This project simulates the motion of electrons and protons using Coulomb's Law. The simulation is visually represented on-screen using OpenGL.

This project requires OpenGL, freeglut and stb_image.h After installing all of these onto your system, the code will run without any issues.

const float width = 10.0f; 
const float halfWidth = width / 2.0f;

// Scale factor for positions (1 piksel = 1 pikometer)
const float SCALE = std::pow(10.0f, -12.0f);

// Charges are given in nano-Coulombs
float q1 = 1.0f;  // nano-Coulombs
float q2 = 1.0f; // nano-Coulombs

...

In this section of the code, various variables that will be used to simulate the electric forces between two particles are declared and initialized.

void updateForces() {
    float r = std::abs(pos2 - pos1) / SCALE   2 * halfWidth ;
    float forceMagnitude = k * std::abs(q1 * q2) / (r * r);
    float direction = (q1 * q2) > 0 ? -1.0f : 1.0f;

    // Convert force to pikometer by multiplying by SCALE
    force1 = direction * forceMagnitude * SCALE / mass1;
    force2 = -direction * forceMagnitude * SCALE / mass2;
}

In this function, r represents the distance, which is |position of q2 - position of q1| / picometer (2 * half width of the electron/proton images). The reason for doing 2 * half width of the electron is to prevent using the center of the image as x=0.

forceMagnitude represents Coulomb's Law which is k * |Q1 * Q2| / |r * r|

direction variable is -1.0f if (q1 * q2) > 0 otherwise direction variable is set to 1.0f. positive value indicates move to right, on the other hand negative value indicates move to left.

force1 = direction * forceMagnitude * SCALE / mass1;
force2 = -direction * forceMagnitude * SCALE / mass2;

This calculations provides us with the particles electrostatic force-induced acceleration, and it is scaled appropriately for the graphical display which is picometer.

void updateVelocities() {
    // Friction force is proportional to the velocity and in the opposite direction
    float frictionForce1 = friction * std::abs(speed1) * -std::copysign(1.0f, speed1);
    float frictionForce2 = friction * std::abs(speed2) * -std::copysign(1.0f, speed2);
    speed1  = (force1   frictionForce1) * dt;
    speed2  = (force2   frictionForce2) * dt;
    pos1  = speed1 * dt;
    pos2  = speed2 * dt;

}

float frictionForce1 = friction * std::abs(speed1) * -std::copysign(1.0f, speed1);
float frictionForce2 = friction * std::abs(speed2) * -std::copysign(1.0f, speed2);

These are the variables i use to take friction into account. In essence, friction is multiplied by the absolute value of the spped, then the signs of the speed variables are obtained and assigned to 1.0f. This is then multiplied by negative sign and the remaining part.

speed1  = (force1   frictionForce1) * dt;
speed2  = (force2   frictionForce2) * dt;
pos1  = speed1 * dt;
pos2  = speed2 * dt;

These lines update the two particles' velocities (speed1 and speed2). The updated velocity is the current velocity multiplied by the time step plus the total force (the sum of the electrostatic and friction forces). We can think of Time Step as slow motion. In other words, our code actually works at 1/1000 of a second. We do this because electrons and protons move very fast. This is an application of Newton's second law of motion (F=ma), which takes the form a = F/m, with the velocity change (delta v) equal to a*dt.

GLuint texture[2]; This line creates an array of two GLuints. This array will hold the references for two textures that will be loaded later.

GLuint LoadTexture(const char* filename, int wrap)
{
    int width, height, comp;
    unsigned char* image = stbi_load(filename, &width, &height, &comp, STBI_rgb_alpha);

    if (image == nullptr)
    {
        return 0;
    }

    GLuint texture;
    glGenTextures(1, &texture);

    glBindTexture(GL_TEXTURE_2D, texture);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, wrap ? GL_REPEAT : GL_CLAMP);
    glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, wrap ? GL_REPEAT : GL_CLAMP);
    glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_UNSIGNED_BYTE, image);

    stbi_image_free(image);
    return texture;
}

The LoadTexture function in this code is used to load an image from a file and create a 2D OpenGL texture from the image data. unsigned char* image = stbi_load(filename, &width, &height, &comp, STBI_rgb_alpha); In this code the function loads an image using stb_image library's stbi_load function, which returns a pointer to the pixel data.

