Function circumcircle

jni/venus/region_operation.cpp:185–202

Let (h,k) be the coordinates of the center of the circle, and r its radius. Then the equation of the circle is: (x-h)^2 + (y-k)^2 = r^2 Since the three points all lie on the circle, their coordinates will satisfy this equation. That gives you three equations: (x1-h)^2 + (y1-k)^2 = r^2 (x2-h)^2 + (y2-k)^2 = r^2 (x3-h)^2 + (y3-k)^2 = r^2 in the three unknowns h, k, and r. To solv

	By means of solving the matrix equation above, we get the circumcircle center point O.
*/
static Point2f circumcircle(const Point2f& A, const Point2f& B, const Point2f& C)
{
	float AB_x = B.x - A.x, AC_x = C.x - A.x;
	float AB_y = B.y - A.y, AC_y = C.y - A.y;

//	[ AB_x  AB_y ] [ x ] = [ AB_x*AB_mx + AB_y*AB_my ]
//	[ AC_x  AC_y ] [ y ] = [ AC_x*AC_mx + AC_y*AC_my ]

	float denorm = AB_x * AC_y - AC_x * AB_y;
	assert(std::abs(denorm) > std::numeric_limits<float>::epsilon());

	float M_x = AB_x*(B.x + A.x)/2 + AB_y*(B.y + A.y)/2;
	float M_y = AC_x*(C.x + A.x)/2 + AC_y*(C.y + A.y)/2;

	float x = (M_x*AC_y - M_y*AB_y)/denorm;
	float y = (AB_x*M_y - AC_x*M_x)/denorm;
	return Point2f(x, y);
}

/*
	Cubic interpolation http://www.paulinternet.nl/?page=bicubic