/* 
        Returns twice the signed area of the triangle determined by a,b,c.
        The area is positive if a,b,c are oriented ccw, negative if cw,
	and zero if the points are collinear.
*/
int     Area2( tPointi a, tPointi b, tPointi c )
{
        return
                a[0] * b[1] - a[1] * b[0] +
                a[1] * c[0] - a[0] * c[1] +
                b[0] * c[1] - c[0] * b[1];
}

/*
	Exclusive or: true iff exactly one argument is true.
	The arguments are negated to ensure that they are 0/1
	values.  Then the bitwise xor operator may apply.
	(This idea is due to Michael Baldwin.)
*/
bool 	xor( bool x, bool y )
{
	return	!x ^ !y;
}
bool    Left( tPointi a, tPointi b, tPointi c )
{
        return  Area2( a, b, c ) > 0;
}

bool    LeftOn( tPointi a, tPointi b, tPointi c )
{
        return  Area2( a, b, c ) >= 0;
}

bool    Collinear( tPointi a, tPointi b, tPointi c )
{
        return  Area2( a, b, c ) == 0;
}

/*
        Puts a - b into c.
*/
void	SubVec( tPointi a, tPointi b, tPointi c )
{
        int     i;
        
        for( i = 0; i < DIM; i++ )
                c[i] = a[i] - b[i];
}

/*
        Returns the dot product of the two input vectors.
*/
int     Dot( tPointi a, tPointi b )
{
        int     i;
        int     sum = 0;

        for( i = 0; i < DIM; i++ )
                sum += sum + a[i] * b[i];
        
        return  sum;
}

/*
        Returns the square of the length of the vector p.
*/
int     Length2( tPointi p )
{
        return  Dot( p, p );
}

/*
	Implements a = b, assignment of points/vectors.
	Assignment between arrays is not possible in C.
*/
void	PointAssign( tPointi a, tPointi b )
{
	int	i;

	for ( i = 0; i < DIM; i++ )
		a[i] = b[i];
}
void	PrintPoint( tPointi p )
{
	int	i;

/*	putchar('('); */
	for ( i = 0; i < DIM; i++ ) {
		printf("%d", p[i]);
		if ( i != DIM-1 ) putchar(' ');
	}
/*	putchar(')');  */
}

/*
	Reads in the coordinates of the vertices of a polygon from stdin,
	puts them into P, and returns n, the number of vertices.
	Formatting conventions: etc.
*/
int	ReadPoly( tPolygoni P )
{
	int	n = 0;

/*	printf("Polygon:\n");  */
/*	printf("  i   x   y\n"); */
	while ( (n < PMAX) && (scanf("%d %d",&P[n][0],&P[n][1]) != EOF) ) {
	/*	printf("%3d%4d%4d\n", n, P[n][0], P[n][1]); */
		++n;
	}
	if (n < PMAX)
	/*	printf("n = %3d vertices read\n",n)*/;
	else	printf("Error in read_poly:  too many points; max is %d\n", PMAX);
	/* putchar('\n'); */

	return	n;
}

void	PrintPoly( int n, tPolygoni P )
{
	int	i;

/*	printf("Polygon:\n");*/
/*	printf("  i   x   y\n"); */
/*	for( i = 0; i < n; i++ )
		printf("%4d%4d\n", P[i][0], P[i][1]);
*/
}