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Chilleesimonlindholm
Chillee
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simonlindholm
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Updated inPolygon (#81)
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9 files changed

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‎content/geometry/InsidePolygon.h‎

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/**
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* Author: Victor Lecomte, chilli
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* Date: 2019-04-26
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* License: CC0
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* Source: https://vlecomte.github.io/cp-geo.pdf
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* Description: Returns true if p lies within the polygon. If strict is true,
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* it returns false for points on the boundary. The algorithm uses
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* products in intermediate steps so watch out for overflow.
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* Time: O(n)
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* Status: fuzz-tested and Kattis problem pointinpolygon
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* Usage:
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* vector<P> v = {P{4,4}, P{1,2}, P{2,1}};
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* bool in = inPolygon(v, P{3, 3}, false);
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*/
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#pragma once
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#include "Point.h"
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#include "onSegment.h"
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#include "SegmentDistance.h"
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template<class P>
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bool inPolygon(vector<P> &p, P a, bool strict = true) {
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int cnt = 0, n = sz(p);
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rep(i,0,n) {
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P q = p[(i + 1) % n];
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if (onSegment(p[i], q, a)) return !strict;
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//or: if (segDist(p[i], q, a) <= eps) return !strict;
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cnt ^= ((a.y<p[i].y) - (a.y<q.y)) * a.cross(p[i], q) > 0;
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}
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return cnt;
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}

‎content/geometry/chapter.tex‎

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@@ -19,7 +19,7 @@ \section{Circles}
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\kactlimport{MinimumEnclosingCircle.h}
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\section{Polygons}
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\kactlimport{insidePolygon.h}
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\kactlimport{InsidePolygon.h}
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\kactlimport{PolygonArea.h}
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\kactlimport{PolygonCenter.h}
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\kactlimport{PolygonCut.h}

‎content/geometry/insidePolygon.h‎

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This file was deleted.

‎content/geometry/onSegment.h‎

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@@ -3,7 +3,8 @@
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* Date: 2019-04-26
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* License: CC0
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* Source: https://vlecomte.github.io/cp-geo.pdf
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* Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point<ll> where overflow is an issue. Use \texttt{(segDist(s,e,p)<=epsilon)} instead when using Point<double>.
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* Description: Returns true iff p lies on the line segment from s to e.
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* Use \texttt{(segDist(s,e,p)<=epsilon)} instead when using Point<double>.
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* Status:
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*/
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#pragma once

‎fuzz-tests/geometry/PointInsideHull.cpp‎

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@@ -12,7 +12,7 @@ typedef vector<int> vi;
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#include "../../content/geometry/ConvexHull.h"
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#include "../../content/geometry/PointInsideHull.h"
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#include "../../content/geometry/insidePolygon.h"
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#include "../../content/geometry/InsidePolygon.h"
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int main() {
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rep(it,0,100000) {
@@ -25,8 +25,8 @@ int main() {
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int x = rand() % 22 - 11;
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int y = rand() % 22 - 11;
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P p{x,y};
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assert(insidePolygon(all(ps2), p, true) == (insideHull(ps2, p) == 2));
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assert(insidePolygon(all(ps2), p, false) == (insideHull(ps2, p) >= 1));
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assert(inPolygon(all(ps2), p, true) == (insideHull(ps2, p) == 2));
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assert(inPolygon(all(ps2), p, false) == (insideHull(ps2, p) >= 1));
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}
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}
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}

‎fuzz-tests/geometry/PolygonArea.cpp‎

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@@ -12,7 +12,7 @@ typedef vector<int> vi;
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#include "../../content/geometry/PolygonArea.h"
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#include "../../content/geometry/PolygonCenter.h"
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#include "../../content/geometry/insidePolygon.h"
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#include "../../content/geometry/InsidePolygon.h"
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int main() {
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srand((int)time(0));
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double y = rand() / (RAND_MAX + 1.0);
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x *= 10;
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y *= 10;
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if (!insidePolygon(all(ps), P{x,y}, true)) continue;
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if (!inPolygon(ps, P{x,y}, true)) continue;
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count++;
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su = su + P{x,y};
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}

‎fuzz-tests/geometry/PolygonCut.cpp‎

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@@ -13,7 +13,7 @@ typedef vector<int> vi;
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#include "../../content/geometry/PolygonArea.h"
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#include "../../content/geometry/PolygonCut.h"
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#include "../../content/geometry/sideOf.h"
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#include "../../content/geometry/insidePolygon.h"
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#include "../../content/geometry/InsidePolygon.h"
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#include "../../content/geometry/SegmentIntersection.h"
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typedef Point<double> P;
@@ -41,7 +41,7 @@ int main() {
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rep(it,0,ITS) {
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double x = rand() / (RAND_MAX + 1.0) * 10 - 5;
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double y = rand() / (RAND_MAX + 1.0) * 10 - 5;
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if (!insidePolygon(all(ps), P{x,y}, true)) continue;
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if (!inPolygon(ps, P{x,y}, true)) continue;
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if (sideOf(p, q, P{x,y}) > 0) continue;
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count++;
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}

