From 93c9b26fedf7bf1a8afd425357405d4b5b293432 Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Apr 2019 01:18:23 -0400 Subject: [PATCH 01/44] Updated onSegment.h and both segment intersections --- content/geometry/Point.h | 2 + content/geometry/SegmentIntersection.h | 39 ++++------- content/geometry/SegmentIntersectionProper.h | 23 +++++++ content/geometry/SegmentIntersectionQ.h | 29 -------- content/geometry/chapter.tex | 4 +- content/geometry/onSegment.h | 6 +- fuzz-tests/segmentIntersection.cpp | 70 ++++++++++++++++++++ 7 files changed, 111 insertions(+), 62 deletions(-) create mode 100644 content/geometry/SegmentIntersectionProper.h delete mode 100644 content/geometry/SegmentIntersectionQ.h create mode 100644 fuzz-tests/segmentIntersection.cpp diff --git a/content/geometry/Point.h b/content/geometry/Point.h index b50b57ebd..3bd3e012d 100644 --- a/content/geometry/Point.h +++ b/content/geometry/Point.h @@ -9,6 +9,8 @@ */ #pragma once +const double EPS=1e-8; +template int sgn(T x) { return x < -EPS ? -1 : x > EPS; } template struct Point { typedef Point P; diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index 9369e410e..0d75e632e 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -23,31 +23,16 @@ Use segmentIntersectionQ to get just a true/false answer. #pragma once #include "Point.h" +#include "onSegment.h" +#include "SegmentIntersectionProper.h" -template -int segmentIntersection(const P& s1, const P& e1, - const P& s2, const P& e2, P& r1, P& r2) { - if (e1==s1) { - if (e2==s2) { - if (e1==e2) { r1 = e1; return 1; } //all equal - else return 0; //different point segments - } else return segmentIntersection(s2,e2,s1,e1,r1,r2);//swap - } - //segment directions and separation - P v1 = e1-s1, v2 = e2-s2, d = s2-s1; - auto a = v1.cross(v2), a1 = v1.cross(d), a2 = v2.cross(d); - if (a == 0) { //if parallel - auto b1=s1.dot(v1), c1=e1.dot(v1), - b2=s2.dot(v1), c2=e2.dot(v1); - if (a1 || a2 || max(b1,min(b2,c2))>min(c1,max(b2,c2))) - return 0; - r1 = min(b2,c2)c1 ? e1 : (b2>c2 ? s2 : e2); - return 2-(r1==r2); - } - if (a < 0) { a = -a; a1 = -a1; a2 = -a2; } - if (0 set

segInter(P a, P b, P c, P d) { + P out; + if (segInterProper(a, b, c, d, out)) return {out}; + set

s; + if (onSegment(c, d, a)) s.insert(a); + if (onSegment(c, d, b)) s.insert(b); + if (onSegment(a, b, c)) s.insert(c); + if (onSegment(a, b, d)) s.insert(d); + return s; +} \ No newline at end of file diff --git a/content/geometry/SegmentIntersectionProper.h b/content/geometry/SegmentIntersectionProper.h new file mode 100644 index 000000000..f2c132234 --- /dev/null +++ b/content/geometry/SegmentIntersectionProper.h @@ -0,0 +1,23 @@ +/** + * Author: Ulf Lundstrom, Simon Lindholm + * Date: 2016-09-24 + * License: CC0 + * Source: SegmentIntersection.h + * Description: Like segmentIntersection, but only returns true/false. + * Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. + * Status: Relatively well tested. + */ +#pragma once + +#include "Point.h" + +template +bool segInterProper(P a, P b, P c, P d, P &out) { + double oa = c.cross(d, a), ob = c.cross(d, b), + oc = a.cross(b, c), od = a.cross(b, d); + if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { + out = (a * ob - b * oa) / (ob - oa); + return true; + } + return false; +} \ No newline at end of file diff --git a/content/geometry/SegmentIntersectionQ.h b/content/geometry/SegmentIntersectionQ.h deleted file mode 100644 index 70ca6cf28..000000000 --- a/content/geometry/SegmentIntersectionQ.h +++ /dev/null @@ -1,29 +0,0 @@ -/** - * Author: Ulf Lundstrom, Simon Lindholm - * Date: 2016-09-24 - * License: CC0 - * Source: SegmentIntersection.h - * Description: Like segmentIntersection, but only returns true/false. - * Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. - * Status: Relatively well tested. - */ -#pragma once - -#include "Point.h" - -template -bool segmentIntersectionQ(P s1, P e1, P s2, P e2) { - if (e1 == s1) { - if (e2 == s2) return e1 == e2; - swap(s1,s2); swap(e1,e2); - } - P v1 = e1-s1, v2 = e2-s2, d = s2-s1; - auto a = v1.cross(v2), a1 = d.cross(v1), a2 = d.cross(v2); - if (a == 0) { // parallel - auto b1 = s1.dot(v1), c1 = e1.dot(v1), - b2 = s2.dot(v1), c2 = e2.dot(v1); - return !a1 && max(b1,min(b2,c2)) <= min(c1,max(b2,c2)); - } - if (a < 0) { a = -a; a1 = -a1; a2 = -a2; } - return (0 <= a1 && a1 <= a && 0 <= a2 && a2 <= a); -} diff --git a/content/geometry/chapter.tex b/content/geometry/chapter.tex index 0a17d98e3..b4ae1b317 100644 --- a/content/geometry/chapter.tex +++ b/content/geometry/chapter.tex @@ -6,7 +6,7 @@ \section{Geometric primitives} \kactlimport{SegmentDistance.h} \columnbreak \kactlimport{SegmentIntersection.h} - \kactlimport{SegmentIntersectionQ.h} + \kactlimport{SegmentIntersectionProper.h} \columnbreak \kactlimport{lineIntersection.h} \kactlimport{sideOf.h} @@ -14,7 +14,7 @@ \section{Geometric primitives} \kactlimport{linearTransformation.h} \kactlimport{Angle.h} -\section{Circles} +\section{Circles} \kactlimport{CircleIntersection.h} \kactlimport{circleTangents.h} \kactlimport{circumcircle.h} diff --git a/content/geometry/onSegment.h b/content/geometry/onSegment.h index 0d3dc2f02..3c0973590 100644 --- a/content/geometry/onSegment.h +++ b/content/geometry/onSegment.h @@ -10,8 +10,6 @@ #include "Point.h" -template -bool onSegment(const P& s, const P& e, const P& p) { - P ds = p-s, de = p-e; - return ds.cross(de) == 0 && ds.dot(de) <= 0; +template bool onSegment(P s, P e, P p) { + return sgn(s.cross(e, p)) == 0 && sgn((s - p).dot(e - p)) <= 0; } diff --git a/fuzz-tests/segmentIntersection.cpp b/fuzz-tests/segmentIntersection.cpp new file mode 100644 index 000000000..08aee2c27 --- /dev/null +++ b/fuzz-tests/segmentIntersection.cpp @@ -0,0 +1,70 @@ +#include +using namespace std; + +#define rep(i, a, b) for(int i = a; i < int(b); ++i) +#define trav(a, v) for(auto& a : v) +#define all(x) x.begin(), x.end() +#define sz(x) (int)(x).size() + +typedef long long ll; +typedef pair pii; +typedef vector vi; + + +#include "../content/geometry/SegmentIntersection.h" +namespace oldImpl { +template +int segmentIntersection(const P& s1, const P& e1, + const P& s2, const P& e2, P& r1, P& r2) { + if (e1==s1) { + if (e2==s2) { + if (e1==e2) { r1 = e1; return 1; } //all equal + else return 0; //different point segments + } else return segmentIntersection(s2,e2,s1,e1,r1,r2);//swap + } + //segment directions and separation + P v1 = e1-s1, v2 = e2-s2, d = s2-s1; + auto a = v1.cross(v2), a1 = v1.cross(d), a2 = v2.cross(d); + if (a == 0) { //if parallel + auto b1=s1.dot(v1), c1=e1.dot(v1), + b2=s2.dot(v1), c2=e2.dot(v1); + if (a1 || a2 || max(b1,min(b2,c2))>min(c1,max(b2,c2))) + return 0; + r1 = min(b2,c2)c1 ? e1 : (b2>c2 ? s2 : e2); + return 2-(r1==r2); + } + if (a < 0) { a = -a; a1 = -a1; a2 = -a2; } + if (0 P; +ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } +bool eq(P a, P b) { + return (a-b).dist() a(res2.begin(), res2.end()); + vector

