Point Plane Distance

point-plane-dist.c

// given 3 points on plane (x1,y1,z1), (x2,y2,z2), (x3,y3,z3)
// get distance to (x,y,z)
double plane_exp_point_dist_3d ( double x1, double y1, double z1, double x2,
  double y2, double z2, double x3, double y3, double z3, double x, double y, double z )
{
  double a;
  double b;
  double c;
  double d;
  double dist;

  plane_exp2imp_3d ( x1, y1, z1, x2, y2, z2, x3, y3, z3,
    &a, &b, &c, &d );

  dist = plane_imp_point_dist_3d ( a, b, c, d, x, y, z );

  return dist;
}

// convert explicit (3 points on plane) representation
// to implicit representation (A,B,C,D)
void plane_exp2imp_3d ( double x1, double y1, double z1, double x2, double y2,
  double z2, double x3, double y3, double z3, double *a, double *b, double *c,
  double *d )
{
  *a = ( y2 - y1 ) * ( z3 - z1 ) - ( z2 - z1 ) * ( y3 - y1 );
  *b = ( z2 - z1 ) * ( x3 - x1 ) - ( x2 - x1 ) * ( z3 - z1 );
  *c = ( x2 - x1 ) * ( y3 - y1 ) - ( y2 - y1 ) * ( x3 - x1 );
  *d = - x2 * *a - y2 * *b - z2 * *c;

  return;
}

// determine distance from plane in implicit representation (A,B,C,D)
// to a point (x,y,z)
double plane_imp_point_dist_3d ( double a, double b, double c, double d,
  double x, double y, double z )
{
  double dist;

  dist =
    fabs ( a * x + b * y + c * z + d ) /
    sqrt ( a * a + b * b + c * c );

  return dist;
}