GLuint texture; glGenTextures(1, &texture); This code generates a new OpenGL texture identifier using the glGenTextures function. The first argument 1 is the number of texture names to be generated. Remember, because the indexing begins from 1 it generates 2 pictures.

glBindTexture(GL_TEXTURE_2D, texture); This code is for binding the texture object that's referenced by the texture variable to the current active 2D texture unit in OpenGL. GL_TEXTURE_2D specifies that the texture is a 2D texture, texture is the identifier of the texture we want to bind.

glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); This code set the minification and magnification filters for the texture, respectively.

glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, wrap ? GL_REPEAT : GL_CLAMP);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, wrap ? GL_REPEAT : GL_CLAMP);

These codes are setting the wrapping mode for the S and T texture coordinates. S corresponds to the X-axis, and T corresponds to the Y-axis

glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_UNSIGNED_BYTE, image); uploads the texture data to the GPU

GL_TEXTURE_2D This is the target texture type, GL_RGBA This is the internal format of the texture. Which means each pixel has Red, Green, Blue, and Alpha components. width and height are the dimensions of the texture. The next GL_RGBA is the format of the pixel data that we're providing. GL_UNSIGNED_BYTE This is the data type of the pixel data. Each component is an unsigned byte, i.e., a value from 0 to 255. image This is the actual pixel data, which we loaded earlier with stbi_load

stbi_image_free(image); This code frees the image data that we loaded into memory with stbi_load It is for free memory that the software do not need anymore.

return texture; the LoadTexture function returns the texture ID that was generated with glGenTexture.

void DrawImage(GLuint texture, float x, float y, float width, float height)
{
    glBindTexture(GL_TEXTURE_2D, texture);
    glEnable(GL_TEXTURE_2D);
    glBegin(GL_QUADS);
    glTexCoord2f(0, 0);
    glVertex2f(x - width / 2, y - height / 2);
    glTexCoord2f(1, 0);
    glVertex2f(x   width / 2, y - height / 2);
    glTexCoord2f(1, 1);
    glVertex2f(x   width / 2, y   height / 2);
    glTexCoord2f(0, 1);
    glVertex2f(x - width / 2, y   height / 2);
    glEnd();
    glDisable(GL_TEXTURE_2D);
}

This is a function used in OpenGL to draw a textured 2D quad (rectangle) at a certain position with certain dimensions.

glBindTexture(GL_TEXTURE_2D, texture); OpenGL uses this function to render a textured 2D quad. glEnable(GL_TEXTURE_2D); This enables 2D Texturing glBegin(GL_QUADS); With this, a new quad is defined. This quad will be regarded as including all the vertices specified after this call but before the corresponding glEnd()

glTexCoord2f(0, 0);
glVertex2f(x - width / 2, y - height / 2);

The bottom-left quadrant's first vertex's texture coordinate is set using this codes. The bottom-left corner of the texture is indicated by the texture coordinate (0, 0) glVertex2f(x - width / 2, y - height / 2) specifies the position of this vertex. glEnd(); This ends the definition of the quad. glDisable(GL_TEXTURE_2D); This disables 2D texturing.

void drawText(const char* text, float x, float y) {
    float currentColor[4];
    glGetFloatv(GL_CURRENT_COLOR, currentColor);

    glColor3f(0.0f, 1.0f, 0.0f); // Set text color green
    glRasterPos2f(x, y);
    int len = strlen(text);
    for (int i = 0; i < len; i  ) {
        glutBitmapCharacter(GLUT_BITMAP_HELVETICA_18, text[i]);
    }
    glColor4fv(currentColor);
}

This is a function used in OpenGL to draw text at a certain position on the screen.

float currentColor[4];
glGetFloatv(GL_CURRENT_COLOR, currentColor);

The current drawing color is saved in float currentColor[4] array. The current color being used for drawing is obtained and stored in currentColor by glGetFloatv(GL_CURRENT_COLOR, currentColor) In short, it prevents the colors of the protons and electrons from being the same as the texts we draw on the screen.

glColor3f(0.0f, 1.0f, 0.0f); This code sets the drawing color to green. Three parameters represents RGB (Red, Green, Blue)

glRasterPos2f(x, y); This code sets the position where the text should be drawn.

int len = strlen(text);
    for (int i = 0; i < len; i  ) {
        glutBitmapCharacter(GLUT_BITMAP_HELVETICA_18, text[i]);
    }

These codes draw the text character by character. strlen(text) This stores lenght of the text and glutBitmapCharacter(GLUT_BITMAP_HELVETICA_18, text[i]); draws the text character by character. Because the glutBitmapCharacter() function in GLUT only manages one character at a time, this is necessary. Furthermore, GLUT_BITMAP_HELVETICA_18 This represents a particular bitmap font Helvetica at a size of 18. text[i] This is the i-th character of the string text

glColor4fv(currentColor); This code restores the drawing color to what it was before the function was called.

