How to apply Rotating, translating, and scaling in cpp programming using xCode.mp4

 
Download How to apply Rotating, translating, and scaling in cpp programming using xCode.mp4

Great question 👍 — let’s go step-by-step on how to perform rotation, translation, and scaling in C++, especially if you’re doing graphics programming in Xcode (which usually means using either OpenGL or a graphics framework).

I’ll cover two approaches:

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🧩 1. Using Plain C++ (Matrix Transformations)

If you’re learning the math behind 2D/3D transformations, you can do this with just matrices and no external libraries.

Here’s a simple 2D transformation example:

✅ Code Example (2D)

#include <iostream>
#include <cmath>
using namespace std;

struct Point {
    float x, y;
};

// Translate point by tx, ty
Point translate(Point p, float tx, float ty) {
    p.x += tx;
    p.y += ty;
    return p;
}

// Scale point by sx, sy
Point scale(Point p, float sx, float sy) {
    p.x *= sx;
    p.y *= sy;
    return p;
}

// Rotate point by angle (in degrees)
Point rotate(Point p, float angle) {
    float rad = angle * M_PI / 180.0;
    float x_new = p.x * cos(rad) - p.y * sin(rad);
    float y_new = p.x * sin(rad) + p.y * cos(rad);
    return {x_new, y_new};
}

int main() {
    Point p = {1, 1};

    cout << "Original: (" << p.x << ", " << p.y << ")\n";

    p = translate(p, 2, 3);
    cout << "Translated: (" << p.x << ", " << p.y << ")\n";

    p = scale(p, 2, 2);
    cout << "Scaled: (" << p.x << ", " << p.y << ")\n";

    p = rotate(p, 45);
    cout << "Rotated (45°): (" << p.x << ", " << p.y << ")\n";

    return 0;
}

🧮 This uses basic math for rotation, translation, and scaling.
You can run this directly in Xcode → New Command Line Tool → Language: C++.

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🎨 2. Using OpenGL (in Xcode)

If you’re actually rendering graphics (2D or 3D), then transformations are done using OpenGL matrices.

✅ Setting up

In Xcode:

1. Create a new macOS → Command Line Tool.

2. Add OpenGL headers:

   #include <GLUT/glut.h> // macOS
   #include <cmath>
   

✅ Example Code

#include <GLUT/glut.h>
#include <cmath>

void display() {
    glClear(GL_COLOR_BUFFER_BIT);

    // Reset transformations
    glLoadIdentity();

    // 1️⃣ Translate
    glTranslatef(0.3f, 0.2f, 0.0f);

    // 2️⃣ Rotate
    glRotatef(45, 0.0f, 0.0f, 1.0f);

    // 3️⃣ Scale
    glScalef(0.5f, 0.5f, 1.0f);

    // Draw a simple triangle
    glBegin(GL_TRIANGLES);
        glColor3f(1, 0, 0);
        glVertex2f(-0.5f, -0.5f);
        glColor3f(0, 1, 0);
        glVertex2f(0.5f, -0.5f);
        glColor3f(0, 0, 1);
        glVertex2f(0.0f, 0.5f);
    glEnd();

    glFlush();
}

int main(int argc, char** argv) {
    glutInit(&argc, argv);
    glutCreateWindow("Transformations in OpenGL");
    glutDisplayFunc(display);
    glutMainLoop();
    return 0;
}

🌀 Explanation:

• glTranslatef(x, y, z) → moves object.

• glRotatef(angle, x, y, z) → rotates object about an axis.

• glScalef(x, y, z) → scales object.

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🧠 Summary

Transformation	Mathematical Formula	OpenGL Function
Translation	(x', y') = (x + tx, y + ty)	glTranslatef(tx, ty, tz)
Scaling	(x', y') = (x * sx, y * sy)	glScalef(sx, sy, sz)
Rotation	(x', y') = (x cosθ – y sinθ, x sinθ + y cosθ)	glRotatef(angle, x, y, z)

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Would you like me to show you how to visualize these transformations (e.g. an animation where a shape rotates, moves, and scales in real time)?
I can give you that version next.