// find intersection between two 2D segments
QVector<GLC_Point2d> glc::findIntersection(const GLC_Point2d& s1p1, const GLC_Point2d& s1p2, const GLC_Point2d& s2p1, const GLC_Point2d& s2p2)
{
const GLC_Vector2d D0= s1p2 - s1p1;
const GLC_Vector2d D1= s2p2 - s2p1;
// The QVector of result points
QVector<GLC_Point2d> result;
const GLC_Vector2d E(s2p1 - s1p1);
double kross= D0 ^ D1;
double sqrKross= kross * kross;
const double sqrLen0= D0.getX() * D0.getX() + D0.getY() * D0.getY();
const double sqrLen1= D1.getX() * D1.getX() + D1.getY() * D1.getY();
// Test if the line are nor parallel
if (sqrKross > (EPSILON * sqrLen0 * sqrLen1))
{
const double s= (E ^ D1) / kross;
if ((s < 0.0) || (s > 1.0))
{
// Intersection of lines is not a point on segment s1p1 + s * DO
return result; // Return empty QVector
}
const double t= (E ^ D0) / kross;
if ((t < 0.0) || (t > 1.0))
{
// Intersection of lines is not a point on segment s2p1 + t * D1
return result; // Return empty QVector
}
// Intersection of lines is a point on each segment
result << (s1p1 + (D0 * s));
return result; // Return a QVector of One Point
}
// Lines of the segments are parallel
const double sqrLenE= E.getX() * E.getX() + E.getY() * E.getY();
kross= E ^ D0;
sqrKross= kross * kross;
if (sqrKross > (EPSILON * sqrLen0 * sqrLenE))
{
// Lines of the segments are different
return result; // Return empty QVector
}
// Lines of the segments are the same. Need to test for overlap of segments.
const double s0= (D0 * E) / sqrLen0;
const double s1= (D0 * D1) / sqrLen0;
const double sMin= qMin(s0, s1);
const double sMax= qMax(s0, s1);
QVector<double> overlaps= findIntersection(0.0, 1.0, sMin, sMax);
const int iMax= overlaps.size();
for (int i= 0; i < iMax; ++i)
{
result.append(s1p1 + (D0 * overlaps[i]));
}
return result;
}
// return true if there is an intersection between 2 segments
bool glc::isIntersected(const GLC_Point2d& s1p1, const GLC_Point2d& s1p2, const GLC_Point2d& s2p1, const GLC_Point2d& s2p2)
{
const GLC_Vector2d D0= s1p2 - s1p1;
const GLC_Vector2d D1= s2p2 - s2p1;
const GLC_Vector2d E(s2p1 - s1p1);
double kross= D0 ^ D1;
double sqrKross= kross * kross;
const double sqrLen0= D0.getX() * D0.getX() + D0.getY() * D0.getY();
const double sqrLen1= D1.getX() * D1.getX() + D1.getY() * D1.getY();
// Test if the line are nor parallel
if (sqrKross > (EPSILON * sqrLen0 * sqrLen1))
{
const double s= (E ^ D1) / kross;
if ((s < 0.0) || (s > 1.0))
{
// Intersection of lines is not a point on segment s1p1 + s * DO
return false;
}
const double t= (E ^ D0) / kross;
if ((t < 0.0) || (t > 1.0))
{
// Intersection of lines is not a point on segment s2p1 + t * D1
return false;
}
// Intersection of lines is a point on each segment
return true;
}
// Lines of the segments are parallel
const double sqrLenE= E.getX() * E.getX() + E.getY() * E.getY();
kross= E ^ D0;
sqrKross= kross * kross;
if (sqrKross > (EPSILON * sqrLen0 * sqrLenE))
{
// Lines of the segments are different
return false;
}
// Lines of the segments are the same. Need to test for overlap of segments.
const double s0= (D0 * E) / sqrLen0;
const double s1= s0 + (D0 * D1) / sqrLen0;
const double sMin= qMin(s0, s1);
const double sMax= qMax(s0, s1);
if (findIntersection(0.0, 1.0, sMin, sMax).size() == 0) return false; else return true;
}
// return true if there is an intersection between a ray and a segment
bool glc::isIntersectedRaySegment(const GLC_Point2d& s1p1, const GLC_Vector2d& s1p2, const GLC_Point2d& s2p1, const GLC_Point2d& s2p2)
{
const GLC_Vector2d D0= s1p2 - s1p1;
const GLC_Vector2d D1= s2p2 - s2p1;
const GLC_Vector2d E(s2p1 - s1p1);
double kross= D0 ^ D1;
double sqrKross= kross * kross;
const double sqrLen0= D0.getX() * D0.getX() + D0.getY() * D0.getY();
const double sqrLen1= D1.getX() * D1.getX() + D1.getY() * D1.getY();
// Test if the line are nor parallel
if (sqrKross > (EPSILON * sqrLen0 * sqrLen1))
{
const double s= (E ^ D1) / kross;
if ((s < 0.0))
{
// Intersection of lines is not a point on segment s1p1 + s * DO
return false;
}
const double t= (E ^ D0) / kross;
if ((t < 0.0) || (t > 1.0))
{
// Intersection of lines is not a point on segment s2p1 + t * D1
return false;
}
// Intersection of lines is a point on each segment
return true;
}
// Lines of the segments are parallel
const double sqrLenE= E.getX() * E.getX() + E.getY() * E.getY();
kross= E ^ D0;
sqrKross= kross * kross;
if (sqrKross > (EPSILON * sqrLen0 * sqrLenE))
{
// Lines of are different
return false;
}
else return true;
}
GLC_Vector2d round(const GLC_Vector2d& vector)
{
GLC_Vector2d subject(glc::round(vector.getX()), glc::round(vector.getY()));
return subject;
}
bool glc::compare(const GLC_Vector2d& v1, const GLC_Vector2d& v2)
{
bool compareResult= (qAbs(v1.getX() - v2.getX()) <= comparedPrecision);
return compareResult && (qAbs(v1.getY() - v2.getY()) <= comparedPrecision);
}