LRESULT CALLBACK WindowProcedure(HWND hwnd, UINT uMsg, WPARAM wParam, LPARAM lParam) {
    switch (uMsg) {
    case WM_CLOSE:
        PostQuitMessage(0);
        break;
    default:
        return DefWindowProc(hwnd, uMsg, wParam, lParam);
    }
    return 0;
}

This is a basic Windows Procedure function which is a component of the Windows API. It handles messages delivered to windows.

int WINAPI WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nShowCmd) {
    const wchar_t CLASS_NAME[] = L"Sample Window Class";

    WNDCLASS wc = { };
    wc.lpfnWndProc = WindowProcedure;
    wc.hInstance = hInstance;
    wc.lpszClassName = CLASS_NAME;

    if (!RegisterClass(&wc)) {
        MessageBox(NULL, L"Window Registration Failed!", L"Error!", MB_ICONEXCLAMATION | MB_OK);
        return 0;
    }

    HWND hwnd = CreateWindow(CLASS_NAME, L"Sample Window", WS_MINIMIZEBOX | WS_SYSMENU, CW_USEDEFAULT, CW_USEDEFAULT, 800, 600, NULL, NULL, hInstance, NULL);

    if (hwnd == NULL) {
        MessageBox(NULL, L"Window Creation Failed!", L"Error!", MB_ICONEXCLAMATION | MB_OK);
        return 0;
    }

    ShowWindow(hwnd, nShowCmd);

    HDC hdc = GetDC(hwnd);
    PIXELFORMATDESCRIPTOR pfd;
    ZeroMemory(&pfd, sizeof(pfd));
    pfd.nSize = sizeof(pfd);
    pfd.nVersion = 1;
    pfd.dwFlags = PFD_DRAW_TO_WINDOW | PFD_SUPPORT_OPENGL | PFD_DOUBLEBUFFER;
    pfd.iPixelType = PFD_TYPE_RGBA;
    pfd.cColorBits = 24;

    int iFormat = ChoosePixelFormat(hdc, &pfd);
    SetPixelFormat(hdc, iFormat, &pfd);

    HGLRC hglrc = wglCreateContext(hdc);
    wglMakeCurrent(hdc, hglrc);
    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

    int argc = 0; 
    char* argv[] = { NULL };
    glutInit(&argc, argv);

    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    glOrtho(-100.0f, 100.0f, -100.0f, 100.0f, -1.0f, 1.0f);
    glMatrixMode(GL_MODELVIEW);

    MSG msg = { 0 };
    bool running = true;

    LARGE_INTEGER frequency;
    QueryPerformanceFrequency(&frequency);
    double freq = static_cast<double>(frequency.QuadPart);
    LARGE_INTEGER startCounter, endCounter;
    QueryPerformanceCounter(&startCounter);

    if (q1 >= 0) {
        texture[0] = LoadTexture("images\\electron.png", 1);
    }
    else {
        texture[0] = LoadTexture("images\\proton.png", 1);
    }

    if (q2 >= 0) {
        texture[1] = LoadTexture("images\\electron.png", 1);
    }
    else {
        texture[1] = LoadTexture("images\\proton.png", 1);
    }
    GLuint background = LoadTexture("images\\space.png", 1);
    while (running) {
        while (PeekMessage(&msg, NULL, 0, 0, PM_REMOVE)) {
            if (msg.message == WM_QUIT) {
                running = false;
            }
            TranslateMessage(&msg);
            DispatchMessage(&msg);
        }

        QueryPerformanceCounter(&endCounter);
        double frameTime = (endCounter.QuadPart - startCounter.QuadPart) / freq;

        if (frameTime > 1.0 / 120.0) {
		
            updateForces();
            updateVelocities();

            glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
            glClear(GL_COLOR_BUFFER_BIT);