b({tmp1, tmp2}); + sort(all(b)); + assert(eq(a[0], b[0]) && eq(a[1],b[1])); + } + } +} From 3b6ac0e7f800112ca64e4066afa90343562a5579 Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Apr 2019 01:50:34 -0400 Subject: [PATCH 02/44] Updated headers --- content/geometry/SegmentIntersection.h | 47 +++++++++++-------- content/geometry/SegmentIntersectionProper.h | 23 --------- content/geometry/chapter.tex | 1 - content/geometry/onSegment.h | 8 ++-- fuzz-tests/segmentIntersection.cpp | 49 ++++++++++---------- 5 files changed, 56 insertions(+), 72 deletions(-) delete mode 100644 content/geometry/SegmentIntersectionProper.h diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index 0d75e632e..ab6798bfe 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -1,38 +1,45 @@ /** - * Author: Ulf Lundstrom - * Date: 2009-03-21 + * Author: Victor Lecomte, chilli + * Date: 2019-04-27 * License: CC0 - * Source: + * Source: https://vlecomte.github.io/cp-geo.pdf * Description:\\ \begin{minipage}{75mm} -If a unique intersetion point between the line segments going from s1 to e1 and from s2 to e2 exists r1 is set to this point and 1 is returned. -If no intersection point exists 0 is returned and if infinitely many exists 2 is returned and r1 and r2 are set to the two ends of the common line. +If a unique intersetion point between the line segments going from s1 to e1 and from s2 to e2 exists then it is returned. +If no intersection point exists an empty vector is returned. If infinitely many exist a vector with 2 elements is returned. The wrong position will be returned if P is Point and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. -Use segmentIntersectionQ to get just a true/false answer. \end{minipage} \begin{minipage}{15mm} \includegraphics[width=\textwidth]{content/geometry/SegmentIntersection} \end{minipage} - * Status: Well tested with unitTest and with Kattis problem intersection. + * Status: Well tested with fuzz-test and with Kattis problem intersection. * Usage: - * Point intersection, dummy; - * if (segmentIntersection(s1,e1,s2,e2,intersection,dummy)==1) - * cout << "segments intersect at " << intersection << endl; + * vector

inter = segInter(s1,e1,s2,e2); + * if (inter.size()==1) + * cout << "segments intersect at " << inter[0] << endl; */ #pragma once #include "Point.h" #include "onSegment.h" -#include "SegmentIntersectionProper.h" -template set

segInter(P a, P b, P c, P d) { - P out; - if (segInterProper(a, b, c, d, out)) return {out}; - set

s; - if (onSegment(c, d, a)) s.insert(a); - if (onSegment(c, d, b)) s.insert(b); - if (onSegment(a, b, c)) s.insert(c); - if (onSegment(a, b, d)) s.insert(d); - return s; +template bool segInterProper(P a, P b, P c, P d, P &out) { + double oa = c.cross(d, a), ob = c.cross(d, b), + oc = a.cross(b, c), od = a.cross(b, d); + if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { + out = (a * ob - b * oa) / (ob - oa); + return true; + } + return false; +} +template vector

segInter(P a, P b, P c, P d) { + P out; + if (segInterProper(a, b, c, d, out)) return {out}; + set

s; + if (onSegment(c, d, a)) s.insert(a); + if (onSegment(c, d, b)) s.insert(b); + if (onSegment(a, b, c)) s.insert(c); + if (onSegment(a, b, d)) s.insert(d); + return vector

(all(s)); } \ No newline at end of file diff --git a/content/geometry/SegmentIntersectionProper.h b/content/geometry/SegmentIntersectionProper.h deleted file mode 100644 index f2c132234..000000000 --- a/content/geometry/SegmentIntersectionProper.h +++ /dev/null @@ -1,23 +0,0 @@ -/** - * Author: Ulf Lundstrom, Simon Lindholm - * Date: 2016-09-24 - * License: CC0 - * Source: SegmentIntersection.h - * Description: Like segmentIntersection, but only returns true/false. - * Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. - * Status: Relatively well tested. - */ -#pragma once - -#include "Point.h" - -template -bool segInterProper(P a, P b, P c, P d, P &out) { - double oa = c.cross(d, a), ob = c.cross(d, b), - oc = a.cross(b, c), od = a.cross(b, d); - if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { - out = (a * ob - b * oa) / (ob - oa); - return true; - } - return false; -} \ No newline at end of file diff --git a/content/geometry/chapter.tex b/content/geometry/chapter.tex index b4ae1b317..140a4bd78 100644 --- a/content/geometry/chapter.tex +++ b/content/geometry/chapter.tex @@ -6,7 +6,6 @@ \section{Geometric primitives} \kactlimport{SegmentDistance.h} \columnbreak \kactlimport{SegmentIntersection.h} - \kactlimport{SegmentIntersectionProper.h} \columnbreak \kactlimport{lineIntersection.h} \kactlimport{sideOf.h} diff --git a/content/geometry/onSegment.h b/content/geometry/onSegment.h index 3c0973590..decf748a7 100644 --- a/content/geometry/onSegment.h +++ b/content/geometry/onSegment.h @@ -1,9 +1,9 @@ /** - * Author: Ulf Lundstrom - * Date: 2009-04-09 + * Author: Victor Lecomte, chilli + * Date: 2019-04-26 * License: CC0 - * Source: Basic geometry - * Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point where overflow is an issue. Use (segDist(s,e,p)<=epsilon) instead when using Point. + * Source: https://vlecomte.github.io/cp-geo.pdf + * Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point where overflow is an issue. * Status: */ #pragma once diff --git a/fuzz-tests/segmentIntersection.cpp b/fuzz-tests/segmentIntersection.cpp index 08aee2c27..ba0eaee27 100644 --- a/fuzz-tests/segmentIntersection.cpp +++ b/fuzz-tests/segmentIntersection.cpp @@ -15,30 +15,30 @@ typedef vector vi; namespace oldImpl { template int segmentIntersection(const P& s1, const P& e1, - const P& s2, const P& e2, P& r1, P& r2) { - if (e1==s1) { - if (e2==s2) { - if (e1==e2) { r1 = e1; return 1; } //all equal - else return 0; //different point segments - } else return segmentIntersection(s2,e2,s1,e1,r1,r2);//swap - } - //segment directions and separation - P v1 = e1-s1, v2 = e2-s2, d = s2-s1; - auto a = v1.cross(v2), a1 = v1.cross(d), a2 = v2.cross(d); - if (a == 0) { //if parallel - auto b1=s1.dot(v1), c1=e1.dot(v1), - b2=s2.dot(v1), c2=e2.dot(v1); - if (a1 || a2 || max(b1,min(b2,c2))>min(c1,max(b2,c2))) - return 0; - r1 = min(b2,c2)c1 ? e1 : (b2>c2 ? s2 : e2); - return 2-(r1==r2); - } - if (a < 0) { a = -a; a1 = -a1; a2 = -a2; } - if (0min(c1,max(b2,c2))) + return 0; + r1 = min(b2,c2)c1 ? e1 : (b2>c2 ? s2 : e2); + return 2-(r1==r2); + } + if (a < 0) { a = -a; a1 = -a1; a2 = -a2; } + if (0 P; @@ -67,4 +67,5 @@ int main() { assert(eq(a[0], b[0]) && eq(a[1],b[1])); } } + cout<<"Tests passed!"< Date: Fri, 26 Apr 2019 01:55:10 -0400 Subject: [PATCH 03/44] Updated some line width issues --- content/geometry/SegmentIntersection.h | 5 +++-- content/geometry/chapter.tex | 1 - content/geometry/onSegment.h | 3 ++- 3 files changed, 5 insertions(+), 4 deletions(-) diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index ab6798bfe..465fedfc2 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -5,7 +5,7 @@ * Source: https://vlecomte.github.io/cp-geo.pdf * Description:\\ \begin{minipage}{75mm} -If a unique intersetion point between the line segments going from s1 to e1 and from s2 to e2 exists then it is returned. +If a unique intersection point between the line segments going from s1 to e1 and from s2 to e2 exists then it is returned. If no intersection point exists an empty vector is returned. If infinitely many exist a vector with 2 elements is returned. The wrong position will be returned if P is Point and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. @@ -24,7 +24,8 @@ Products of three coordinates are used in intermediate steps so watch out for ov #include "Point.h" #include "onSegment.h" -template bool segInterProper(P a, P b, P c, P d, P &out) { +template bool segInterProper(P a, P b, P c, P d, + P &out) { double oa = c.cross(d, a), ob = c.cross(d, b), oc = a.cross(b, c), od = a.cross(b, d); if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { diff --git a/content/geometry/chapter.tex b/content/geometry/chapter.tex index 140a4bd78..2a994da2d 100644 --- a/content/geometry/chapter.tex +++ b/content/geometry/chapter.tex @@ -6,7 +6,6 @@ \section{Geometric primitives} \kactlimport{SegmentDistance.h} \columnbreak \kactlimport{SegmentIntersection.h} - \columnbreak \kactlimport{lineIntersection.h} \kactlimport{sideOf.h} \kactlimport{onSegment.h} diff --git a/content/geometry/onSegment.h b/content/geometry/onSegment.h index decf748a7..7e3aeb6ea 100644 --- a/content/geometry/onSegment.h +++ b/content/geometry/onSegment.h @@ -11,5 +11,6 @@ #include "Point.h" template bool onSegment(P s, P e, P p) { - return sgn(s.cross(e, p)) == 0 && sgn((s - p).dot(e - p)) <= 0; + return sgn(s.cross(e, p)) == 0 && + sgn((s - p).dot(e - p)) <= 0; } From bccd1cb0f41028af8dd38b0b0953c5676ee942fc Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Apr 2019 01:58:34 -0400 Subject: [PATCH 04/44] Fixed broken dependency --- content/geometry/SegmentIntersection.h | 2 +- fuzz-tests/geometry/PolygonCut.cpp | 14 +++++++++++--- 2 files changed, 12 insertions(+), 4 deletions(-) diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index 465fedfc2..d7268df4b 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -43,4 +43,4 @@ template vector

