# 2D Scaling Program in C: Understanding Graphics Transformation with Detailed Explanation

## 🎯 Introduction

In computer graphics, scaling is a fundamental transformation that alters the size of an object while preserving its shape. It is commonly used to zoom in or out of an image, adjust the size of graphical elements, and resize geometrical shapes. This blog post presents a 2D scaling program implemented in C programming language. The program takes user inputs for the coordinates of a triangle, performs the scaling transformation based on user-defined scaling factors, and displays the scaled triangle on the screen.

## 🎯 Concept of Scaling

Scaling is a transformation that multiplies the coordinates of an object by scaling factors along the x and y axes. Given a point (x, y) in the original object, the new coordinates after scaling are (x * scaleX, y * scaleY), where scaleX and scaleY are the scaling factors along the x and y axes, respectively. To apply scaling to a 2D shape, we typically perform the following steps:

## 🎯 2D scaling program in C

Below is the 2D scaling program in C with a detailed explanation:

#include <stdio.h>

#include <conio.h>

#include <graphics.h>

#include <process.h>

#include <math.h>

int x1, y1, x2, y2, x3, y3;

void draw();

void scale();

void main()

{

int gd = DETECT, gm;

int c;

initgraph(&gd, &gm, " ");

printf("Enter the 1st point for the triangle:");

scanf("%d%d", &x1, &y1);

printf("Enter the 2nd point for the triangle:");

scanf("%d%d", &x2, &y2);

printf("Enter the 3rd point for the triangle:");

scanf("%d%d", &x3, &y3);

draw();

scale();

}

void draw()

{

line(x1, y1, x2, y2);

line(x2, y2, x3, y3);

line(x3, y3, x1, y1);

}

void scale()

{

int x, y;

int mx, my;

printf("Enter the scaling factors (x y): ");

scanf("%d%d", &x, &y);

mx = (x1 + x2 + x3) / 3;

my = (y1 + y2 + y3) / 3;

cleardevice();

int a1, a2, a3, b1, b2, b3;

a1 = mx + (x1 - mx) * x;

b1 = my + (y1 - my) * y;

a2 = mx + (x2 - mx) * x;

b2 = my + (y2 - my) * y;

a3 = mx + (x3 - mx) * x;

b3 = my + (y3 - my) * y;

line(a1, b1, a2, b2);

line(a2, b2, a3, b3);

line(a3, b3, a1, b1);

draw();

getch();

}

Now you have both the C program and the detailed explanation for the 2D scaling program. Remember that the graphics-related functions in this program are specific to certain compilers and might not work in modern C compilers. For cross-platform graphics rendering, consider using alternative libraries like SDL or OpenGL.

## 🎯 Summary

This C program demonstrates 2D scaling using the graphics.h library. It allows the user to input the coordinates of a triangle and specify the scaling factors along the x and y axes. The program then calculates the centroid of the triangle and applies the scaling transformation to the vertices. The scaled triangle is displayed on the screen, providing a visual representation of the scaling effect.