2D_Transformations.c

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

void grid()
{
    line(0, 240, 640, 240);
    line(320, 0, 320, 480);
}

void draw(int c00, int c01, int c10, int c11, int c20, int c21)
{
    line(320+c00, 240-c01, 320+c10, 240-c11);
    line(320+c00, 240-c01, 320+c20, 240-c21);
    line(320+c10, 240-c11, 320+c20, 240-c21);
}

void matrixMulti(double a[10][10], double b[10][10], double c[10][10], int m, int n, int p)
{
    int i, j, k;
    for (i = 0; i < m; i++)
    {
        for (j = 0; j < p; j++)
        {
            c[i][j] = 0;
            for (k = 0; k < n; k++)
            {
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

void addElements(double a[10][10], double num1, double num2, double num3, 
                double num4, double num5, double num6, 
                double num7, double num8, double num9)
{
    a[0][0] = num1;
    a[0][1] = num2;
    a[0][2] = num3;
    a[1][0] = num4;
    a[1][1] = num5;
    a[1][2] = num6;
    a[2][0] = num7;
    a[2][1] = num8;
    a[2][2] = num9;
}

void main()
{
    int gd = DETECT, gm;
    int x1, y1, x2, y2, x3, y3, tx, ty, theta, ch,
        rot1, rot2, sx, sy, sc1, sc2, slope, c, r1, r2, sh;
    double thetaRad = 0, thetaRef = 0;
    double mat1[10][10], mat2[10][10], result1[10][10], result2[10][10];
    
    clrscr();
    printf("Enter the coordinates of triangle\n");
    printf("Point 1: ");
    scanf("%d%d", &x1, &y1);
    printf("Point 2: ");
    scanf("%d%d", &x2, &y2);
    printf("Point 3: ");
    scanf("%d%d", &x3, &y3);
    
    do {
        printf("******************MENU******************\n");
        printf("1. Translation\n");
        printf("2. Rotation about origin\n");
        printf("3. Rotation about a fixed point\n");
        printf("4. Scaling about origin\n");
        printf("5. Scaling about a fixed point\n");
        printf("6. Reflection about x-axis\n");
        printf("7. Reflection about y-axis\n");
        printf("8. Reflection about origin\n");
        printf("9. Reflection about any line y = mx + c\n");
        printf("10. Shearing in x-direction\n");
        printf("11. Shearing in y-direction\n");
        printf("12. Exit\n");
        printf("\nEnter your choice: ");
        scanf("%d", &ch);
        
        if (ch == 1)
        {
            printf("Enter the translation coordinates: ");
            scanf("%d%d", &tx, &ty);
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            addElements(mat2, 1, 0, tx, 0, 1, ty, 0, 0, 1);
            matrixMulti(mat2, mat1, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 2)
        {
            printf("Enter the angle (in degrees) by which you want to rotate the triangle: ");
            scanf("%d", &theta);
            thetaRad = (double)theta * 3.14 / 180.0;
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, cos(thetaRad), -sin(thetaRad), 0, 
                              sin(thetaRad), cos(thetaRad), 0, 
                              0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 3)
        {
            printf("Enter the coordinates of the point about which you want to rotate the triangle: ");
            scanf("%d%d", &rot1, &rot2);
            printf("Enter the angle (in degrees) by which you want to rotate the triangle: ");
            scanf("%d", &theta);
            thetaRad = (double)theta * 3.14 / 180.0;
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            
            // Translate to origin
            addElements(mat1, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            addElements(mat2, 1, 0, -rot1, 0, 1, -rot2, 0, 0, 1);
            matrixMulti(mat2, mat1, result1, 3, 3, 3);
            
            // Rotate
            addElements(mat1, cos(thetaRad), -sin(thetaRad), 0, 
                              sin(thetaRad), cos(thetaRad), 0, 
                              0, 0, 1);
            addElements(mat2, result1[0][0], result1[0][1], result1[0][2], 
                              result1[1][0], result1[1][1], result1[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result2, 3, 3, 3);
            