segInter(P a, P b, P c, P d) { if (onSegment(a, b, c)) s.insert(c); if (onSegment(a, b, d)) s.insert(d); return vector

(all(s)); -} \ No newline at end of file +} diff --git a/fuzz-tests/geometry/PolygonCut.cpp b/fuzz-tests/geometry/PolygonCut.cpp index 88aecbfbb..e71a473ee 100644 --- a/fuzz-tests/geometry/PolygonCut.cpp +++ b/fuzz-tests/geometry/PolygonCut.cpp @@ -10,11 +10,19 @@ typedef long long ll; typedef pair pii; typedef vector vi; +<<<<<<< HEAD:fuzz-tests/geometry/PolygonCut.cpp #include "../../content/geometry/PolygonArea.h" #include "../../content/geometry/PolygonCut.h" #include "../../content/geometry/sideOf.h" #include "../../content/geometry/insidePolygon.h" #include "../../content/geometry/SegmentIntersection.h" +======= +#include "../content/geometry/PolygonArea.h" +#include "../content/geometry/PolygonCut.h" +#include "../content/geometry/sideOf.h" +#include "../content/geometry/insidePolygon.h" +#include "../content/geometry/SegmentIntersection.h" +>>>>>>> Fixed broken dependency:fuzz-tests/polygon-cut.cpp typedef Point P; int main() { @@ -27,9 +35,9 @@ int main() { P a = ps[i], b = ps[(i+1)%N]; P c = ps[j], d = ps[(j+1)%N]; P r1, r2; - int r = segmentIntersection(a, b, c, d, r1, r2); - if (r == 2) goto fail; - if (r == 1) { + auto r = segInter(a, b, c, d); + if (sz(r) == 2) goto fail; + if (sz(r) == 1) { if (i+1 == j || (j+1) % N == i) ; else goto fail; } From d2e700a0e9d2cdc700b7d11f36caf755bda93a3c Mon Sep 17 00:00:00 2001 From: Horace He Date: Sat, 27 Apr 2019 12:13:14 -0400 Subject: [PATCH 05/44] removed automatic epsilon checks --- content/geometry/Point.h | 3 +-- content/geometry/onSegment.h | 4 ++-- 2 files changed, 3 insertions(+), 4 deletions(-) diff --git a/content/geometry/Point.h b/content/geometry/Point.h index 3bd3e012d..f38e9e4da 100644 --- a/content/geometry/Point.h +++ b/content/geometry/Point.h @@ -9,8 +9,7 @@ */ #pragma once -const double EPS=1e-8; -template int sgn(T x) { return x < -EPS ? -1 : x > EPS; } +template int sgn(T x) { return (x>0) - (x<0);} template struct Point { typedef Point P; diff --git a/content/geometry/onSegment.h b/content/geometry/onSegment.h index 7e3aeb6ea..0bd52a770 100644 --- a/content/geometry/onSegment.h +++ b/content/geometry/onSegment.h @@ -11,6 +11,6 @@ #include "Point.h" template bool onSegment(P s, P e, P p) { - return sgn(s.cross(e, p)) == 0 && - sgn((s - p).dot(e - p)) <= 0; + return s.cross(e, p) == 0 && + (s - p).dot(e - p) <= 0; } From 59f8511b18927dd3008b67bf37a22e37eadd2ecb Mon Sep 17 00:00:00 2001 From: Horace He Date: Sat, 27 Apr 2019 12:16:11 -0400 Subject: [PATCH 06/44] Put it on one line now --- content/geometry/onSegment.h | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/content/geometry/onSegment.h b/content/geometry/onSegment.h index 0bd52a770..f365344d3 100644 --- a/content/geometry/onSegment.h +++ b/content/geometry/onSegment.h @@ -11,6 +11,5 @@ #include "Point.h" template bool onSegment(P s, P e, P p) { - return s.cross(e, p) == 0 && - (s - p).dot(e - p) <= 0; + return s.cross(e, p) == 0 && (s - p).dot(e - p) <= 0; } From 1bdf870470e19a676a376bf21369d6a7924d45c7 Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 29 Apr 2019 03:04:18 -0400 Subject: [PATCH 07/44] Moved template up a line to fit parameters on one line --- content/geometry/SegmentIntersection.h | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index d7268df4b..670cee057 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -24,8 +24,8 @@ Products of three coordinates are used in intermediate steps so watch out for ov #include "Point.h" #include "onSegment.h" -template bool segInterProper(P a, P b, P c, P d, - P &out) { +template +bool segInterProper(P a, P b, P c, P d, P &out) { double oa = c.cross(d, a), ob = c.cross(d, b), oc = a.cross(b, c), od = a.cross(b, d); if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { From 2f32d6374988381e81e9c5335ce04fc4402eda8b Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 29 Apr 2019 03:06:43 -0400 Subject: [PATCH 08/44] Changed tabs to spaces so it'll align --- content/geometry/SegmentIntersection.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index 670cee057..6b525ad25 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -27,7 +27,7 @@ Products of three coordinates are used in intermediate steps so watch out for ov template bool segInterProper(P a, P b, P c, P d, P &out) { double oa = c.cross(d, a), ob = c.cross(d, b), - oc = a.cross(b, c), od = a.cross(b, d); + oc = a.cross(b, c), od = a.cross(b, d); if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { out = (a * ob - b * oa) / (ob - oa); return true; From 28456a19b88387298d607db8cc6f68bb51a6be30 Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 29 Apr 2019 03:18:01 -0400 Subject: [PATCH 09/44] Fixed some misc issues --- content/geometry/Point.h | 2 +- fuzz-tests/segmentIntersection.cpp | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/content/geometry/Point.h b/content/geometry/Point.h index f38e9e4da..599919a03 100644 --- a/content/geometry/Point.h +++ b/content/geometry/Point.h @@ -9,7 +9,7 @@ */ #pragma once -template int sgn(T x) { return (x>0) - (x<0);} +template int sgn(T x) { return (x > 0) - (x < 0);} template struct Point { typedef Point P; diff --git a/fuzz-tests/segmentIntersection.cpp b/fuzz-tests/segmentIntersection.cpp index ba0eaee27..437d57d91 100644 --- a/fuzz-tests/segmentIntersection.cpp +++ b/fuzz-tests/segmentIntersection.cpp @@ -44,7 +44,7 @@ int segmentIntersection(const P& s1, const P& e1, typedef Point P; ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } bool eq(P a, P b) { - return (a-b).dist() Date: Mon, 29 Apr 2019 03:19:29 -0400 Subject: [PATCH 10/44] Readded relevant description --- content/geometry/onSegment.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/geometry/onSegment.h b/content/geometry/onSegment.h index f365344d3..94511014a 100644 --- a/content/geometry/onSegment.h +++ b/content/geometry/onSegment.h @@ -3,7 +3,7 @@ * Date: 2019-04-26 * License: CC0 * Source: https://vlecomte.github.io/cp-geo.pdf - * Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point where overflow is an issue. + * Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point where overflow is an issue. Use (segDist(s,e,p)<=epsilon) instead when using Point. * Status: */ #pragma once From ba9395d3fb38e8750235ede0b6d24bb57559e2e4 Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 29 Apr 2019 22:01:04 -0400 Subject: [PATCH 11/44] Fixed formatting issue --- content/geometry/SegmentIntersection.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/geometry/SegmentIntersection.h b/content/geometry/SegmentIntersection.h index 6b525ad25..cf7cabf5c 100644 --- a/content/geometry/SegmentIntersection.h +++ b/content/geometry/SegmentIntersection.h @@ -25,7 +25,7 @@ Products of three coordinates are used in intermediate steps so watch out for ov #include "onSegment.h" template -bool segInterProper(P a, P b, P c, P d, P &out) { +bool segInterProper(P a, P b, P c, P d, P& out) { double oa = c.cross(d, a), ob = c.cross(d, b), oc = a.cross(b, c), od = a.cross(b, d); if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) { From fab7b2eb488fa1e5dcfbb44395e7d661590be4e1 Mon Sep 17 00:00:00 2001 From: Horace He Date: Thu, 2 May 2019 01:35:12 -0400 Subject: [PATCH 12/44] made change --- content/geometry/lineIntersection.h | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/content/geometry/lineIntersection.h b/content/geometry/lineIntersection.h index b486495c1..dc054597e 100644 --- a/content/geometry/lineIntersection.h +++ b/content/geometry/lineIntersection.h @@ -5,13 +5,13 @@ * Source: * Description:\\ \begin{minipage}{75mm} -If a unique intersetion point of the lines going through s1,e1 and s2,e2 exists r is set to this point and 1 is returned. If no intersection point exists 0 is returned and if infinitely many exists -1 is returned. If s1==e1 or s2==e2 -1 is returned. The wrong position will be returned if P is Point and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. +If a unique intersection point of the lines going through s1,e1 and s2,e2 exists r is set to this point and 1 is returned. If no intersection point exists 0 is returned and if infinitely many exists -1 is returned. If s1==e1 or s2==e2 -1 is returned. The wrong position will be returned if P is Point and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. \end{minipage} \begin{minipage}{15mm} \includegraphics[width=\textwidth]{content/geometry/lineIntersection} \end{minipage} * Status: tested - * Usage: + * Usage: * point intersection; * if (1 == LineIntersection(s1,e1,s2,e2,intersection)) * cout << "intersection point at " << intersection << endl; @@ -21,11 +21,10 @@ If a unique intersetion point of the lines going through s1,e1 and s2,e2 exists #include "Point.h" template -int lineIntersection(const P& s1, const P& e1, const P& s2, - const P& e2, P& r) { - if ((e1-s1).cross(e2-s2)) { //if not parallell - r = s2-(e2-s2)*(e1-s1).cross(s2-s1)/(e1-s1).cross(e2-s2); - return 1; - } else - return -((e1-s1).cross(s2-s1)==0 || s2==e2); +pair lineIntersection(P s1, P e1, P s2, P e2) { + auto d = (e1-s1).cross(e2-s2); + if (d == 0) //if parallel + return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; + else + return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; } From e99191f9c8714e6a05de2c98cdbc9cba53052c1f Mon Sep 17 00:00:00 2001 From: Horace He Date: Thu, 2 May 2019 12:51:17 -0400 Subject: [PATCH 13/44] Added first commit of halfPlane --- content/geometry/halfPlane.h | 50 ++++++++++++++++++++++++++++++ fuzz-tests/geometry/PolygonCut.cpp | 8 ----- 2 files changed, 50 insertions(+), 8 deletions(-) create mode 100644 content/geometry/halfPlane.h diff --git a/content/geometry/halfPlane.h b/content/geometry/halfPlane.h new file mode 100644 index 000000000..abf8262ef --- /dev/null +++ b/content/geometry/halfPlane.h @@ -0,0 +1,50 @@ + +/** + * Author: + * Date: + * License: + * Source: + * Description: + * Time: + * Status: + * Usage: + */ +#pragma once + +#include "Point.h" +#include "sideOf.h" + +typedef Point P; +typedef array Line; +#define v(a) (a[1] - a[0]) +#define c(a) (v(a).cross(a[0])) +pair lineInter(Line a, Line b) { + auto d = v(a).cross(v(b)); + if (d == 0) return {-(c(a) == c(b)), P(0,0)}; + else return {1, (v(b)*c(a) - v(a)*c(b))/d}; +} + +#define ang(a) atan2(v(a).y, v(a).x) +int sideOf(Line l, P p) {return sideOf(l[0], l[1], p);} +vector

