void clip_polygon_by_half_plane(
const Polygon2d& P,
const vec2& q1,
const vec2& q2,
Polygon2d& result,
bool invert
) {
result.clear() ;
if(P.size() == 0) {
return ;
}
if(P.size() == 1) {
if(point_is_in_half_plane(P[0], q1, q2, invert)) {
result.push_back(P[0]) ;
}
return ;
}
vec2 prev_p = P[P.size() - 1] ;
Sign prev_status = point_is_in_half_plane(
prev_p, q1, q2, invert
) ;
for(unsigned int i=0; i<P.size(); i++) {
vec2 p = P[i] ;
Sign status = point_is_in_half_plane(
p, q1, q2, invert
) ;
if(
status != prev_status &&
status != ZERO &&
prev_status != ZERO
) {
vec2 intersect ;
if(intersect_segments(prev_p, p, q1, q2, intersect)) {
result.push_back(intersect) ;
} else {
}
}
switch(status) {
case NEGATIVE:
break ;
case ZERO:
result.push_back(p) ;
break ;
case POSITIVE:
result.push_back(p) ;
break ;
}
prev_p = p ;
prev_status = status ;
}
}
void minimum_area_enclosing_rectangle(
const Polygon2d& PP,
vec2& S, vec2& T
) {
// Note: this implementation has O(n2) complexity :-(
// (where n is the number of vertices in the convex hull)
// If this appears to be a bottleneck, use a smarter
// implementation with better complexity.
Polygon2d P ;
convex_hull(PP, P) ;
int N = P.size() ;
// Add the first vertex at the end of P
P.push_back(P[0]) ;
double min_area = Numeric::big_double ;
for(int i=1; i<=N; i++) {
vec2 Si = P[i] - P[i-1] ;
if( ( Si.length2() ) < 1e-20) {
continue ;
}
vec2 Ti(-Si.y, Si.x) ;
normalize(Si) ;
normalize(Ti) ;
double s0 = Numeric::big_double ;
double s1 = -Numeric::big_double ;
double t0 = Numeric::big_double ;
double t1 = -Numeric::big_double ;
for(int j=1; j<N; j++) {
vec2 D = P[j] - P[0] ;
double s = dot(Si, D) ;
s0 = gx_min(s0, s) ;
s1 = gx_max(s1, s) ;
double t = dot(Ti, D) ;
t0 = gx_min(t0, t) ;
t1 = gx_max(t1, t) ;
}
double area = (s1 - s0) * (t1 - t0) ;
if(area < min_area) {
min_area = area ;
if((s1 - s0) < (t1 - t0)) {
S = Si ;
T = Ti ;
} else {
S = Ti ;
T = Si ;
}
}
}
}
void convex_hull(const Polygon2d& PP, Polygon2d& result) {
result.clear() ;
int n = PP.size() ;
vec2* P = new vec2[n+1] ;
{ for(int i=0; i<n; i++) {
P[i] = PP[i] ;
}}
int u = make_chain(P, n, cmpl);
P[n] = P[0];
int ch = u+make_chain(P+u, n-u+1, cmph);
{for(int i=0; i<ch; i++) {
result.push_back(P[i]) ;
}}
delete[] P ;
}