2D Transformation Graphics Program in C

Aim

To write a C program to implement two dimensional transformations such as translation, rotation, scaling, shearing and reflection on objects.

Algorithm

Translation

1. Input the line endpoints (x1, y1) and (x2, y2).
2. Input the translation co-ordinates (tx, ty).
3. Draw the line with endpoints (x1, y1) and (x2, y2).
4. Add tx to the co-ordinates x1 and x2.
5. Add ty to the co-ordinates y1 and y2.
6. Draw the translated line with endpoints (x1, y1) and (x2, y2).

Rotation

1. Input the line endpoints (x1, y1) and (x2, y2).
2. Input the rotation angle Ɵ.
3. Draw the line with endpoints (x1, y1) and (x2, y2).
4. Calculate r = (Ɵ * 3.14) / 180.
5. Calculate xn = x2 * cos(r) - y2 * sin(r).
6. Calculate yn = y2 * cos(r) + x2 * sin(r).
7. Draw the rotated line with endpoints (x1, y1) and (xn, yn).

Scaling

1. Input the 3 endpoints of the triangle (x1, y1), (x2, y2) and (x3, y3).
2. Input the scaling factors sx and sy.
3. Draw the triangle with endpoints (x1, y1), (x2, y2) and (x3, y3).
4. Update x1, x2 and x3 by multiplying sx to them.
5. Update y1, y2 and y3 by multiplying sy to them.
6. Draw the scaled triangle with points (x1, y1), (x2, y2) and (x3, y3).

Shearing

1. Input the 4 endpoints of the rectangle (x1, y1), (x2, y2), (x3, y3) and (x4, y4).
2. Input the value for shearing ‘sh’.
3. Draw the rectangle with endpoints (x1, y1), (x2, y2), (x3, y3) and (x4, y4).
4. If shearing along X-axis, update x1, x2, x3 and x4 by adding (sh*y1), (sh*y2), (sh*y3) and (sh*y4) to them respectively.
5. If shearing along Y-axis, update y1, y2, y3 and y4 by adding (sh*x1), (sh*x2), (sh*x3) and (sh*x4) to them respectively.
6. Draw the sheared rectangle with endpoints (x1,y1), (x2, y2), (x3, y3), (x4, y4).

X axis shear

Y axis Shear

Reflection

1. Input the 3 endpoints of the triangle (x1, y1), (x2, y2) and (x3, y3).
2. Calculate middle value of X axis as ‘midx’ and Y axis as ‘midy’.
3. Draw the triangle with endpoints (x1, y1), (x2, y2) and (x3, y3).
4. If reflection about X axis, set y1, y2 and y3 as (midy-y1) + midy, (midy-y2) + midy and (midy-y3) + midy respectively.
5. If reflection about Y axis, set x1, x2 and x3 as (midx-x1) + midx, (midx-x2) + midx and (midx-x3) + midx respectively.
6. Draw the reflected triangle with endpoints (x1, y1), (x2, y2) and (x3, y3).

Reflection about X axis

Reflection about Y axis

Program Code

#include <stdio.h>
#include <conio.h>
#include <graphics.h>
#include <math.h>

void main()
{
    int gd = DETECT, gm;
    int x1, y1, x2, y2, x3, y3, x4, y4, xn, yn, choice;
    int tx, ty, sx, sy, theta, axis, maxx, maxy, midx, midy;
    float rad, sh;
    clrscr();
    initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
    maxx = getmaxx();
    maxy = getmaxy();
    midx = maxx / 2;
    midy = maxy / 2;
    
    do
    {
        printf("1. Translation\n2. Rotation\n3. Scaling\n4. Shearing\n5. Reflection\n6. Exit");
        printf("\nEnter your choice: ");
        scanf("%d", &choice);
        