halfPlaneIntersection(vector vs) { + sort(all(vs), [](auto a, auto b) { return ang(a) < ang(b);}); + vs.resize(unique(all(vs), [](auto a, auto b){ return ang(a) == ang(b);}) - vs.begin()); + deque deq({vs[0]}); + deque

ans; + for (int i = 1; i < sz(vs); ++i) { + if (sgn(ang(vs[i]) - ang(vs[i-1])) == 0) continue; + while (sz(ans) && sideOf(vs[i], ans.back())< 0) + ans.pop_back(), deq.pop_back(); + while(sz(ans) && sideOf(vs[i], ans.front()) < 0) + ans.pop_front(), deq.pop_front(); + ans.push_back(lineInter(deq.back(), vs[i]).second); + deq.push_back(vs[i]); + } + while (sz(ans) && sideOf(deq.front(), ans.back()) < 0) + ans.pop_back(), deq.pop_back(); + while (sz(ans) && sideOf(deq.back(), ans.front()) < 0) + ans.pop_front(), deq.pop_front(); + if (sz(deq) <= 2) return {}; + ans.push_back(lineInter(deq.front(), deq.back()).second); + return vector

(all(ans)); +} \ No newline at end of file diff --git a/fuzz-tests/geometry/PolygonCut.cpp b/fuzz-tests/geometry/PolygonCut.cpp index e71a473ee..333a181b1 100644 --- a/fuzz-tests/geometry/PolygonCut.cpp +++ b/fuzz-tests/geometry/PolygonCut.cpp @@ -10,19 +10,11 @@ typedef long long ll; typedef pair pii; typedef vector vi; -<<<<<<< HEAD:fuzz-tests/geometry/PolygonCut.cpp #include "../../content/geometry/PolygonArea.h" #include "../../content/geometry/PolygonCut.h" #include "../../content/geometry/sideOf.h" #include "../../content/geometry/insidePolygon.h" #include "../../content/geometry/SegmentIntersection.h" -======= -#include "../content/geometry/PolygonArea.h" -#include "../content/geometry/PolygonCut.h" -#include "../content/geometry/sideOf.h" -#include "../content/geometry/insidePolygon.h" -#include "../content/geometry/SegmentIntersection.h" ->>>>>>> Fixed broken dependency:fuzz-tests/polygon-cut.cpp typedef Point P; int main() { From 63425c3bcecfd5a15c537bcbced865542f8a6e81 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sat, 4 May 2019 22:17:20 -0400 Subject: [PATCH 14/44] Simplified/shortened the code --- content/geometry/halfPlane.h | 41 ++++++++++++++---------------------- 1 file changed, 16 insertions(+), 25 deletions(-) diff --git a/content/geometry/halfPlane.h b/content/geometry/halfPlane.h index abf8262ef..4f394a98b 100644 --- a/content/geometry/halfPlane.h +++ b/content/geometry/halfPlane.h @@ -16,35 +16,26 @@ typedef Point P; typedef array Line; -#define v(a) (a[1] - a[0]) -#define c(a) (v(a).cross(a[0])) -pair lineInter(Line a, Line b) { - auto d = v(a).cross(v(b)); - if (d == 0) return {-(c(a) == c(b)), P(0,0)}; - else return {1, (v(b)*c(a) - v(a)*c(b))/d}; -} +#define sp(a) a[0], a[1] +#define ang(a) atan2((a[1] - a[0]).y, (a[1] - a[0]).x) -#define ang(a) atan2(v(a).y, v(a).x) -int sideOf(Line l, P p) {return sideOf(l[0], l[1], p);} vector

