bool lineSegmentIntersection(
const POINT& _p1,
const POINT& _p2,
const POINT& _p3,
const POINT& _p4,
POINT& _point)
{
typedef typename POINT::Scalar scalar_type;
// Store the values for fast access and easy
// equations-to-code conversion
scalar_type x1 = _p1.x(), x2 = _p2.x(), x3 = _p3.x(), x4 = _p4.x();
scalar_type y1 = _p1.y(), y2 = _p2.y(), y3 = _p3.y(), y4 = _p4.y();
scalar_type d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
// If d is zero, there is no intersection
if (d == 0) return false;
// Get the x and y
scalar_type pre = (x1*y2 - y1*x2), post = (x3*y4 - y3*x4);
scalar_type x = ( pre * (x3 - x4) - (x1 - x2) * post ) / d;
scalar_type y = ( pre * (y3 - y4) - (y1 - y2) * post ) / d;
// Check if the x and y coordinates are within both lines
if ( x < std::min(x1, x2) || x > std::max(x1, x2) ||
x < std::min(x3, x4) || x > std::max(x3, x4) ) return false;
if ( y < std::min(y1, y2) || y > std::max(y1, y2) ||
y < std::min(y3, y4) || y > std::max(y3, y4) ) return false;
// Return the point of intersection
_point(0) = x; _point(1) = y;
return true;
}
typename POINT::Scalar determinant(
const POINT& _a,
const POINT& _b,
const POINT& _c)
{
return (_b.x() * _c.y() + _a.x() * _b.y() + _a.y()*_c.x()) -
(_a.y() * _b.x() + _b.y() * _c.x() + _a.x()*_c.y());
}
void rotatePoint(const ORIGIN& _o, ANGLE _theta, POINT& _p)
{
auto _d = _p - _o;
_p.x() = cos(_theta) * _d.x() - sin(_theta) * _d.y() + _o.x();
_p.y() = sin(_theta) * _d.x() + cos(_theta) * _d.y() + _o.x();
}
static inline
double inner (const POINT &a, const POINT &b) {
return CGAL::to_double (a.x()*b.x() + a.y()*b.y() + a.z()*b.z());
}
