/**
* Classify a point with respect to an edge, i.e. left, right of edge etc.
* @param pt :: A point as V2D
* @param edge :: A test edge object
* @returns The type of the point
*/
PointClassification classify(const V2D &pt, const PolygonEdge &edge) {
V2D p2 = pt;
const V2D &a = edge.direction();
V2D b = p2 - edge.start();
double sa = a.X() * b.Y() - b.X() * a.Y();
if (sa > 0.0) {
return OnLeft;
}
if (sa < 0.0) {
return OnRight;
}
if ((a.X() * b.X() < 0.0) || (a.Y() * b.Y() < 0.0)) {
return Behind;
}
if (a.norm() < b.norm()) {
return Beyond;
}
if (edge.start() == p2) {
return Origin;
}
if (edge.end() == p2) {
return Destination;
}
return Between;
}
/**
* Insert a new vertex.
* @param pt A new point for the shape
*/
void ConvexPolygon::insert(const V2D &pt) {
m_vertices.push_back(pt);
// Update extrema
m_minX = std::min(m_minX, pt.X());
m_maxX = std::max(m_maxX, pt.X());
m_minY = std::min(m_minY, pt.Y());
m_maxY = std::max(m_maxY, pt.Y());
}
/**
* Compute the area of a triangle given by 3 points (a,b,c) using the
* convention in "Computational Geometry in C" by J. O'Rourke
* @param a :: The first vertex in the set
* @param b :: The second vertex in the set
* @param c :: The third vertex in the set
*/
double ConvexPolygon::triangleArea(const V2D &a, const V2D &b,
const V2D &c) const {
return 0.5 * (b.X() - a.X()) * (c.Y() - a.Y()) -
(c.X() - a.X()) * (b.Y() - a.Y());
}
