function area(n){var r,e=-1,t=n.length,o=n[t-1],l=0;while(++e<t){r=o;o=n[e];l+=r[1]*o[0]-r[0]*o[1]}return l/2}function centroid(n){var r,e,t=-1,o=n.length,l=0,u=0,a=n[o-1],h=0;while(++t<o){r=a;a=n[t];h+=e=r[0]*a[1]-a[0]*r[1];l+=(r[0]+a[0])*e;u+=(r[1]+a[1])*e}return h*=3,[l/h,u/h]}function cross(n,r,e){return(r[0]-n[0])*(e[1]-n[1])-(r[1]-n[1])*(e[0]-n[0])}function lexicographicOrder(n,r){return n[0]-r[0]||n[1]-r[1]}function computeUpperHullIndexes(n){const r=n.length,e=[0,1];let t,o=2;for(t=2;t<r;++t){while(o>1&&cross(n[e[o-2]],n[e[o-1]],n[t])<=0)--o;e[o++]=t}return e.slice(0,o)}function hull(n){if((e=n.length)<3)return null;var r,e,t=new Array(e),o=new Array(e);for(r=0;r<e;++r)t[r]=[+n[r][0],+n[r][1],r];t.sort(lexicographicOrder);for(r=0;r<e;++r)o[r]=[t[r][0],-t[r][1]];var l=computeUpperHullIndexes(t),u=computeUpperHullIndexes(o);var a=u[0]===l[0],h=u[u.length-1]===l[l.length-1],i=[];for(r=l.length-1;r>=0;--r)i.push(n[t[l[r]][2]]);for(r=+a;r<u.length-h;++r)i.push(n[t[u[r]][2]]);return i}function contains(n,r){var e,t,o=n.length,l=n[o-1],u=r[0],a=r[1],h=l[0],i=l[1],c=false;for(var s=0;s<o;++s){l=n[s],e=l[0],t=l[1];t>a!==i>a&&u<(h-e)*(a-t)/(i-t)+e&&(c=!c);h=e,i=t}return c}function length(n){var r,e,t=-1,o=n.length,l=n[o-1],u=l[0],a=l[1],h=0;while(++t<o){r=u;e=a;l=n[t];u=l[0];a=l[1];r-=u;e-=a;h+=Math.hypot(r,e)}return h}export{area as polygonArea,centroid as polygonCentroid,contains as polygonContains,hull as polygonHull,length as polygonLength};