‎fuzz-tests/geometry/insidePolygon.cpp‎

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#include <bits/stdc++.h>
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using namespace std;
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#define rep(i, a, b) for(int i = a; i < int(b); ++i)
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#define trav(a, v) for(auto& a : v)
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#define all(x) x.begin(), x.end()
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#define sz(x) (int)(x).size()
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typedef long long ll;
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typedef pair<int, int> pii;
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typedef vector<int> vi;
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const double EPS =1e-8;
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#include "../utilities/genPolygon.h"
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#include "../../content/geometry/InsidePolygon.h"
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namespace old {
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#include "../../content/geometry/onSegment.h"
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#include "../../content/geometry/SegmentDistance.h"
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template<class It, class P>
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bool insidePolygon(It begin, It end, const P& p,
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bool strict = true) {
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int n = 0; //number of isects with line from p to (inf,p.y)
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for (It i = begin, j = end-1; i != end; j = i++) {
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//if p is on edge of polygon
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if (onSegment(*i, *j, p)) return !strict;
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//or: if (segDist(*i, *j, p) <= epsilon) return !strict;
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//increment n if segment intersects line from p
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n += (max(i->y,j->y) > p.y && min(i->y,j->y) <= p.y &&
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((*j-*i).cross(p-*i) > 0) == (i->y <= p.y));
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}
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return n&1; //inside if odd number of intersections
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}
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}
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typedef Point<double> P;
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ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; }
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bool eq(P a, P b) {
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return (a-b).dist()<EPS;
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}
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const int NUMPOLY=100;
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const int PTPERPOLY=100;
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void test(int numPts, int range) {
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rep(i,0,NUMPOLY) {
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vector<P> poly;
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rep(j,0, numPts)
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poly.push_back(P(rand()%range, rand()%range));
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poly = genPolygon(poly);
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rep(i,0,PTPERPOLY){
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P p(rand()%range, rand()%range);
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assert(inPolygon(poly, p, true) == old::insidePolygon(all(poly), p, true));
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assert(inPolygon(poly, p, false) == old::insidePolygon(all(poly), p, false));
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}
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}
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}
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int main() {
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test(20,5);
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test(1001,100);
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test(1000,1000);
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cout<<"Tests passed!"<<endl;
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}

‎fuzz-tests/utilities/genPolygon.h‎

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#pragma once
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// Translated from Python code posted here: https://codeforces.com/blog/entry/63058?#comment-472788
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// May generate polygons with colinear points. Won't generate polygons with duplicate points.
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#include "../../content/geometry/Point.h"
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mt19937_64 rng(time(0));
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template<class P> pair<bool, vector<P>> conquer(vector<P> pts, int depth) {
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if (depth>100) {
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return {false, {}};
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}
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if (sz(pts) <= 2) return {true,pts};
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if (sz(pts) == 3) {
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swap(pts[1], pts[2]);
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return {true,pts};
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}
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uniform_int_distribution<int> uni(2, sz(pts)-1);
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int divideId = uni(rng);
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P p1 = pts[divideId];
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uniform_real_distribution<> uniFloat(0.01, 0.99);
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double divideK = uniFloat(rng);
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P p2(divideK*(pts[1].x-pts[0].x) + pts[0].x, divideK*(pts[1].y - pts[0].y) + pts[0].y);
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vector<double> line = {p2.y - p1.y, p1.x - p2.x, -p1.x*p2.y + p1.y*p2.x};
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int idx0 = ((line[0]*pts[0].x + line[1]*pts[0].y + line[2]) >=0);
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int idx1 = ((line[0]*pts[1].x + line[1]*pts[1].y + line[2]) >=0);
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if (idx0==idx1)
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return conquer(pts, depth+1);
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array<vector<P>, 2> S;
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S[idx0].push_back(pts[0]);
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S[idx0].push_back(p1);
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S[!idx0].push_back(p1);
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S[!idx0].push_back(pts[1]);
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rep(i,2,sz(pts)) {
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if (i == divideId) continue;
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int idx = ((line[0]*pts[i].x + line[1]*pts[i].y + line[2]) >=0);
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S[idx].push_back(pts[i]);
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}
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auto pa = conquer(S[idx0], depth+1);
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auto pb = conquer(S[!idx0], depth+1);
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if (!pa.first || !pb.first) return {false, {}};
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pb.second.erase(pb.second.begin());
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pa.second.insert(pa.second.end(), all(pb.second));
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return pa;
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}
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template<class P> vector<P> genPolygon(vector<P> pts) {
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sort(all(pts));
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pts.resize(unique(all(pts)) - pts.begin());
49+
random_shuffle(all(pts));
50+
if (sz(pts) <=3) return pts;
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vector<double> line ={pts[1].y-pts[0].y, pts[0].x - pts[1].x, -pts[0].x*pts[1].y + pts[0].y*pts[1].x};
52+
array<vector<P>, 2> S;
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S[0].push_back(pts[0]);
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S[0].push_back(pts[1]);
55+
S[1].push_back(pts[1]);
56+
S[1].push_back(pts[0]);
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rep(i,2,sz(pts)) {
58+
int idx = (line[0]*pts[i].x + line[1]*pts[i].y + line[2]) >=0;
59+
S[idx].push_back(pts[i]);
60+
}
61+
auto ta = conquer(S[0],0);
62+
auto tb = conquer(S[1],0);
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auto pa=ta.second, pb=tb.second;
64+
if (!ta.first || !tb.first) {
65+
return genPolygon(pts);
66+
}
67+
pa.erase(pa.begin());
68+
pb.erase(pb.begin());
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pa.insert(pa.end(), all(pb));
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return pa;
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}

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