halfPlaneIntersection(vector vs) { sort(all(vs), [](auto a, auto b) { return ang(a) < ang(b);}); vs.resize(unique(all(vs), [](auto a, auto b){ return ang(a) == ang(b);}) - vs.begin()); - deque deq({vs[0]}); - deque

ans; + vector deq(sz(vs)+5); + vector

ans(sz(vs)+5); + int dh = 0, dt = 1, ah=0, at=0; + deq[0] = vs[0]; for (int i = 1; i < sz(vs); ++i) { - if (sgn(ang(vs[i]) - ang(vs[i-1])) == 0) continue; - while (sz(ans) && sideOf(vs[i], ans.back())< 0) - ans.pop_back(), deq.pop_back(); - while(sz(ans) && sideOf(vs[i], ans.front()) < 0) - ans.pop_front(), deq.pop_front(); - ans.push_back(lineInter(deq.back(), vs[i]).second); - deq.push_back(vs[i]); + if (ang(vs[i]) - ang(vs[i-1]) == 0) continue; + while (ah < at && sideOf(sp(vs[i]), ans[at-1])< 0) at--, dt--; + while (ah < at && sideOf(sp(vs[i]), ans[ah]) < 0) ah++, dh++; + ans[at++] = lineInter(sp(deq[dt-1]), sp(vs[i])).second; + deq[dt++] = vs[i]; } - while (sz(ans) && sideOf(deq.front(), ans.back()) < 0) - ans.pop_back(), deq.pop_back(); - while (sz(ans) && sideOf(deq.back(), ans.front()) < 0) - ans.pop_front(), deq.pop_front(); - if (sz(deq) <= 2) return {}; - ans.push_back(lineInter(deq.front(), deq.back()).second); - return vector

(all(ans)); + while (ah < at && sideOf(sp(deq[dh]), ans[at-1]) < 0) at--, dt--; + while (ah < at && sideOf(sp(deq[dt]), ans[ah]) < 0) ah++, dh++; + if (dt-dh <= 2) return {}; + ans[at++] = lineInter(sp(deq[dh]), sp(deq[dt-1])).second; + return {ans.begin()+ah, ans.begin()+at}; } \ No newline at end of file From ed75bf954ceab516cc16ba255668cce7c3f07696 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sat, 4 May 2019 22:49:06 -0400 Subject: [PATCH 15/44] Fixed some issues --- content/geometry/halfPlane.h | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/content/geometry/halfPlane.h b/content/geometry/halfPlane.h index 4f394a98b..6cb7b6b2b 100644 --- a/content/geometry/halfPlane.h +++ b/content/geometry/halfPlane.h @@ -18,10 +18,12 @@ typedef Point P; typedef array Line; #define sp(a) a[0], a[1] #define ang(a) atan2((a[1] - a[0]).y, (a[1] - a[0]).x) - +bool cmp(Line a, Line b) { + auto s = ang(a) - ang(b); + return s == 0 ? sideOf(sp(b), a[0]) >=0 : s < 0; +} vector

halfPlaneIntersection(vector vs) { - sort(all(vs), [](auto a, auto b) { return ang(a) < ang(b);}); - vs.resize(unique(all(vs), [](auto a, auto b){ return ang(a) == ang(b);}) - vs.begin()); + sort(all(vs), cmp); vector deq(sz(vs)+5); vector

ans(sz(vs)+5); int dh = 0, dt = 1, ah=0, at=0; @@ -37,5 +39,7 @@ vector

halfPlaneIntersection(vector vs) { while (ah < at && sideOf(sp(deq[dt]), ans[ah]) < 0) ah++, dh++; if (dt-dh <= 2) return {}; ans[at++] = lineInter(sp(deq[dh]), sp(deq[dt-1])).second; - return {ans.begin()+ah, ans.begin()+at}; + vector

res = {ans.begin()+ah, ans.begin()+at}; + res.erase(unique(all(res)), res.end()); + return res; } \ No newline at end of file From 85713903366b9eed361f55f4554a9972339e7dcb Mon Sep 17 00:00:00 2001 From: Horace He Date: Sat, 4 May 2019 23:28:29 -0400 Subject: [PATCH 16/44] Added some unit tests for halfplane --- content/geometry/{halfPlane.h => HalfPlane.h} | 5 +- fuzz-tests/geometry/HalfPlane.cpp | 160 ++++++++++++++++++ fuzz-tests/segmentIntersection.cpp | 71 -------- 3 files changed, 162 insertions(+), 74 deletions(-) rename content/geometry/{halfPlane.h => HalfPlane.h} (90%) create mode 100644 fuzz-tests/geometry/HalfPlane.cpp delete mode 100644 fuzz-tests/segmentIntersection.cpp diff --git a/content/geometry/halfPlane.h b/content/geometry/HalfPlane.h similarity index 90% rename from content/geometry/halfPlane.h rename to content/geometry/HalfPlane.h index 6cb7b6b2b..4efa0e936 100644 --- a/content/geometry/halfPlane.h +++ b/content/geometry/HalfPlane.h @@ -13,6 +13,7 @@ #include "Point.h" #include "sideOf.h" +#include "lineIntersection.h" typedef Point P; typedef array Line; @@ -39,7 +40,5 @@ vector

halfPlaneIntersection(vector vs) { while (ah < at && sideOf(sp(deq[dt]), ans[ah]) < 0) ah++, dh++; if (dt-dh <= 2) return {}; ans[at++] = lineInter(sp(deq[dh]), sp(deq[dt-1])).second; - vector

res = {ans.begin()+ah, ans.begin()+at}; - res.erase(unique(all(res)), res.end()); - return res; + return {ans.begin()+ah, ans.begin()+at}; } \ No newline at end of file diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp new file mode 100644 index 000000000..cd2675600 --- /dev/null +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -0,0 +1,160 @@ +#include +using namespace std; + +#define rep(i, a, b) for(int i = a; i < int(b); ++i) +#define trav(a, v) for(auto& a : v) +#define all(x) x.begin(), x.end() +#define sz(x) (int)(x).size() + +typedef long long ll; +typedef pair pii; +typedef vector vi; + +#include "../../content/geometry/HalfPlane.h" +#include "../../content/geometry/PolygonArea.h" +typedef Point P; + +ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } + +namespace MIT { +#define eps 1e-8 +typedef Point P; + +template +pair lineIntersection(P s1, P e1, P s2, P e2) { + auto d = (e1-s1).cross(e2-s2); + if (d == 0) //if parallel + return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; + else + return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; +} + +struct Line { + P P1, P2; + // Right hand side of the ray P1 -> P2 + explicit Line(P a = P(), P b = P()) : P1(a), P2(b) {}; + P intpo(Line y) { + auto res = lineIntersection(P1, P2, y.P1, y.P2); + assert(res.first == 1); + return res.second; + } + P dir() { + return P2 - P1; + } + bool contains(P x) { + return (P2 - P1).cross(x - P1) < eps; + } + bool out(P x) { + return !contains(x); + } +}; + +template +bool mycmp(Point a, Point b) { + // return atan2(a.y, a.x) < atan2(b.y, b.x); + if (a.x * b.x < 0) return a.x < 0; + if (abs(a.x) < eps) { + if (abs(b.x) < eps) return a.y > 0 && b.y < 0; + if (b.x < 0) return a.y > 0; + if (b.x > 0) return true; + } + if (abs(b.x) < eps) { + if (a.x < 0) return b.y < 0; + if (a.x > 0) return false; + } + return a.cross(b) > 0; +} + +bool cmp(Line a, Line b) { + return mycmp(a.dir(), b.dir()); +} + +double Intersection_Area(vector b) { + sort(b.begin(), b.end(), cmp); + int n = b.size(); + int q = 1, h = 0, i; + vector ca(b.size() + 10); + for (i = 0; i < n; i++) { + while (q < h && b[i].out(ca[h].intpo(ca[h - 1]))) h--; + while (q < h && b[i].out(ca[q].intpo(ca[q + 1]))) q++; + ca[++h] = b[i]; + if (q < h && abs(ca[h].dir().cross(ca[h - 1].dir())) < eps) { + h--; + if (b[i].out(ca[h].P1)) ca[h] = b[i]; + } + } + while (q < h - 1 && ca[q].out(ca[h].intpo(ca[h - 1]))) h--; + while (q < h - 1 && ca[h].out(ca[q].intpo(ca[q + 1]))) q++; + // Intersection is empty. This is sometimes different from the case when + // the intersection area is 0. + if (h - q <= 1) return 0; + ca[h + 1] = ca[q]; + vector