            DrawImage(background, 0.0f, 0.0f, 800, 600); // assuming 800x600 window size
            DrawImage(texture[0], pos1   ((q1 > 0) ? halfWidth : -halfWidth), 0.0f, width, width);
            DrawImage(texture[1], pos2   ((q2 > 0) ? halfWidth : -halfWidth), 0.0f, width, width);

            char text[1024];
            const char* formats[] = {
                "Charge Q1: %.2f nC",
                "Charge Q2: %.2f nC",
                "Speed Q1: %.2e pm/s",
                "Speed Q2: %.2e pm/s",
                "Position Q1: %.2e pm",
                "Position Q2: %.2e pm",
                "Friction: %.2f N * dt / m",
                "Distance between Q1 and Q2: %.4e pm",
                "Force Applied to Q1: %.2e N/m",
                "Force Applied to Q2: %.2e N/m"
            };

            float values[] = {
                q1, q2,  std::abs(speed1 / SCALE * dt),  std::abs(speed2 / SCALE * dt), pos1 / SCALE, pos2 / SCALE, friction, abs(pos1 - pos2) / SCALE, force1 * SCALE, force1 * SCALE, force2 * SCALE
            };

            for (int lineNumber = 0; lineNumber < 10; lineNumber  ) {
                char text[1024];
                sprintf_s(text, sizeof(text), formats[lineNumber], values[lineNumber]);

                drawText(text, -100.0f, 95.0f - 8.0f * lineNumber);
            }
			
            SwapBuffers(hdc);
            startCounter = endCounter;
        }
    }

    wglMakeCurrent(NULL, NULL);
    wglDeleteContext(hglrc);
    ReleaseDC(hwnd, hdc);
    return msg.wParam;
}

This is a Windows Application that utilizes the Win32 API and OpenGL for rendering.

int WINAPI WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nShowCmd) { is the entry point for a Windows application. HINSTANCE hInstance This is a handle to the application instance. HINSTANCE hPrevInstance This is a handle to the previous instance of the application, if there is one. If this is the first instance of the application, then hPrevInstance is NULL. LPSTR lpCmdLine This is a pointer to a string that contains the command line arguments passed to the application. If there are no command line arguments, then lpCmdLine is NULL. int nShowCmd This is an integer value that specifies how the application should be shown. i.e. SW_SHOW, SW_HIDE, SW_MINIMIZE, or SW_MAXIMIZE.

const wchar_t CLASS_NAME[] = L"Sample Window Class"; This line of code defines a constant string that contains the name of a window class. The value "Sample Window Class" is assigned to the CLASS_NAME constant, which is defined as an array of wide characters wchar_t. This indicates that the window class name is a string made up of 15 characters: "S," "a," "m," "p," "l," "e," "", "," "W," "i," "n," "d," "o," "w," "C," "l," "a," "s," "s."

WNDCLASS wc = { };
wc.lpfnWndProc = WindowProcedure;
wc.hInstance = hInstance;
wc.lpszClassName = CLASS_NAME;

The window class attributes are contained in a structure called WNDCLASS in the Windows API. Here, a WNDCLASS structure is being set up. hInstance is a handle to an instance, lpfnWndProc is a pointer to the window procedure, and lpszClassName is the name of the class.

if (!RegisterClass(&wc)) {
	MessageBox(NULL, L"Window Registration Failed!", L"Error!", MB_ICONEXCLAMATION | MB_OK);
        return 0;
    }

HWND hwnd = CreateWindow(CLASS_NAME, L"Sample Window", WS_MINIMIZEBOX | WS_SYSMENU, CW_USEDEFAULT, CW_USEDEFAULT, 800, 600, NULL, NULL, hInstance, NULL);

if (hwnd == NULL) {
        MessageBox(NULL, L"Window Creation Failed!", L"Error!", MB_ICONEXCLAMATION | MB_OK);
        return 0;
    }

if (!RegisterClass(&wc)) { This line checks if the RegisterClass function call was successful. If the RegisterClass function call fails, the code displays an error message using MessageBox and returns 0, indicating failure.

