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R2Convex.cpp
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R2Convex.cpp
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#include "R2.h"
ConvexHull::ConvexHull(const R2Point* a, int n): Points(0),Convex(0),numConvex(0),numPoints(n) {
if(a != 0 && n != 0) {
double Xmin = a[0].x,Xmax = a[0].x,c = 0;
int nminX = 0,nmaxX = 0,l = 0,j = 0,i = 0,k = 0,q,p = 0; R2Vector e1(0,1),e2(0,-1);
int *convex;
convex = new int[numPoints + 1];
for(i = 0; i < numPoints; i++) {
if(a[i].x < Xmin) { Xmin = a[i].x; nminX = i;}
if(a[i].x > Xmax) { Xmax = a[i].x; nmaxX = i;}
} convex[0] = nminX; q = nminX + 1; numConvex = 1;
while(q != nminX) {
if(numConvex - 1 == 0) q = nminX;
if(q == nmaxX) l = 1;
for(i = 0; i < numPoints; i++) {
switch(l) {
case 0 :
if(i != q && ((k == 0||(c < e1.cos(a[i] - a[q]))) && a[i] > a[q])) { c = e1.cos(a[i] - a[q]); p = i; ++k;}
break;
case 1 :
if(i != q && ((j == 0||(c < e2.cos(a[i] - a[q]))) && a[i] < a[q])) { c = e2.cos(a[i] - a[q]); p = i; ++j;}
break;
}
} k = 0; j = 0; convex[numConvex] = p; q = p; ++numConvex;
} --numConvex; k = 0;
Convex = new R2Point[numConvex];
for(i = 0; i < numConvex; i++) Convex[i] = a[convex[i]];
i = 0; if(numPoints - numConvex > 0) { Points = new R2Point[numPoints - numConvex];
for(j = 0; j < numPoints; j++) {
for(l = 0; l < numConvex; l++) { if(j != convex[l]) ++k; }
if(k == numConvex) { Points[i] = a[j]; i++; }
k = 0;
} }
delete[] convex;
}
}
void ConvexHull::AddPoint(const R2Point& a) {
//if(numPoints == MAX_POINTS) throw(1);
for(int i = 0; i < numPoints; i++) { if(i < numConvex) { if(a == Convex[i]) return;} else { if(a == Points[i - numConvex]) return; } }
R2Point *m;
m = new R2Point[numPoints + 1];
for(int i = 0; i < numPoints; i++) { if(i < numConvex) m[i] = Convex[i]; else m[i] = Points[i - numConvex]; }
m[numPoints] = a;
ConvexHull r(m, numPoints + 1);
*this = r;
delete[] m;
}
void ConvexHull::DeletePoint(const R2Point& a) {
if(numConvex == 0) throw(1);
int i,j,k = 0,t = 0,n = numConvex,n1 = numPoints - numConvex;
for(i = 0; i < numPoints; i++) { if(i < numConvex) {
if(a != Convex[i]) ++k; else n = i;
}
else {
if(Points != 0 && a != Points[i - numConvex]) ++t ; else n1 = i - numConvex;
}
}
if(k == numConvex && t == numPoints - numConvex) throw(2);
if(numConvex > 1) {
R2Point *m;
m = new R2Point[numPoints - 1];
for(i = 0, j = 0; i < numPoints; i++) { if(i < numConvex && i != n) { m[j] = Convex[i]; j++;}
if(i >= numConvex) {
if(Points != 0 && i - numConvex != n1) { m[j] = Points[i - numConvex]; j++; }
}
}
ConvexHull r(m, numPoints - 1);
*this = r;
delete[] m;
}
else { ConvexHull r; *this = r; }
}
bool ConvexHull::Inside(const R2Point& a) {
if(numConvex < 3) throw(3);
int j = 0;
for(int i = 0; i < numConvex; i++) {
if((R2Point::signed_area(iterConv(i),iterConv(i + 1), iterConv(i - 1))*R2Point::signed_area(iterConv(i),iterConv(i + 1), a)) > R2_EPSILON) ++j;
}
if(j == numConvex) return true;
else return false;
}
bool ConvexHull::Inside(const R2Point& a) const {
if(numConvex < 3) throw(3);
int j = 0;
