1;
    if (numOfIterations != 0) {
        dt = dt / numOfIterations;
    }
    for (int i = 0; i < numOfIterations; ++i) {
        constantVelocity->operate(dt);
        motionUnderGravitation->operate(dt);
        massConnectedWithSpring->operate(dt);
    }
}

void Draw(void)
{
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();

    gluLookAt(0, 0, 40, 0, 0, 0, 0, 1, 0);

    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
    glColor3ub(0, 0, 255);               // Blue
    
    glBegin(GL_LINES);
    for (float x = -20; x <= 20; x += 1.0f) {
        glVertex3f(x, 20, 0);
        glVertex3f(x, -20, 0);
    }
    for (float y = -20; y <= 20; y += 1.0f)
    {
        glVertex3f(20, y, 0);
        glVertex3f(-20, y, 0);
    }
    glEnd();

    glColor3ub(255, 0, 0);
    for (int i = 0; i < constantVelocity->numOfMasses; ++i) {
        Mass* mass = constantVelocity->getMass(i);
        Vector3D* pos = &mass->pos;

        glPrint(pos->x, pos->y + 1, pos->z, "Mass with constant vel");
        glPointSize(4);
        glBegin(GL_POINTS);
            glVertex3f(pos->x, pos->y, pos->z);
        glEnd();
    }

    glColor3ub(255, 255, 0);
    for (int i = 0; i < motionUnderGravitation->numOfMasses; ++i) {
        Mass* mass = motionUnderGravitation->getMass(i);
        Vector3D* pos = &mass->pos;

        glPrint(pos->x, pos->y + 1, pos->z, "Motion under gravitation");
        glPointSize(4);
        glBegin(GL_POINTS);
            glVertex3f(pos->x, pos->y, pos->z);
        glEnd();
    }

    glColor3ub(0, 255, 0);
    for (int i = 0; i < massConnectedWithSpring->numOfMasses; ++i) {
        Mass* mass = massConnectedWithSpring->getMass(i);
        Vector3D* pos = &mass->pos;

        glPrint(pos->x, pos->y + 1, pos->z, "Mass connected with spring");
        glPointSize(8);
        glBegin(GL_POINTS);
            glVertex3f(pos->x, pos->y, pos->z);
        glEnd();

        glBegin(GL_LINES);
            glVertex3f(pos->x, pos->y, pos->z);
            pos = &massConnectedWithSpring->connectionPos;
            glVertex3f(pos->x, pos->y, pos->z);
        glEnd();
    }

    glColor3ub(255, 255, 255);
    glPrint(-5.0f, 14, 0, "Time elapsed (seconds): %.2f", timeElapsed);
    glPrint(-5.0f, 13, 0, "Slow motion ratio: %.2f", slowMotionRatio);
    glPrint(-5.0f, 12, 0, "Press F2 for normal motion");
    glPrint(-5.0f, 11, 0, "Press F3 for slow motion");

    glFlush();
}

Thanks for Nehe's tutorials, this is his home.