HWND hwnd = CreateWindow(CLASS_NAME, L"Sample Window", WS_MINIMIZEBOX | WS_SYSMENU, CW_USEDEFAULT, CW_USEDEFAULT, 800, 600, NULL, NULL, hInstance, NULL); This line creates a new window using the CreateWindow function. CLASS_NAME is the name of the window class that was registered earlier. L"Sample Window" is the title of the window. WS_MINIMIZEBOX | WS_SYSMENU are window styles that specify the appearance and behavior of the window. WS_MINIMIZEBOX adds a minimize button to the window, and WS_SYSMENU adds a system menu (minimize, maximize, and close). CW_USEDEFAULT and CW_USEDEFAULT are used to specify the default settings for the window's width and height. 800 and 600 are the width and height of the window, respectively. NULL and NULL indicate that the window does not have a parent window or a menu. hInstance is a handle to the instance of the application. NULL indicates that the window does not have a creation data (i.e., user data that is passed to the window's creation function). The CreateWindow function returns a handle to the newly created window (HWND) if successful, or NULL if it fails.

if (hwnd == NULL) {
        MessageBox(NULL, L"Window Creation Failed!", L"Error!", MB_ICONEXCLAMATION | MB_OK);
        return 0;
    }

This if statement checks if the CreateWindow function call was successful by checking if the hwnd variable is non-NULL. If hwnd is NULL, it means that the CreateWindow function failed, and the code displays an error message using MessageBox and returns 0.

ShowWindow(hwnd, nShowCmd); This code shows the window using the ShowWindow function. The function takes two parameters. The first is the handle to the window (HWND), and the second is a value that specifies how the window should be shown (SW_SHOW, SW_HIDE, SW_MINIMIZE, and SW_MAXIMIZE)

HDC hdc = GetDC(hwnd); This line retrieves a handle to a device context (DC) for the client area of a specified window (hwnd). A device context is a Windows data structure containing information about the drawing attributes of a device like a display or a printer.

PIXELFORMATDESCRIPTOR pfd; 
ZeroMemory(&pfd, sizeof(pfd));

A PIXELFORMATDESCRIPTOR is a structure that describes the pixel format of a drawing surface. All of its members are initialized to zero using ZeroMemory.

pfd.nSize = sizeof(pfd);
pfd.nVersion = 1;
pfd.dwFlags = PFD_DRAW_TO_WINDOW | PFD_SUPPORT_OPENGL | PFD_DOUBLEBUFFER;
pfd.iPixelType = PFD_TYPE_RGBA;
pfd.cColorBits = 24;

These lines define the values for the PIXELFORMATDESCRIPTOR structure's members. They define details about the pixel format, including the number of color bits and the type of buffer to use.

int iFormat = ChoosePixelFormat(hdc, &pfd);
SetPixelFormat(hdc, iFormat, &pfd);

These lines let Windows to select the most suitable pixel format for the HDC device context. Then, after calling SetPixelFormat, the device context's pixel format is changed to match the format specified by iFormat.

HGLRC hglrc = wglCreateContext(hdc); 
wglMakeCurrent(hdc, hglrc);

These lines establish a new OpenGL rendering context, a state machine that holds all of the information necessary for rendering graphics. The OpenGL rendering context hglrc is made the calling thread's current rendering context by wglMakeCurrent.

HGLRC is for encapsulate and store variables, buffers, shaders, and so on. HDC is bridge between the low-level drawing capabilities of the operating system and the high-level, abstracted drawing capabilities of OpenGL. HGLRC hglrc = wglCreateContext(hdc); in this code, wglCreateContext is a function that creates a new OpenGL rendering context for drawing on a device in the Windows operating system. wglMakeCurrent(hdc, hglrc); The OpenGL context must be made the current context once it has been created. The wglMakeCurrent function changes the calling thread's current rendering context to the specified OpenGL context.

glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

These lines enable blending (the process of combining color data) and specify pixel arithmetic, respectively. ALPHA in an RGBA color model stands for transparency. GL_SRC_ALPHA refers to the alpha value of the source blending factor, and GL_ONE_MINUS_SRC_ALPHA refers to 1 minus the alpha value of the source blending factor.

int argc = 0; char* argv[] = { NULL };
glutInit(&argc, argv);

These lines initialize the GLUT library.

glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(-100.0f, 100.0f, -100.0f, 100.0f, -1.0f, 1.0f);
glMatrixMode(GL_MODELVIEW);

These lines is to set up how 2D scene is projected onto the 2D surface of the screen. This involves the use of transformation matrices.

glMatrixMode(GL_PROJECTION); This function establishes the current matrix mode, meaning that the matrix specified will be used for all ensuing matrix operations (such as glLoadIdentity, glOrtho, etc.) GL_PROJECTION sets the current matrix to the projection matrix in this situation. glLoadIdentity(); This function replaces the current matrix with the identity matrix. In other words, it clears out any previous projection matrix. glOrtho(-100.0f, 100.0f, -100.0f, 100.0f, -1.0f, 1.0f); This function multiplies the current matrix by an orthographic matrix, defined by the parameters. The box's left and right edges are at x=-100 and x=100, the bottom and top edges are at y=-100 and y=100, and the near and far clipping planes are at z=-1 and z=1. glMatrixMode(GL_MODELVIEW); This line switches the current matrix mode back to the ModelView matrix. This means subsequent transformations will apply to the ModelView matrix, not the Projection matrix.

