/* programa para calculo dos coeficientes do plano dos 3 ptos */

#include <stdio.h>


/* determinante de uma matriz 3x3 */
float det3x3(m)
float m[3][3];
{
    float res, d0, d1, d2;

    d0 = m[1][1]*m[2][2] - m[1][2]*m[2][1];
    d1 = m[1][0]*m[2][2] - m[1][2]*m[2][0];
    d2 = m[1][0]*m[2][1] - m[1][1]*m[2][0];
    res = d0 * m[0][0] - d1 * m[0][1] + d2 * m[0][2];

    return(res);
}


main()
{
  float p1[4], p2[4], p3[4],
        w, x, y, z;
  float m[3][3];
  

  while(1)
    {
      printf("\n\n   Entre com coordenadas homogeneas.\n --->>> OS PTOS devem estar no sentido de  rotacao do relogio em relacao ao plano.");
      printf("\n\n  ponto 1: ");
      scanf("%f %f %f %f",&p1[0],&p1[1],&p1[2],&p1[3]);
      
      printf("\n  ponto 2: ");
      scanf("%f %f %f %f",&p2[0],&p2[1],&p2[2],&p2[3]);
      
      printf("\n  ponto 3: ");
      scanf("%f %f %f %f",&p3[0],&p3[1],&p3[2],&p3[3]);

      m[0][0] = p1[1];
      m[0][1] = p1[2];
      m[0][2] = p1[3];
      
      m[1][0] = p2[1];
      m[1][1] = p2[2];
      m[1][2] = p2[3];
      
      m[2][0] = p3[1];
      m[2][1] = p3[2];
      m[2][2] = p3[3];
      
      w = det3x3(m);
      
      m[0][0] = p1[0];
      m[0][1] = p1[2];
      m[0][2] = p1[3];
      
      m[1][0] = p2[0];
      m[1][1] = p2[2];
      m[1][2] = p2[3];
      
      m[2][0] = p3[0];
      m[2][1] = p3[2];
      m[2][2] = p3[3];
      
      x = -1*det3x3(m);
      
      m[0][0] = p1[0];
      m[0][1] = p1[1];
      m[0][2] = p1[3];
      
      m[1][0] = p2[0];
      m[1][1] = p2[1];
      m[1][2] = p2[3];
      
      m[2][0] = p3[0];
      m[2][1] = p3[1];
      m[2][2] = p3[3];
      
      y = det3x3(m);
      
      m[0][0] = p1[0];
      m[0][1] = p1[1];
      m[0][2] = p1[2];
  
      m[1][0] = p2[0];
      m[1][1] = p2[1];
      m[1][2] = p2[2];
      
      m[2][0] = p3[0];
      m[2][1] = p3[1];
      m[2][2] = p3[2];
      
      z = -1*det3x3(m);


      printf("\n Coeficientes do plano:\n  w = %.4f   x = %.4f   y = %.4f  
          z = %.4f\n\n",w,x,y,z);
      
    }

}