s; + for (i = q; i <= h; i++) s.push_back(ca[i].intpo(ca[i + 1])); + s.push_back(s[0]); + double ans = 0; + for (i = 0; i < (int) s.size() - 1; i++) ans += s[i].cross(s[i + 1]); + return ans / 2; +} +} +vector convert(vector x) { + vector res; + for (auto i: x) + res.push_back(MIT::Line(i[1], i[0])); + return res; +} + +const double INF = 1e9; +void addInf(vector &res) { + vector

infPts({P(INF, INF), P(-INF, INF), P(-INF, -INF), P(INF, -INF)}); + for (int i=0; i<4; i++) + res.push_back({infPts[i], infPts[(i+1)%4]}); +} +void test1() { + vector t({{P(0,0),P(5,0)}, {P(5,-2), P(5,2)}, {P(5,2),P(2,2)}, {P(0,3),P(0,-3)}}); + auto res = halfPlaneIntersection(t); + cout< t({{P(0,0), P(5,0)}}); + addInf(t); + auto res = halfPlaneIntersection(t); + assert(polygonArea2(res)/4e18); + t = vector({{P(0,0), P(5,0)}, {P(0,0), P(0,5)}}); + addInf(t); + res = halfPlaneIntersection(t); + assert(polygonArea2(res)/2e18 == 1); +} +void testLine() { + vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}}); + addInf(t); + auto res = halfPlaneIntersection(t); + assert(sz(res) >= 2); + assert(polygonArea2(res) == 0); +} +void testPoint() { + vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}, {P(0,0), P(0,5)}, {P(0,5), P(0,0)}}); + addInf(t); + auto res = halfPlaneIntersection(t); + assert(sz(res) >= 1); + assert(polygonArea2(res) == 0); +} +void testEmpty() { + vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}, {P(0,0), P(0,5)}, {P(0,5), P(0,0)}, + {P(0,2), P(5,2)}}); + addInf(t); + auto res = halfPlaneIntersection(t); + assert(sz(res) == 0); +} + +int main() { + test1(); + testInf(); + testLine(); + testPoint(); + testEmpty(); +} diff --git a/fuzz-tests/segmentIntersection.cpp b/fuzz-tests/segmentIntersection.cpp deleted file mode 100644 index 437d57d91..000000000 --- a/fuzz-tests/segmentIntersection.cpp +++ /dev/null @@ -1,71 +0,0 @@ -#include -using namespace std; - -#define rep(i, a, b) for(int i = a; i < int(b); ++i) -#define trav(a, v) for(auto& a : v) -#define all(x) x.begin(), x.end() -#define sz(x) (int)(x).size() - -typedef long long ll; -typedef pair pii; -typedef vector vi; - - -#include "../content/geometry/SegmentIntersection.h" -namespace oldImpl { -template -int segmentIntersection(const P& s1, const P& e1, - const P& s2, const P& e2, P& r1, P& r2) { - if (e1==s1) { - if (e2==s2) { - if (e1==e2) { r1 = e1; return 1; } //all equal - else return 0; //different point segments - } else return segmentIntersection(s2,e2,s1,e1,r1,r2);//swap - } - //segment directions and separation - P v1 = e1-s1, v2 = e2-s2, d = s2-s1; - auto a = v1.cross(v2), a1 = v1.cross(d), a2 = v2.cross(d); - if (a == 0) { //if parallel - auto b1=s1.dot(v1), c1=e1.dot(v1), - b2=s2.dot(v1), c2=e2.dot(v1); - if (a1 || a2 || max(b1,min(b2,c2))>min(c1,max(b2,c2))) - return 0; - r1 = min(b2,c2)c1 ? e1 : (b2>c2 ? s2 : e2); - return 2-(r1==r2); - } - if (a < 0) { a = -a; a1 = -a1; a2 = -a2; } - if (0 P; -ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } -bool eq(P a, P b) { - return (a-b).dist()<1e-8; -} -int main() { - rep(t,0,100000) { - const int GRID=5; - P a(rand()%GRID, rand()%GRID), b(rand()%GRID, rand()%GRID), c(rand()%GRID, rand()%GRID), d(rand()%GRID, rand()%GRID); - P tmp1, tmp2; - auto res = oldImpl::segmentIntersection(a,b,c,d, tmp1, tmp2); - auto res2 = segInter(a,b,c,d); - if (res != res2.size()) { - cout< a(res2.begin(), res2.end()); - vector

b({tmp1, tmp2}); - sort(all(b)); - assert(eq(a[0], b[0]) && eq(a[1],b[1])); - } - } - cout<<"Tests passed!"< Date: Sun, 5 May 2019 00:14:44 -0400 Subject: [PATCH 17/44] Add failure example for MIT's halfplane code --- content/geometry/PolygonArea.h | 3 +- fuzz-tests/geometry/HalfPlane.cpp | 54 +++++++++++++++++++++++++------ 2 files changed, 46 insertions(+), 11 deletions(-) diff --git a/content/geometry/PolygonArea.h b/content/geometry/PolygonArea.h index f70e7db8d..e22560617 100644 --- a/content/geometry/PolygonArea.h +++ b/content/geometry/PolygonArea.h @@ -12,7 +12,8 @@ #include "Point.h" template -T polygonArea2(vector>& v) { +T polygonArea2(vector> v) { + if (sz(v) < 3) return 0; T a = v.back().cross(v[0]); rep(i,0,sz(v)-1) a += v[i].cross(v[i+1]); return a; diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index cd2675600..70456f03a 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -92,6 +92,8 @@ double Intersection_Area(vector b) { vector

s; for (i = q; i <= h; i++) s.push_back(ca[i].intpo(ca[i + 1])); s.push_back(s[0]); + // for (auto i: s) cout< convert(vector x) { return res; } -const double INF = 1e9; -void addInf(vector &res) { +const double INF = 1e1; +const double EPS = 1e-8; +void addInf(vector &res, double INF=INF) { vector