MSG msg = { 0 };
bool running = true;

This creates a MSG structure that will receive information about a message from the Windows procedure function, and a boolean variable to control the main program loop.

LARGE_INTEGER frequency;
QueryPerformanceFrequency(&frequency);
double freq = static_cast<double>(frequency.QuadPart);
LARGE_INTEGER startCounter, endCounter;
QueryPerformanceCounter(&startCounter);

This code is using the high-resolution Windows Performance Counter to measure time. LARGE_INTEGER frequency; This line declares a variable frequency of type LARGE_INTEGER. LARGE_INTEGER is a union that represents a 64-bit signed integer. QueryPerformanceFrequency(&frequency); This line is a way of asking the computer "how fast does the computer's high-resolution performance counter tick?" and stores the returning value as frequency. double freq = static_cast<double>(frequency.QuadPart); This line is converting the frequency value to a double. LARGE_INTEGER is a union that can be accessed as an __int64 and QuadPart is the __int64 representation. This gives the number of counts per second as a double. LARGE_INTEGER startCounter, endCounter; These lines declare two more LARGE_INTEGER variables, startCounter and endCounter. QueryPerformanceCounter(&startCounter); This line is a way of asking the computer "What is the current tick (or count) of your precision clock right now?" and stores the returning value as startCounter.

if (q1 >= 0) {
	texture[0] = LoadTexture("images\\electron.png", 1);
    }
else {
        texture[0] = LoadTexture("images\\proton.png", 1);
    }

if (q2 >= 0) {
        texture[1] = LoadTexture("images\\electron.png", 1);
    }
else {
        texture[1] = LoadTexture("images\\proton.png", 1);
    }
GLuint background = LoadTexture("images\\space.png", 1);

The if statements are checking the values of q1 and q2 to determine if the charge is proton or electron. The loaded textures are stored in the texture array at indices 0 and 1 respectively. GLuint LoadTexture(const char* filename, int wrap) If wrap is 1, then the texture repeats; if wrap is 0, the texture is clamped to its edge. texture[..] = LoadTexture("images\\...png", 1); if the texture is sampled outside of its usual range, it will repeat.

while (running) {
	while (PeekMessage(&msg, NULL, 0, 0, PM_REMOVE)) {
            if (msg.message == WM_QUIT) {
                running = false;
            }
            TranslateMessage(&msg);
            DispatchMessage(&msg);
        }

while (running) { loop is the main loop of the application. PeekMessage(&msg, NULL, 0, 0, PM_REMOVE) This function is part of the Windows API and is used to handle window messages. These messages could be user input or system commands. &msg This is a pointer to a MSG structure msg where PeekMessage will store the details of the next message in the queue. NULL This parameter is used to filter the messages for a specific window. Any window that is a part of the current thread will have its messages retrieved by the function if it returns NULL. (0, 0) Messages are filtered using these parameters based on their message-value. When they are set to 0, no message-value-based filtering is carried out. PM_REMOVE This flag means that PeekMessage should remove the message from the queue after it has been retrieved. while (PeekMessage(&msg, NULL, 0, 0, PM_REMOVE)) This loop continues as long as there are messages in the queue. if (msg.message == WM_QUIT) If the message is WM_QUIT, an application termination request has been made. In this case, it changes running to false, causing the main loop to end. TranslateMessage(&msg) This function is used to generate additional messages, like WM_CHAR messages that are produced when a key is pressed. DispatchMessage(&msg) This function sends the message to the window's associated Window Procedure (WndProc) function. After all available messages have been processed, the application proceeds with the rest of the code in the main loop.

QueryPerformanceCounter(&endCounter);
double frameTime = (endCounter.QuadPart - startCounter.QuadPart) / freq;

QueryPerformanceCounter(&endCounter) The function retrieves the current value of the high-resolution performance counter. The value is stored in endCounter. double frameTime = (endCounter.QuadPart - startCounter.QuadPart) / freq This line calculates the time taken for the current frame in seconds. endCounter.QuadPart - startCounter.QuadPart gives the number of ticks between the start of the frame and the end. Dividing by freq gives the frame time in seconds. if (frameTime > 1.0 / 120.0) { This code is limiting the frame rate to 120 frames per second.

