Doesn't move and rotate the triangle around a point - C Bgi graphics

Question

Greeting,

I have this graphic homework in BGI graphic. We must use DevCPP and BGI, and matrices.

I wrote this code, and I think the transformations is good. But my triangle doesn't move and rotate around the circle, And I don't understand, why not it moves around the circle...

I don't know where and what I have to rewrite.

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

#define PI 3.14159265

typedef float Matrix3x3[3][3];
Matrix3x3 theMatrix;

int Round( double n ){
    return (int)( n + 0.5 );
}

void matrix3x3SetIdentity(Matrix3x3 m)
{
     int i, j;
     for(i=0; i<3; i++)
              for(j=0; j<3;j++)
                       m[i][j]=(i==j);
}

/* Multiplies matrix, result in b matrix */
void matrix3x3PreMultiply(Matrix3x3 a, Matrix3x3 b)
{
     int r, c;
     Matrix3x3 tmp;

     for(r=0; r<3;r++)
       for(c=0; c<3;c++)
         tmp[r][c]=
           a[r][0]*b[0][c]+a[r][1]*b[1][c]+a[r][2]*b[2][c];

     for(r=0; r<3;r++)
       for(c=0; c<3; c++)
         b[r][c]-tmp[r][c];

 }

void translate2(int tx, int ty)
{
     Matrix3x3 m;

     matrix3x3SetIdentity (m);
     m[0][2] = tx;
     m[1][2] = ty;
     matrix3x3PreMultiply(m, theMatrix);
}

void scale2 (float sx, float sy, pont2d refpt)
{
Matrix3x3 m;
matrix3x3SetIdentity(m); 
m[0][0]=sx;
m[0][2]=(1-sx)*refpt.x;
m[1][1]=sy;
m[1][2]=(1-sy)*refpt.y;
matrix3x3PreMultiply(m, theMatrix);
}


void rotate2 (float a, pont2d refpt) 
{
     Matrix3x3 m;
     matrix3x3SetIdentity(m);
     a=a/PI;
     m[0][0] = cosf(a);
     m[0][1] = -sinf(a);
     m[0][2] = refpt.x * (1-cosf(a)) + refpt.y * sinf(a);
     m[1][0] = sinf (a);
     m[1][1] = cosf (a);
     m[1][2] = refpt.y * (1-cosf(a)) - refpt.x * sinf(a);
     matrix3x3PreMultiply(m, theMatrix);
}

void transformPoints2 (int npts, pont2d *pts)
{
  int k;
  float tmp;

  for (k = 0; k < npts; k++) {
    tmp = theMatrix[0][0] * pts[k].x + theMatrix[0][1] * 
      pts[k].y + theMatrix[0][2];
    pts[k].y = theMatrix[1][0] * pts[k].x + theMatrix[1][1] * 
      pts[k].y + theMatrix[1][2];
    pts[k].x = tmp;
  }
}


int main()
{
int gd, gm, i, page=0;
gd=VGA;gm=VGAHI;
initgraph(&gd,&gm,"");
int ap;

while(!kbhit())
{
    setactivepage(page);
    cleardevice();


     pont2d P[3] = { 50.0, 50.0, 150.0, 50.0, 100.0, 150.0};
     pont2d refPt = {200.0, 250.0};

     // Drawing the Triangle
     moveto( Round( P[ 0 ].x ), Round( P[ 0 ].y ) );
     for( i = 1; i < 3; i++ )
          lineto( Round( P[ i ].x ), Round( P[ i ].y ) );          
     lineto( Round( P[ 0 ].x ), Round( P[ 0 ].y ) );

     // Drawing the Circle
     fillellipse(200, 250, 5,5);
     setcolor (BLUE);
     matrix3x3SetIdentity (theMatrix);
     scale2 (0.5, 0.5, refPt);
     //scale2 (20, 20, refPt);
     rotate2 (90.0, refPt);
     translate2 (0, 150);
     transformPoints2 (3, P);

     setvisualpage(page);
     page = 1-page;     

}

getch();

closegraph();

return 0;

}

Answer 1

If you want to see the object "spin", then rotations should be performed about the local origin. Rotation about the global origin will cause the object to "orbit" the global origin. Thus, to spin the object:

1. Translate the object to global origin
2. Apply the rotation
3. Translate the object back to its original position

Look at the discussion regarding transformation order here for an illustration. Specifically, look for the section entitled "Demonstration of the importance of transformation order".

Answer 2

To rotate a triangle, get the three points and use the formula:

x' = x + r cos (theta) y' = y - r sin (theta)

The above formula can be applied into a loop where there being 0 to 360. You can have a graphics simulation by putting a delay (200) milliseconds in the loop.