infPts({P(INF, INF), P(-INF, INF), P(-INF, -INF), P(INF, -INF)}); for (int i=0; i<4; i++) res.push_back({infPts[i], infPts[(i+1)%4]}); } +P randPt(int lim = INF) { + return P(rand() % lim, rand() % lim); +} void test1() { vector t({{P(0,0),P(5,0)}, {P(5,-2), P(5,2)}, {P(5,2),P(2,2)}, {P(0,3),P(0,-3)}}); auto res = halfPlaneIntersection(t); - cout< t({{P(0,0), P(5,0)}}); addInf(t); auto res = halfPlaneIntersection(t); - assert(polygonArea2(res)/4e18); + assert(polygonArea2(res)/(4*INF*INF) == 1); t = vector({{P(0,0), P(5,0)}, {P(0,0), P(0,5)}}); addInf(t); res = halfPlaneIntersection(t); - assert(polygonArea2(res)/2e18 == 1); + assert(polygonArea2(res)/(2*INF*INF) == 1); } void testLine() { vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}}); @@ -150,11 +155,40 @@ void testEmpty() { auto res = halfPlaneIntersection(t); assert(sz(res) == 0); } +void testRandom() { + for (int i=0; i<1000; i++) { + vector t; + for (int i=0; i<3; i++){ + Line cand{P(0,0), P(0,0)}; + while (cand[0] == cand[1]) + cand = {randPt(), randPt()}; + t.push_back(cand); + } + addInf(t); + auto res = halfPlaneIntersection(t); + double area = MIT::Intersection_Area(convert(t)); + double diff = abs(2*area - polygonArea2(res)); + if (diff > EPS) { + cout<"< t({{P(9,8), P(9,1)}, {P(3,3),P(3,5)},{P(7,6),P(0,8)}}); + addInf(t); + cout< Date: Sun, 5 May 2019 00:24:48 -0400 Subject: [PATCH 18/44] Added fuzz tests with SJTU code --- fuzz-tests/geometry/HalfPlane.cpp | 288 ++++++++++++++++++------------ 1 file changed, 169 insertions(+), 119 deletions(-) diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 70456f03a..3c4285d35 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -1,8 +1,8 @@ #include using namespace std; -#define rep(i, a, b) for(int i = a; i < int(b); ++i) -#define trav(a, v) for(auto& a : v) +#define rep(i, a, b) for (int i = a; i < int(b); ++i) +#define trav(a, v) for (auto &a : v) #define all(x) x.begin(), x.end() #define sz(x) (int)(x).size() @@ -16,108 +16,154 @@ typedef Point P; ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } -namespace MIT { -#define eps 1e-8 -typedef Point P; +namespace sjtu { +const double EPS = 1e-8; +inline int sign(double a) { return a < -EPS ? -1 : a > EPS; } +struct Point { + double x, y; + Point() {} + Point(double _x, double _y) : x(_x), y(_y) {} + Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); } + Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); } + Point operator*(double d) const { return Point(x * d, y * d); } + Point operator/(double d) const { return Point(x / d, y / d); } + bool operator<(const Point &p) const { + int c = sign(x - p.x); + if (c) + return c == -1; + return sign(y - p.y) == -1; + } + double dot(const Point &p) const { return x * p.x + y * p.y; } + double det(const Point &p) const { return x * p.y - y * p.x; } + double alpha() const { return atan2(y, x); } + double distTo(const Point &p) const { + double dx = x - p.x, dy = y - p.y; + return hypot(dx, dy); + } + double alphaTo(const Point &p) const { + double dx = x - p.x, dy = y - p.y; + return atan2(dy, dx); + } + // clockwise + Point rotAlpha(const double &alpha, const Point &o = Point(0, 0)) const { + double nx = cos(alpha) * (x - o.x) + sin(alpha) * (y - o.y); + double ny = -sin(alpha) * (x - o.x) + cos(alpha) * (y - o.y); + return Point(nx, ny) + o; + } + Point rot90() const { return Point(-y, x); } + Point unit() { return *this / abs(); } + void read() { scanf("%lf%lf", &x, &y); } + double abs() { return hypot(x, y); } + double abs2() { return x * x + y * y; } + void write() { cout << "(" << x << "," << y << ")" << endl; } +}; +#define cross(p1, p2, p3) ((p2.x - p1.x) * (p3.y - p1.y) - (p3.x - p1.x) * (p2.y - p1.y)) +#define crossOp(p1, p2, p3) sign(cross(p1, p2, p3)) -template -pair lineIntersection(P s1, P e1, P s2, P e2) { - auto d = (e1-s1).cross(e2-s2); - if (d == 0) //if parallel - return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; - else - return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; +Point isSS(Point p1, Point p2, Point q1, Point q2) { + double a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2); + return (p1 * a2 + p2 * a1) / (a1 + a2); } - -struct Line { - P P1, P2; - // Right hand side of the ray P1 -> P2 - explicit Line(P a = P(), P b = P()) : P1(a), P2(b) {}; - P intpo(Line y) { - auto res = lineIntersection(P1, P2, y.P1, y.P2); - assert(res.first == 1); - return res.second; - } - P dir() { - return P2 - P1; - } - bool contains(P x) { - return (P2 - P1).cross(x - P1) < eps; - } - bool out(P x) { - return !contains(x); - } +struct Border { + Point p1, p2; + double alpha; + void setAlpha() { alpha = atan2(p2.y - p1.y, p2.x - p1.x); } + void read() { + p1.read(); + p2.read(); + setAlpha(); + } }; -template -bool mycmp(Point a, Point b) { - // return atan2(a.y, a.x) < atan2(b.y, b.x); - if (a.x * b.x < 0) return a.x < 0; - if (abs(a.x) < eps) { - if (abs(b.x) < eps) return a.y > 0 && b.y < 0; - if (b.x < 0) return a.y > 0; - if (b.x > 0) return true; - } - if (abs(b.x) < eps) { - if (a.x < 0) return b.y < 0; - if (a.x > 0) return false; - } - return a.cross(b) > 0; +int n; +const int MAX_N_BORDER = 20000 + 10; +Border border[MAX_N_BORDER]; + +bool operator<(const Border &a, const Border &b) { + int c = sign(a.alpha - b.alpha); + if (c != 0) + return c == 1; + return crossOp(b.p1, b.p2, a.p1) >= 0; +} + +bool operator==(const Border &a, const Border &b) { return sign(a.alpha - b.alpha) == 0; } + +void add(double x, double y, double nx, double ny) { + border[n].p1 = Point(x, y); + border[n].p2 = Point(nx, ny); + border[n].setAlpha(); + n++; } -bool cmp(Line a, Line b) { - return mycmp(a.dir(), b.dir()); +Point isBorder(const Border &a, const Border &b) { return isSS(a.p1, a.p2, b.p1, b.p2); } + +Border que[MAX_N_BORDER]; +int qh, qt; + +bool check(const Border &a, const Border &b, const Border &me) { + Point is = isBorder(a, b); + return crossOp(me.p1, me.p2, is) > 0; } -double Intersection_Area(vector b) { - sort(b.begin(), b.end(), cmp); - int n = b.size(); - int q = 1, h = 0, i; - vector ca(b.size() + 10); - for (i = 0; i < n; i++) { - while (q < h && b[i].out(ca[h].intpo(ca[h - 1]))) h--; - while (q < h && b[i].out(ca[q].intpo(ca[q + 1]))) q++; - ca[++h] = b[i]; - if (q < h && abs(ca[h].dir().cross(ca[h - 1].dir())) < eps) { - h--; - if (b[i].out(ca[h].P1)) ca[h] = b[i]; - } - } - while (q < h - 1 && ca[q].out(ca[h].intpo(ca[h - 1]))) h--; - while (q < h - 1 && ca[h].out(ca[q].intpo(ca[q + 1]))) q++; - // Intersection is empty. This is sometimes different from the case when - // the intersection area is 0. - if (h - q <= 1) return 0; - ca[h + 1] = ca[q]; - vector

s; - for (i = q; i <= h; i++) s.push_back(ca[i].intpo(ca[i + 1])); - s.push_back(s[0]); - // for (auto i: s) cout< convert(vector x) { - vector res; - for (auto i: x) - res.push_back(MIT::Line(i[1], i[0])); - return res; + +double halfPlaneIntersection(vector cur) { + n = 0; + for (auto i: cur) + add(i[0].x, i[0].y, i[1].x, i[1].y); + convexIntersection(); + return calcArea(); } +} // namespace sjtu -const double INF = 1e1; +const double INF = 100; const double EPS = 1e-8; -void addInf(vector &res, double INF=INF) { +void addInf(vector &res, double INF = INF) { vector

