Program To Implement 3D Scaling

#include<graphics.h>

#include<stdlib.h>

#include<stdio.h>

#include<conio.h>

int a[1][4],i,j,sx,sy,sz,k,b[4][4],c[1][4];

int left=150,top=50,right=200,bottom=150,depth=25,topflag;

void far bar3d(int left,int top,int right,int bottom,int depth,int topflag);

void main()

{

int gd=DETECT,gm;

clrscr();

initgraph(&gd,&gm,"c:\\turboc3\\bgi");

setfillstyle(LINE_FILL,2);

bar3d(left,top,right,bottom,depth,1);

i=0;

for(j=0;j<3;j++)

c[i][j]=0;

printf("\nEnter the scaling points:");

scanf("%d%d%d",&sx,&sy,&sz);

for(i=0;i<4;i++)

for(j=0;j<4;j++)

{

if(i==j)

b[i][j]=1;

else

b[i][j]=0;

}

b[0][0]=sx;

b[1][1]=sy;

b[2][2]=sz;

a[0][0]=left;

a[0][1]=top;

a[0][2]=depth;

a[0][3]=1;

i=0;

for(j=0;j<4;j++)

{

for(k=0;k<4;k++)

c[i][j]=c[i][j]+a[i][k]*b[k][j];

if(j==0)

left=c[i][j];

if(j==1)

top=c[i][j];

if(j==2)

depth=c[i][j];

c[i][j]=0;

}

a[0][0]=right;

a[0][1]=bottom;

a[0][2]=depth;

a[0][3]=1;

i=0;

for(j=0;j<4;j++) {

for(k=0;k<4;k++)

c[i][j]=c[i][j]+a[i][k]*b[k][j];

if(j==0)

right=c[i][j];

if(j==1)

bottom=c[i][j];

if(j==2)

depth=c[i][j];

c[i][j]=0;

}

bar3d(left,top,right,bottom,depth,1);

getch();

}

Program To Implement 3D Rotation About An Arbitrary Axis

#include<iostream.h>

#include<math.h>

#include<conio.h>

 //using namespace std;

 typedef struct {

    float x;

    float y;

    float z;

}Point;

Point points;

 float rotationMatrix[4][4];

float inputMatrix[4][1] = {0.0, 0.0, 0.0, 0.0};

float outputMatrix[4][1] = {0.0, 0.0, 0.0, 0.0};

 void showPoint(){

    cout<<"("<<outputMatrix[0][0]<<","<<outputMatrix[1][0]<<","<<outputMatrix[2][0]<<")"<<endl;

}

 void multiplyMatrix()

{

    for(int i = 0; i < 4; i++ ){

            for(int j = 0; j < 1; j++){

                outputMatrix[i][j] = 0;

                for(int k = 0; k < 4; k++){

                        outputMatrix[i][j] += rotationMatrix[i][k] * inputMatrix[k][j];

                }

            }

    }

}

void setUpRotationMatrix(float angle, float u, float v, float w)

{

    float L = (u*u + v * v + w * w);

    angle = angle * M_PI / 180.0; //converting to radian value

    float u2 = u * u;

    float v2 = v * v;

    float w2 = w * w;

    rotationMatrix[0][0] = (u2 + (v2 + w2) * cos(angle)) / L;

    rotationMatrix[0][1] = (u * v * (1 - cos(angle)) - w * sqrt(L) * sin(angle)) / L;

    rotationMatrix[0][2] = (u * w * (1 - cos(angle)) + v * sqrt(L) * sin(angle)) / L;

    rotationMatrix[0][3] = 0.0;

    rotationMatrix[1][0] = (u * v * (1 - cos(angle)) + w * sqrt(L) * sin(angle)) / L;

    rotationMatrix[1][1] = (v2 + (u2 + w2) * cos(angle)) / L;

    rotationMatrix[1][2] = (v * w * (1 - cos(angle)) - u * sqrt(L) * sin(angle)) / L;

    rotationMatrix[1][3] = 0.0;

    rotationMatrix[2][0] = (u * w * (1 - cos(angle)) - v * sqrt(L) * sin(angle)) / L;

    rotationMatrix[2][1] = (v * w * (1 - cos(angle)) + u * sqrt(L) * sin(angle)) / L;

    rotationMatrix[2][2] = (w2 + (u2 + v2) * cos(angle)) / L;

    rotationMatrix[2][3] = 0.0;

    rotationMatrix[3][0] = 0.0;

    rotationMatrix[3][1] = 0.0;

    rotationMatrix[3][2] = 0.0;

    rotationMatrix[3][3] = 1.0;