for(int i = 0; i < numConvex; i++) {
if((R2Point::signed_area(iterConv(i),iterConv(i + 1), iterConv(i - 1))*R2Point::signed_area(iterConv(i),iterConv(i + 1), a)) > R2_EPSILON) ++j;
}
if(j == numConvex) return true;
else return false;
}
bool ConvexHull::On_Convex(const R2Point& a) {
if(numConvex < 2) throw(3);
for(int i = 0; i < numConvex; i++) {
if(a.between(iterConv(i),iterConv(i + 1))) return true;
}
return false;
}
bool ConvexHull::On_Convex(const R2Point& a) const {
if(numConvex < 2) throw(3);
for(int i = 0; i < numConvex; i++) {
if(a.between(iterConv(i),iterConv(i + 1))) return true;
}
return false;
}
double ConvexHull::square() {
if(numConvex < 3) throw(3);
double S = 0;
for(int i = 1; i < numConvex - 1; i++) {
S += R2Point::area(iterConv(0),iterConv(i), iterConv(i + 1));
}
return S;
}
double ConvexHull::perimeter() {
if(numConvex < 2) throw(3);
double P = 0;
for(int i = 0; i < numConvex; i++) P += R2Point::distance(iterConv(i),iterConv(i + 1));
return P;
}
//============================ intersection of Convex hulls ========================================
ConvexHull ConvexHull::intersection(const ConvexHull& a,const ConvexHull& b) {
int n = 0; //ConvexHull r;
R2Point *m = 0,p;
for(int i = 0; i < a.numConvex; i++) {
if(b.Inside(a.iterConv((i)))||b.On_Convex(a.iterConv(i))) n++;
}
for(int i = 0; i < b.numConvex; i++) {
if(a.Inside(b.iterConv(i))||a.On_Convex(b.iterConv(i))) n++;
}
for(int i = 0; i < a.numConvex; i++) {
for(int j = 0; j < b.numConvex; j++) {
if(fabs(R2Vector::signed_area(a.iterConv(i + 1) - a.iterConv(i),b.iterConv(j) - b.iterConv(j + 1))) > R2_EPSILON) {
p = a.iterConv(i) + (a.iterConv(i + 1) - a.iterConv(i))*(R2Vector::signed_area(b.iterConv(j) - a.iterConv(i),b.iterConv(j) - b.iterConv(j + 1))/R2Vector::signed_area(a.iterConv(i + 1) - a.iterConv(i),b.iterConv(j) - b.iterConv(j + 1)));
if(p.between(a.iterConv(i),a.iterConv(i + 1)) && p.between(b.iterConv(j),b.iterConv(j + 1))) n++;
}
}
}
if(n > 0) { m = new R2Point[n]; n = 0;
for(int i = 0; i < a.numConvex; i++) {
if(b.Inside(a.iterConv(i))||b.On_Convex(a.iterConv(i))) {m[n] = a.iterConv(i); n++;}
}
for(int i = 0; i < b.numConvex; i++) {
if(a.Inside(b.iterConv(i))||a.On_Convex(b.iterConv(i))) {m[n] = b.iterConv(i); n++;}
}
for(int i = 0; i < a.numConvex; i++) {
for(int j = 0; j < b.numConvex; j++) {
if(fabs(R2Vector::signed_area(a.iterConv(i + 1) - a.iterConv(i),b.iterConv(j) - b.iterConv(j + 1))) > R2_EPSILON) {
p = a.iterConv(i) + (a.iterConv(i + 1) - a.iterConv(i))*(R2Vector::signed_area(b.iterConv(j) - a.iterConv(i),b.iterConv(j) - b.iterConv(j + 1))/R2Vector::signed_area(a.iterConv(i + 1) - a.iterConv(i),b.iterConv(j) - b.iterConv(j + 1)));
if(p.between(a.iterConv(i),a.iterConv(i + 1)) && p.between(b.iterConv(j),b.iterConv(j + 1))) {m[n] = p; n++; }
}
}
}
} ConvexHull r(m,n); if(n > 0) delete[] m;
return r;
}
//==================================================================================================
//if(i != q) v(a[i] - a[q]); //C=-1*B*nodeY[nminX]-A*nodeX[nminX]; A = a[i].y - a[q].y; B = a[q].x - a[i].x; cos < A/sqrt(A*A+B*B) cos = A/sqrt(A*A+B*B);