        switch (choice)
        {
        case 1:
            printf("\nEnter two line endpoints (x1, y1), (x2, y2): ");
            scanf("%d %d %d %d", &x1, &y1, &x2, &y2);
            printf("Enter translation co-ordinates (tx, ty): ");
            scanf("%d %d", &tx, &ty);
            cleardevice();
            line(x1, y1, x2, y2);
            x1 += tx;
            y1 += ty;
            x2 += tx;
            y2 += ty;
            setcolor(GREEN);
            line(x1, y1, x2, y2);
            getch();
            break;
        case 2:
            printf("\nEnter two line endpoints (x1, y1), (x2, y2): ");
            scanf("%d %d %d %d", &x1, &y1, &x2, &y2);
            printf("Enter the angle for rotation: ");
            scanf("%d", &theta);
            cleardevice();
            line(x1, y1, x2, y2);
            rad = (theta * 3.14) / 180;
            xn = x2 * cos(rad) - y2 * sin(rad);
            yn = y2 * cos(rad) + x2 * sin(rad);
            setcolor(GREEN);
            line(x1, y1, xn, yn);
            getch();
            break;
         case 3:
            printf("\nEnter the 1st point for the triangle (x1, y1): ");
            scanf("%d %d", &x1, &y1);
            printf("Enter the 2nd point for the triangle (x2, y2): ");
            scanf("%d %d", &x2, &y2);
            printf("Enter the 3rd point for the triangle (x3, y3): ");
            scanf("%d %d", &x3, &y3);
            printf("Enter the scaling factor (sx, sy): ");
            scanf("%d %d", &sx, &sy);
            cleardevice();
            line(x1, y1, x2, y2);
            line(x2, y2, x3, y3);
            line(x3, y3, x1, y1);
            x1 *= sx;
            y1 *= sy;
            x2 *= sx;
            y2 *= sy;
            x3 *= sx;
            y3 *= sy;
            setcolor(GREEN);
            line(x1, y1, x2, y2);
            line(x2, y2, x3, y3);
            line(x3, y3, x1, y1);
            getch();
            break;
        case 4:
            printf("\nEnter the 1st point for the rectangle (x1, y1): ");
            scanf("%d %d", &x1, &y1);
            printf("Enter the 2nd point for the rectangle (x2, y2): ");
            scanf("%d %d", &x2, &y2);
            printf("Enter the 3rd point for the rectangle (x3, y3): ");
            scanf("%d %d", &x3, &y3);
            printf("Enter the 4th point for the rectangle (x4, y4): ");
            scanf("%d %d", &x4, &y4);
            printf("1. X axis shearing\n2. Y axis shearing\n");
            printf("Enter your choice: ");
            scanf("%d", &axis);
            printf("Enter the value for shearing: ");
            scanf("%f", &sh);
            cleardevice();
            line(midx+x1, midy-y1, midx+x2, midy-y2);
            line(midx+x2, midy-y2, midx+x3, midy-y3);
            line(midx+x3, midy-y3, midx+x4, midy-y4);
            line(midx+x4, midy-y4, midx+x1, midy-y1);
            setcolor(3);
            line(0, midy, maxx, midy);
            line(midx, 0, midx, maxy);
            if (axis == 1) {
            x1 = x1 + (sh * y1);
            x2 = x2 + (sh * y2);
            x3 = x3 + (sh * y3);
            x4 = x4 + (sh * y4);
            }
            else {
            y1 = y1 + (sh * x1);
            y2 = y2 + (sh * x2);
            y3 = y3 + (sh * x3);
            y4 = y4 + (sh * x4);
            }
            setcolor(GREEN);
            line(midx+x1, midy-y1, midx+x2, midy-y2);
            line(midx+x2, midy-y2, midx+x3, midy-y3);
            line(midx+x3, midy-y3, midx+x4, midy-y4);
            line(midx+x4, midy-y4, midx+x1, midy-y1);
            getch();
            break;
        case 5:
            printf("\nEnter the 1st point for the triangle (x1, y1): ");
            scanf("%d %d", &x1, &y1);
            printf("Enter the 2nd point for the triangle (x2, y2): ");
            scanf("%d %d", &x2, &y2);
            printf("Enter the 3rd point for the triangle (x3, y3): ");
            scanf("%d %d", &x3, &y3);
            printf("1. Reflection about X axis\n2. Reflection about Y axis\n");
            printf("Enter your choice: ");
            scanf("%d", &axis);
            cleardevice();
            line(x1, y1, x2, y2);
            line(x2, y2, x3, y3);
            line(x3, y3, x1, y1);
            setcolor(3);
            line(0, midy, maxx, midy);
            line(midx, 0, midx, maxy);
            if (axis == 1) {
            y1 = (midy - y1) + midy;
            y2 = (midy - y2) + midy;
            y3 = (midy - y3) + midy;
            }
            else {
            x1 = (midx - x1) + midx;
            x2 = (midx - x2) + midx;
            x3 = (midx - x3) + midx;
            }
            setcolor(GREEN);
            line(x1, y1, x2, y2);
            line(x2, y2, x3, y3);
            line(x3, y3, x1, y1);
            getch();
            break;
        }
        
        clrscr();
        cleardevice();
        setcolor(WHITE);
    
    } while (choice != 6);
    closegraph();
}