}

int main()

{

    float angle;

    float u, v, w;

    clrscr();

    cout<<" PROGRAM FOR THE ROTATION \n";

    cout<<" Enter the initial point you want to transform:";

    cin>>points.x>>points.y>>points.z;

    inputMatrix[0][0] = points.x;

    inputMatrix[1][0] = points.y;

    inputMatrix[2][0] = points.z;

    inputMatrix[3][0] = 1.0;

    cout<<" Enter axis vector: ";

    cin>>u>>v>>w;

    cout<<" Enter the rotating angle in degree: ";

    cin>>angle;

    setUpRotationMatrix(angle, u, v, w);

    multiplyMatrix();

    showPoint();

    return 0;

}

. Program To Implement Scaling,Rotation and Translation of The Triangle

#include <graphics.h>

#include <stdlib.h>

#include <stdio.h>

#include <conio.h>

#include<math.h>

void main()

{

            int gm;

            int gd=DETECT;

            int x1,x2,x3,y1,y2,y3,nx1,nx2,nx3,ny1,ny2,ny3,c;

            int sx,sy,xt,yt,r;

            float t;

                initgraph(&gd,&gm,"c:\\turboc3\\bgi");

            printf("\t Program for basic transactions");

            printf("\n\t Enter the points of triangle");

                setcolor(15);

                scanf("%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3);

                line(x1,y1,x2,y2);

                line(x2,y2,x3,y3);

                line(x3,y3,x1,y1);

                getch();

                printf("\n 1.Transaction\n 2.Rotation\n 3.Scalling\n 4.Exit");

                printf("\nEnter your choice:");

                scanf("%d",&c);

                switch(c)

                {

                                    case 1:

                                                    printf("\n Enter the translation factor");

                                                    scanf("%d%d",&xt,&yt);

                                                    nx1=x1+xt;

                                                    ny1=y1+yt;

                                                    nx2=x2+xt;

                                                    ny2=y2+yt;

                                                    nx3=x3+xt;

                                                    ny3=y3+yt;

                                                    line(nx1,ny1,nx2,ny2);

                                                    line(nx2,ny2,nx3,ny3);

                                                    line(nx3,ny3,nx1,ny1);

                                                    getch();

                                                    break;

                                    case 2:

                                                    printf("\n Enter the angle of rotation");

                                                    scanf("%d",&r);

                                                    t=3.14*r/180;

                                                    nx1=abs(x1*cos(t)-y1*sin(t));

                                                    ny1=abs(x1*sin(t)+y1*cos(t));

                                                    nx2=abs(x2*cos(t)-y2*sin(t));

                                                    ny2=abs(x2*sin(t)+y2*cos(t));

                                                    nx3=abs(x3*cos(t)-y3*sin(t));

                                                    ny3=abs(x3*sin(t)+y3*cos(t));

                                                    line(nx1,ny1,nx2,ny2);

                                                    line(nx2,ny2,nx3,ny3);

                                                    line(nx3,ny3,nx1,ny1);

                                                    getch();

                                                    break;

                                    case 3:

                                                    printf("\n Enter the scalling factor");

                                                    scanf("%d%d",&sx,&sy);

                                                    nx1=x1*sx;

                                                    ny1=y2*sy;

                                                    nx2=x2*sx;

                                                    ny2=y2*sy;

                                                    nx3=x3*sx;

                                                    ny3=y3*sy;

                                                    line(nx1,ny1,nx2,ny2);

                                                    line(nx2,ny2,nx3,ny3);

                                                    line(nx3,ny3,nx1,ny1);

                                                    getch();

                                                    break;

                                    case 4:

                                                    break;

                                    default:

                                                    printf("Enter the correct choice");

                                                    }

                                                    closegraph();

                                                    }

Program To Implement A Line Using Slope Intercept Formula

#include<stdio.h>

#include<conio.h>

#include<graphics.h>

#include<math.h>

void main()

{

float m,x1,y1,x2,y2;

int x,y;

int gdriver=DETECT,gmode,gerror;

clrscr();

printf(" PROGRAM FOR THE LINE INTERCEPT \n");

printf(" Enter the value of x1");

scanf("%f",&x1);

printf(" Enter the value of y1");

scanf("%f",&y1);

printf(" Enter the value of x2");

scanf("%f",&x2);

printf(" Enter the value of y2");

scanf("%f",&y2);

initgraph(&gdriver,&gmode,"c:\\turboc3\\bgi");

m=(y2-y1)/(x2-x1);

for(x=1;x<=x2;x++)

{

y=m*(x-x1)+y1;

putpixel(x,y,15);

delay(50);

}

getch();

closegraph();

}

Program To Implement 2D Translation of Polygon.

