/**
* Is the given polygon completely encosed by this one
* @param poly Another polygon
* @return True if the given polygon is enclosed by this, false otherwise
*/
bool ConvexPolygon::contains(const ConvexPolygon &poly) const {
// Basically just have to test if each point is inside us, this could be
// slow
const Vertex2D *current = poly.head();
for (size_t i = 0; i < poly.numVertices(); ++i) {
if (!this->contains(*current))
return false;
current = current->next();
}
return true;
}
/**
* Compute the polygon that defines the intersection between two
* other concex polygons using the method of chasing edges
* @param P :: A reference to the first polygon
* @param Q :: A reference to the second polygon
* @returns A new polygon defining the region of intersection
*/
ConvexPolygon intersectionByORourke(const ConvexPolygon &P, const ConvexPolygon &Q)
{
const size_t nverts_p(P.numVertices()), nverts_q(Q.numVertices());
const V2D origin(0.0,0.0);
size_t count_p(0), count_q(0); // Number of vertices visited
unsigned int inflag(Unknown);
bool firstPoint(true);
// Avoid vertex list reallocations
Vertex2DList originAB(3);
originAB[0] = origin;
Vertex2DList aHB(3);
Vertex2DList bHA(3);
// Final list
Vertex2DList intersectList;
do
{
size_t pi(0), pim1(0), qi(0), qim1(0);
// Compute a vector between the previous point in the direction of the next
pim1 = (pi + nverts_p - 1) % nverts_p;
qim1 = (qi + nverts_q - 1) % nverts_q;
V2D edge_p = P[pi] - P[pim1];
V2D edge_q = Q[qi] - Q[qim1];
// Orientations
originAB[1] = edge_p;
originAB[2] = edge_q;
int cross = ConvexPolygon(originAB).orientation();
aHB[0] = Q[qim1];
aHB[1] = Q[qi];
aHB[2] = P[pi];
int aHB_dir = ConvexPolygon(aHB).orientation();
bHA[0] = P[pim1];
bHA[1] = P[pi];
bHA[2] = Q[qi];
int bHA_dir = ConvexPolygon(bHA).orientation();
// Test for line intersection
V2D intersect;
unsigned int type = intersection(P[pim1],P[pi], Q[qim1],Q[qi], intersect);
if( type == 1 || type == 2 )
{
if( inflag == Unknown && firstPoint )
{
count_p = count_q = 0;
firstPoint = false;
}
if( aHB_dir > 0 ) inflag = Pin;
else if( bHA_dir > 0 ) inflag = Qin;
else {};
intersectList.insert(intersect);
}
// Deal with advance of indices
/* Special case: A & B overlap and oppositely oriented. */
if ( type == 3 && edge_p.scalar_prod(edge_q) < 0.0 )
{
throw std::runtime_error("Single segment intersection");
}
/* Special case: A & B parallel and separated. */
else if ( cross == 0 && (aHB_dir < 0) && (bHA_dir < 0) )
{
throw std::runtime_error("AxB=0 and both are left-hand oriented so no intersection");
}
/* Special case: A & B collinear. */
else if ( cross == 0 && (aHB_dir == 0) && (bHA_dir == 0) )
{
/* Advance but do not output point. */
if ( inflag == Pin )
qi = advanceVertex(qi, count_q, nverts_q, false, Q[qi], intersectList);
else
pi = advanceVertex(pi, count_p, nverts_p, false, P[pi], intersectList);
}
/* Generic cases. */
else if ( cross >= 0 )
{
if ( bHA_dir > 0)
pi = advanceVertex(pi, count_p, nverts_p, inflag == Pin, P[pi], intersectList);
else
qi = advanceVertex(qi, count_q, nverts_q, inflag == Qin, Q[qi], intersectList);
}
else /* if ( cross < 0 ) */
{
if ( aHB_dir > 0)
qi = advanceVertex(qi, count_q, nverts_q, inflag == Qin, Q[qi], intersectList);
else
pi = advanceVertex(pi, count_p, nverts_p, inflag == Pin, P[pi], intersectList);
}
}
while( (count_p < nverts_p || count_q < nverts_q) &&
(count_p < 2*nverts_p) && (count_q < 2*nverts_q) );
if( intersectList.size() < 3 )
{
throw std::runtime_error("Intersection points do not form a bounded polygon.");
}
return ConvexPolygon(intersectList);
}
