# Program to show the 3D Shearing Transformation along y-axis

``` # include <iostream.h>
# include <graphics.h>
# include    <conio.h>
# include     <math.h>

# define  f                 0.3
# define  projection_angle   45

void show_screen( );

void apply_y_shearing(int[5][3],const float,const float);
void multiply_matrices(const float[4],const float[4][4],float[4]);

void draw_pyramid(const int [5][3]);
void get_projected_point(int&,int&,int&);

void Line(const int,const int,const int,const int);

int main( )
{
int driver=VGA;
int mode=VGAHI;

initgraph(&driver,&mode,\"..\\\\Bgi\");

show_screen( );

int pyramid[5][3]={
{270,300,50},      //  base front left
{370,300,50},      //  base front right
{370,300,-50},     //  base back right
{270,300,-50},     //  base back left
{320,150,0}        //  top
};

setcolor(15);
draw_pyramid(pyramid);

setcolor(15);
settextstyle(0,0,1);
outtextxy(50,415,\"*** Press any key to see the 3D Shearing along y-axis.\");

apply_y_shearing(pyramid,0.5,0.1);

getch( );

setcolor(10);
draw_pyramid(pyramid);

getch( );
return 0;
}

//------------------------  Funcion Definitions  ------------------------//

//-------------------------  apply_y_shearing( )  --------------------//

void apply_y_shearing(int edge_points[5][3],const float a,const float b)
{
for(int count=0;count<5;count++)
{
float matrix_a[4]={edge_points[count][0],edge_points[count][1],
edge_points[count][2],1};
float matrix_b[4][4]={
{ 1,0,0,0 } ,
{ a,1,b,0 } ,
{ 0,0,1,0 } ,
{ 0,0,0,1 }
};

float matrix_c[4]={0};

multiply_matrices(matrix_a,matrix_b,matrix_c);

edge_points[count][0]=(int)(matrix_c[0]+0.5);
edge_points[count][1]=(int)(matrix_c[1]+0.5);
edge_points[count][2]=(int)(matrix_c[2]+0.5);
}
}

/************************************************************************/
//----------------------  multiply_matrices( )  ------------------------//
/************************************************************************/

void multiply_matrices(const float matrix_1[4],
const float matrix_2[4][4],float matrix_3[4])
{
for(int count_1=0;count_1<4;count_1++)
{
for(int count_2=0;count_2<4;count_2++)
matrix_3[count_1]+=
(matrix_1[count_2]*matrix_2[count_2][count_1]);
}
}

/************************************************************************/
//--------------------------  draw_pyramid( )  -------------------------//
/************************************************************************/

void draw_pyramid(const int points[5][3])
{
int edge_points[5][3];

for(int i=0;i<5;i++)
{
edge_points[i][0]=points[i][0];
edge_points[i][1]=points[i][1];
edge_points[i][2]=points[i][2];

get_projected_point(edge_points[i][0],
edge_points[i][1],edge_points[i][2]);
}

Line(edge_points[0][0],edge_points[0][1],
edge_points[1][0],edge_points[1][1]);
Line(edge_points[1][0],edge_points[1][1],
edge_points[2][0],edge_points[2][1]);
Line(edge_points[2][0],edge_points[2][1],
edge_points[3][0],edge_points[3][1]);
Line(edge_points[3][0],edge_points[3][1],
edge_points[0][0],edge_points[0][1]);

Line(edge_points[0][0],edge_points[0][1],
edge_points[4][0],edge_points[4][1]);
Line(edge_points[1][0],edge_points[1][1],
edge_points[4][0],edge_points[4][1]);
Line(edge_points[2][0],edge_points[2][1],
edge_points[4][0],edge_points[4][1]);
Line(edge_points[3][0],edge_points[3][1],
edge_points[4][0],edge_points[4][1]);
}

/************************************************************************/
//---------------------  get_projected_point( )  -----------------------//
/************************************************************************/

void get_projected_point(int& x,int& y,int& z)
{
float fcos0=(f*cos(projection_angle*(M_PI/180)));
float fsin0=(f*sin(projection_angle*(M_PI/180)));

float Par_v[4][4]={
{1,0,0,0},
{0,1,0,0},
{fcos0,fsin0,0,0},
{0,0,0,1}
};

float xy[4]={x,y,z,1};
float new_xy[4]={0};

multiply_matrices(xy,Par_v,new_xy);

x=(int)(new_xy[0]+0.5);
y=(int)(new_xy[1]+0.5);
z=(int)(new_xy[2]+0.5);
}

//-------------------------------  Line( )  -----------------------------//

void Line(const int x_1,const int y_1,const int x_2,const int y_2)
{
int color=getcolor( );

int x1=x_1;
int y1=y_1;

int x2=x_2;
int y2=y_2;

if(x_1>x_2)
{
x1=x_2;
y1=y_2;

x2=x_1;
y2=y_1;
}

int dx=abs(x2-x1);
int dy=abs(y2-y1);
int inc_dec=((y2>=y1)?1:-1);

if(dx>dy)
{
int two_dy=(2*dy);
int two_dy_dx=(2*(dy-dx));
int p=((2*dy)-dx);

int x=x1;
int y=y1;

putpixel(x,y,color);

while(x<x2)
{
x++;

if(p<0)
p+=two_dy;

else
{
y+=inc_dec;
p+=two_dy_dx;
}

putpixel(x,y,color);
}
}

else
{
int two_dx=(2*dx);
int two_dx_dy=(2*(dx-dy));
int p=((2*dx)-dy);

int x=x1;
int y=y1;

putpixel(x,y,color);

while(y!=y2)
{
y+=inc_dec;

if(p<0)
p+=two_dx;

else
{
x++;
p+=two_dx_dy;
}

putpixel(x,y,color);
}
}
}

//--------------------------  show_screen( )  ---------------------------//

void show_screen( )
{
setfillstyle(1,1);
bar(210,26,420,38);

settextstyle(0,0,1);
setcolor(15);
outtextxy(5,5,\"******************************************************************************\");
outtextxy(5,17,\"*-**************************************************************************-*\");
outtextxy(5,29,\"*-----------------------                             ------------------------*\");
outtextxy(5,41,\"*-**************************************************************************-*\");
outtextxy(5,53,\"*-**************************************************************************-*\");

setcolor(11);
outtextxy(218,29,\"3D Shearing along y-axis\");

setcolor(15);

for(int count=0;count<=30;count++)
outtextxy(5,(65+(count*12)),\"*-*                                                                        *-*\");

outtextxy(5,438,\"*-**************************************************************************-*\");
outtextxy(5,450,\"*-------------------------                          -------------------------*\");
outtextxy(5,462,\"******************************************************************************\");

setcolor(12);
outtextxy(229,450,\"Press any Key to exit.\");
}
```

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