#include<stdio.h>

#include<conio.h>

#include<graphics.h>

#include<process.h>

#include<math.h>

int x1,y1,x2,y2,x3,y3,X4,Y4,mx,my;

void draw();

void poly();

 void main()

{

    int gd=DETECT,gm;

    int c;

    initgraph(&gd,&gm,"c:\\turboc3\\bgi ");

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

    scanf("%d%d",&x1,&y1);

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

    scanf("%d%d",&x2,&y2);

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

    scanf("%d%d",&x3,&y3);

    printf("Enter the 4th point for the polygon:");

    scanf("%d%d",&x4,&y4);

    cleardevice();

    draw();

    getch();

    poly();

    getch();

}

void draw()

{

    line(x1,y1,x2,y2);

    line(x2,y2,x3,y3);

    line(x3,y3,x4,y4);

    line(x4,y4,x1,y1);

}

void poly()

{

    int x,y,a1,a2,a3,a4,b1,b2,b3,b4;

    printf("Enter the Transaction coordinates");

    scanf("%d%d",&x,&y);

    cleardevice();

    a1=x1+x;

    b1=y1+y;

    a2=x2+x;

    b2=y2+y;

    a3=x3+x;

    b3=y3+y;

    a4=x4+x;

    b4=y4+y;

    line(a1,b1,a2,b2);

    line(a2,b2,a3,b3);

    line(a3,b3,a4,b4);

    line(a4,b4,a1,b1);

}

Program To Implement 2D Translation of Triangle

#include<conio.h>

#include<graphics.h>

#include<math.h>

#include<stdio.h>

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

void draw();

void tri();

void main()

{

int gdriver=DETECT,gmode,gerror;

initgraph(&gdriver,&gmode,"c:\\turboc3\\bgi");

printf("\n");

printf("  Enter first point coordinates");

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

printf("  Enter second point coordinates");

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

printf("  Enter third point coordinates");

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

cleardevice();

draw();

getch();

tri();

getch();

}

void draw()

{

line(x1,y1,x2,y2);

line(x2,y2,x3,y3);

line(x3,y3,x1,y1);

}

void  tri()

{

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

printf("Enter translation coordinates");

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

cleardevice;

a1=x1+x;

b1=y1+y;

a2=x2+x;

b2=y2+y;

a3=x3+x;

b3=y3+y;

line(a1,b1,a2,b2);

line(a2,b2,a3,b3);

line(a3,b3,a1,b1);}

PROGRAM TO IMPLEMENT BEZIR'S ALGORITHM

#include<stdio.h>
#include<conio.h>
#include<graphics.h>
int x,y,z;
void main()
{
float u;
int gd,gm,ymax,i,n,c[4][3];
for(i=0;i<4;i++) { c[i][0]=0; c[i][1]=0; }
printf("\n\n Enter four points : \n\n");
for(i=0; i<4; i++)
{
printf("\t X%d Y%d : ",i,i);
scanf("%d %d",&c[i][0],&c[i][1]);
}
c[4][0]=c[0][0];
c[4][1]=c[0][1];
detectgraph(&gd,&gm);
initgraph(&gd,&gm,"c:\\turboc3\\bgi");
ymax = 480;
setcolor(13);
for(i=0;i<3;i++)
{
line(c[i][0],ymax-c[i][1],c[i+1][0],ymax-c[i+1][1]);
}
setcolor(3);
n=3;
for(i=0;i<=40;i++)
{
u=(float)i/40.0;
bezier(u,n,c);
if(i==0)
{ moveto(x,ymax-y);}
else
{ lineto(x,ymax-y); }
getch();
}
getch();
}
bezier(u,n,p)
float u;int n; int p[4][3];
{
int j;
float v,b;
float blend(int,int,float);
x=0;y=0;z=0;
for(j=0;j<=n;j++)
{
b=blend(j,n,u);
x=x+(p[j][0]*b);
y=y+(p[j][1]*b);
z=z+(p[j][2]*b);
}
}

float blend(int j,int n,float u)
{
int k;
float v,blend;
v=C(n,j);
for(k=0;k<j;k++)
{ v*=u; }
for(k=1;k<=(n-j);k++)
{ v *= (1-u); }
blend=v;
return(blend);
}

C(int n,int j)
{
int k,a,c;
a=1;
for(k=j+1;k<=n;k++) { a*=k; }
for(k=1;k<=(n-j);k++) { a=a/k; }
c=a;
return(c);
}