From the beginning of the code

const float width = 10.0f;  // The width of the image
const float halfWidth = width / 2.0f;  // Half the width

glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
and glClear(GL_COLOR_BUFFER_BIT);

These two lines clear the screen before the new frame is drawn. glClearColor(0.0f, 0.0f, 0.0f, 1.0f); This line is setting the color that OpenGL uses when it clears the color buffer. The four values represent the red, green, blue, and alpha components of the color, respectively. glClear(GL_COLOR_BUFFER_BIT); This line tells OpenGL to clear the color buffer, which is essentially the same as erasing the screen before drawing the new frame. DrawImage(background, 0.0f, 0.0f, 800, 600); This line draws an image on the screen. The background parameter is the image that will be drawn. The next two parameters (0.0f, 0.0f) are the coordinates where the image will be drawn. The last two parameters (800, 600) specify the width and height of the image in pixels. DrawImage(texture[0], pos1 ((q1 > 0) ? halfWidth : -halfWidth), 0.0f, width, width); This line is similar to the previous DrawImage call but it draws the first particle's image. texture[0] is the image to be drawn. The next value pos1 ((q1 > 0) ? halfWidth : -halfWidth) is the x-coordinate where the image will be drawn. The y-coordinate is 0.0f. The width and height of the image are both set to width variable.

char text[1024];
const char* formats[] = {
	"Charge Q1: %.2f nC",
	"Charge Q2: %.2f nC",
	"Speed Q1: %.2e pm/s",
	"Speed Q2: %.2e pm/s",
	"Position Q1: %.2e pm",
	"Position Q2: %.2e pm",
	"Friction: %.2f N * dt / m",
	"Distance between Q1 and Q2: %.4e pm",
	"Force Applied to Q1: %.2e N/m",
	"Force Applied to Q2: %.2e N/m"
            };

float values[] = {
	q1,
 	q2,
	std::abs(speed1 / SCALE * dt),
	std::abs(speed2 / SCALE * dt),
	pos1 / SCALE,
	pos2 / SCALE,
	friction,
	abs(pos1 - pos2) / SCALE,
	force1 * SCALE,
	force1 * SCALE,
	force2 * SCALE
            };

char text[1024]; This array is used to store formatted strings hat will be displayed in the simulation. const char* formats[] is an array of constant character pointers, where each pointer is pointing to a string. float values[] is an array of floating-point numbers. std::abs() function takes absolute value of variables. In the code, operations such as dividing by SCALE, multiplying by dt, multiplying by SCALE are used only for unit conversation. Therefore, it is possible to draw the coordinates on our computer screen. Here, the values are getting converted into reasonable structures before drawing to the screen.

for (int lineNumber = 0; lineNumber < 10; lineNumber  ) {
	char text[1024];
	sprintf_s(text, sizeof(text), formats[lineNumber], values[lineNumber]);
	drawText(text, -100.0f, 95.0f - 8.0f * lineNumber);
            }

The loop for (int lineNumber = 0; lineNumber < 10; lineNumber ) runs ten times, which corresponds to the number of format strings in in the formats array. Array char text[1024] will be used to hold the resulting string after formatting. sprintf_s(text, sizeof(text), formats[lineNumber], values[lineNumber]); This function writes the formatted data from the values array into the text array. drawText(text, -100.0f, 95.0f - 8.0f * lineNumber); function is called to render the resulting text string onto the screen. After the text is drawn, SwapBuffers(hdc) is called. This is a function that swaps the front and back buffers. The back buffer is where all the rendering commands have been executed, and by swapping it to the front, all the rendered content becomes visible on the screen. startCounter = endCounter; is used to reset the start time. The wglMakeCurrent(NULL, NULL) function call makes the current rendering context no longer current. The wglDeleteContext(hglrc) function call deletes the OpenGL rendering context that was created earlier in the program. ReleaseDC(hwnd, hdc) function call releases the device context (hdc) that was used for the window (hwnd). Finally, the program returns msg.wParam. When the WM_QUIT message is received, it sets running to false, which causes the program to exit the loop and start cleaning up.

case WM_CLOSE:
	PostQuitMessage(0);
	break;