            // Translate back
            addElements(mat1, 1, 0, rot1, 0, 1, rot2, 0, 0, 1);
            addElements(mat2, result2[0][0], result2[0][1], result2[0][2], 
                              result2[1][0], result2[1][1], result2[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 4)
        {
            printf("Enter the scaling factors: ");
            scanf("%d%d", &sx, &sy);
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, sx, 0, 0, 0, sy, 0, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 5)
        {
            printf("Enter the coordinates of the point about which you want to scale the triangle: ");
            scanf("%d%d", &sc1, &sc2);
            printf("Enter the scaling factors: ");
            scanf("%d%d", &sx, &sy);
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            
            // Translate to origin
            addElements(mat1, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            addElements(mat2, 1, 0, -sc1, 0, 1, -sc2, 0, 0, 1);
            matrixMulti(mat2, mat1, result1, 3, 3, 3);
            
            // Scale
            addElements(mat1, sx, 0, 0, 0, sy, 0, 0, 0, 1);
            addElements(mat2, result1[0][0], result1[0][1], result1[0][2], 
                              result1[1][0], result1[1][1], result1[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result2, 3, 3, 3);
            
            // Translate back
            addElements(mat1, 1, 0, sc1, 0, 1, sc2, 0, 0, 1);
            addElements(mat2, result2[0][0], result2[0][1], result2[0][2], 
                              result2[1][0], result2[1][1], result2[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 6)
        {
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, 1, 0, 0, 0, -1, 0, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 7)
        {
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, -1, 0, 0, 0, 1, 0, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 8)
        {
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, -1, 0, 0, 0, -1, 0, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 9)
        {
            printf("Enter the values of m and c respectively: ");
            scanf("%d%d", &slope, &c);
            thetaRef = atan((double)slope) * 180.0 / 3.14;
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            
            // Translate to y-intercept
            addElements(mat1, 1, 0, 0, 0, 1, -c, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            
            // Rotate to align with x-axis
            addElements(mat1, cos(thetaRef), sin(thetaRef), 0, 
                              -sin(thetaRef), cos(thetaRef), 0, 
                              0, 0, 1);
            addElements(mat2, result1[0][0], result1[0][1], result1[0][2], 
                              result1[1][0], result1[1][1], result1[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result2, 3, 3, 3);
            
            // Reflect about x-axis
            addElements(mat1, 1, 0, 0, 0, -1, 0, 0, 0, 1);
            addElements(mat2, result2[0][0], result2[0][1], result2[0][2], 
                              result2[1][0], result2[1][1], result2[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            
            // Rotate back
            addElements(mat1, cos(thetaRef), -sin(thetaRef), 0, 
                              sin(thetaRef), cos(thetaRef), 0, 
                              0, 0, 1);
            addElements(mat2, result1[0][0], result1[0][1], result1[0][2], 
                              result1[1][0], result1[1][1], result1[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result2, 3, 3, 3);
            
            // Translate back
            addElements(mat1, 1, 0, 0, 0, 1, c, 0, 0, 1);
            addElements(mat2, result2[0][0], result2[0][1], result2[0][2], 
                              result2[1][0], result2[1][1], result2[1][2], 
                              1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 10)
        {
            printf("Enter the shearing parameter: ");
            scanf("%d", &sh);
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, 1, sh, 0, 0, 1, 0, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 11)
        {
            printf("Enter the shearing parameter: ");
            scanf("%d", &sh);
            initgraph(&gd, &gm, "C:\\TURBOC3\\BGI");
            grid();
            draw(x1, y1, x2, y2, x3, y3);
            addElements(mat1, 1, 0, 0, sh, 1, 0, 0, 0, 1);
            addElements(mat2, x1, x2, x3, y1, y2, y3, 1, 1, 1);
            matrixMulti(mat1, mat2, result1, 3, 3, 3);
            delay(2000);
            setcolor(14);
            draw((int)result1[0][0], (int)result1[1][0], 
                 (int)result1[0][1], (int)result1[1][1], 
                 (int)result1[0][2], (int)result1[1][2]);
            getch();
            closegraph();
        }
        else if (ch == 12)
        {
            printf("Exiting the program\n");
        }
        else
        {
            printf("Invalid input \nTry again\n");
        }
    } while (ch != 12);
}