infPts({P(INF, INF), P(-INF, INF), P(-INF, -INF), P(INF, -INF)}); - for (int i=0; i<4; i++) - res.push_back({infPts[i], infPts[(i+1)%4]}); -} -P randPt(int lim = INF) { - return P(rand() % lim, rand() % lim); + for (int i = 0; i < 4; i++) + res.push_back({infPts[i], infPts[(i + 1) % 4]}); } +P randPt(int lim = INF) { return P(rand() % lim, rand() % lim); } void test1() { - vector t({{P(0,0),P(5,0)}, {P(5,-2), P(5,2)}, {P(5,2),P(2,2)}, {P(0,3),P(0,-3)}}); + vector t({{P(0, 0), P(5, 0)}, {P(5, -2), P(5, 2)}, {P(5, 2), P(2, 2)}, {P(0, 3), P(0, -3)}}); auto res = halfPlaneIntersection(t); assert(polygonArea2(res) == 20); addInf(t); @@ -125,70 +171,74 @@ void test1() { assert(polygonArea2(res) == 20); } void testInf() { - vector t({{P(0,0), P(5,0)}}); + vector t({{P(0, 0), P(5, 0)}}); addInf(t); auto res = halfPlaneIntersection(t); - assert(polygonArea2(res)/(4*INF*INF) == 1); - t = vector({{P(0,0), P(5,0)}, {P(0,0), P(0,5)}}); + assert(polygonArea2(res) / (4 * INF * INF) == 1); + t = vector({{P(0, 0), P(5, 0)}, {P(0, 0), P(0, 5)}}); addInf(t); res = halfPlaneIntersection(t); - assert(polygonArea2(res)/(2*INF*INF) == 1); + assert(polygonArea2(res) / (2 * INF * INF) == 1); } void testLine() { - vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}}); + vector t({{P(0, 0), P(5, 0)}, {P(5, 0), P(0, 0)}}); addInf(t); auto res = halfPlaneIntersection(t); assert(sz(res) >= 2); assert(polygonArea2(res) == 0); } void testPoint() { - vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}, {P(0,0), P(0,5)}, {P(0,5), P(0,0)}}); + vector t({{P(0, 0), P(5, 0)}, {P(5, 0), P(0, 0)}, {P(0, 0), P(0, 5)}, {P(0, 5), P(0, 0)}}); addInf(t); auto res = halfPlaneIntersection(t); assert(sz(res) >= 1); assert(polygonArea2(res) == 0); } void testEmpty() { - vector t({{P(0,0), P(5,0)}, {P(5,0), P(0,0)}, {P(0,0), P(0,5)}, {P(0,5), P(0,0)}, - {P(0,2), P(5,2)}}); + vector t( + {{P(0, 0), P(5, 0)}, {P(5, 0), P(0, 0)}, {P(0, 0), P(0, 5)}, {P(0, 5), P(0, 0)}, {P(0, 2), P(5, 2)}}); addInf(t); auto res = halfPlaneIntersection(t); assert(sz(res) == 0); } void testRandom() { - for (int i=0; i<1000; i++) { + int lim = 10; + for (int i = 0; i < 1000; i++) { vector t; - for (int i=0; i<3; i++){ - Line cand{P(0,0), P(0,0)}; + for (int i = 0; i < 6; i++) { + Line cand{P(0, 0), P(0, 0)}; while (cand[0] == cand[1]) - cand = {randPt(), randPt()}; + cand = {randPt(lim), randPt(lim)}; t.push_back(cand); } - addInf(t); + addInf(t, lim); auto res = halfPlaneIntersection(t); - double area = MIT::Intersection_Area(convert(t)); - double diff = abs(2*area - polygonArea2(res)); + double area = sjtu::halfPlaneIntersection(t); + double diff = abs(2 * area - polygonArea2(res)); if (diff > EPS) { - cout<"<" << i[1] << ' '; + cout << endl; + for (auto i : res) + cout << i << ','; + cout << endl; } assert(diff < EPS); } } int main() { - // test1(); - // testInf(); - // testLine(); - // testPoint(); - // testEmpty(); - // testRandom(); - vector t({{P(9,8), P(9,1)}, {P(3,3),P(3,5)},{P(7,6),P(0,8)}}); - addInf(t); - cout< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); + // addInf(t); + // cout << polygonArea2(halfPlaneIntersection(t)) << endl; + // cout << MIT::Intersection_Area(convert(t)) << endl; + cout << "Tests passed!" << endl; } From 4df6e0ed91c4bc1475f4226e2442e58bfd1ae324 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 00:29:14 -0400 Subject: [PATCH 19/44] Fit stuff within 63 columns --- content/geometry/HalfPlane.h | 38 ++++++++++++++++++------------------ 1 file changed, 19 insertions(+), 19 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 4efa0e936..2adff4cff 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -20,25 +20,25 @@ typedef array Line; #define sp(a) a[0], a[1] #define ang(a) atan2((a[1] - a[0]).y, (a[1] - a[0]).x) bool cmp(Line a, Line b) { - auto s = ang(a) - ang(b); - return s == 0 ? sideOf(sp(b), a[0]) >=0 : s < 0; + auto s = ang(a) - ang(b); + return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; } vector

halfPlaneIntersection(vector vs) { - sort(all(vs), cmp); - vector deq(sz(vs)+5); - vector

ans(sz(vs)+5); - int dh = 0, dt = 1, ah=0, at=0; - deq[0] = vs[0]; - for (int i = 1; i < sz(vs); ++i) { - if (ang(vs[i]) - ang(vs[i-1]) == 0) continue; - while (ah < at && sideOf(sp(vs[i]), ans[at-1])< 0) at--, dt--; - while (ah < at && sideOf(sp(vs[i]), ans[ah]) < 0) ah++, dh++; - ans[at++] = lineInter(sp(deq[dt-1]), sp(vs[i])).second; - deq[dt++] = vs[i]; - } - while (ah < at && sideOf(sp(deq[dh]), ans[at-1]) < 0) at--, dt--; - while (ah < at && sideOf(sp(deq[dt]), ans[ah]) < 0) ah++, dh++; - if (dt-dh <= 2) return {}; - ans[at++] = lineInter(sp(deq[dh]), sp(deq[dt-1])).second; - return {ans.begin()+ah, ans.begin()+at}; + sort(all(vs), cmp); + vector deq(sz(vs) + 5); + vector

ans(sz(vs) + 5); + int dh = 0, dt = 1, ah = 0, at = 0; + deq[0] = vs[0]; + for (int i = 1; i < sz(vs); ++i) { + if (ang(vs[i]) - ang(vs[i - 1]) == 0) continue; + while (ah Date: Sun, 5 May 2019 01:05:25 -0400 Subject: [PATCH 20/44] Added option for long double in Halfplane tests --- fuzz-tests/geometry/HalfPlane.cpp | 56 +++++++++++++++++-------------- fuzz-tests/utils/genConvex.h | 0 2 files changed, 30 insertions(+), 26 deletions(-) create mode 100644 fuzz-tests/utils/genConvex.h diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 3c4285d35..cfb7ae049 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -17,56 +17,57 @@ typedef Point P; ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } namespace sjtu { -const double EPS = 1e-8; -inline int sign(double a) { return a < -EPS ? -1 : a > EPS; } +typedef double T; +const T EPS = 1e-8; +inline int sign(T a) { return a < -EPS ? -1 : a > EPS; } struct Point { - double x, y; + T x, y; Point() {} - Point(double _x, double _y) : x(_x), y(_y) {} + Point(T _x, T _y) : x(_x), y(_y) {} Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); } Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); } - Point operator*(double d) const { return Point(x * d, y * d); } - Point operator/(double d) const { return Point(x / d, y / d); } + Point operator*(T d) const { return Point(x * d, y * d); } + Point operator/(T d) const { return Point(x / d, y / d); } bool operator<(const Point &p) const { int c = sign(x - p.x); if (c) return c == -1; return sign(y - p.y) == -1; } - double dot(const Point &p) const { return x * p.x + y * p.y; } - double det(const Point &p) const { return x * p.y - y * p.x; } - double alpha() const { return atan2(y, x); } - double distTo(const Point &p) const { - double dx = x - p.x, dy = y - p.y; + T dot(const Point &p) const { return x * p.x + y * p.y; } + T det(const Point &p) const { return x * p.y - y * p.x; } + T alpha() const { return atan2(y, x); } + T distTo(const Point &p) const { + T dx = x - p.x, dy = y - p.y; return hypot(dx, dy); } - double alphaTo(const Point &p) const { - double dx = x - p.x, dy = y - p.y; + T alphaTo(const Point &p) const { + T dx = x - p.x, dy = y - p.y; return atan2(dy, dx); } // clockwise - Point rotAlpha(const double &alpha, const Point &o = Point(0, 0)) const { - double nx = cos(alpha) * (x - o.x) + sin(alpha) * (y - o.y); - double ny = -sin(alpha) * (x - o.x) + cos(alpha) * (y - o.y); + Point rotAlpha(const T &alpha, const Point &o = Point(0, 0)) const { + T nx = cos(alpha) * (x - o.x) + sin(alpha) * (y - o.y); + T ny = -sin(alpha) * (x - o.x) + cos(alpha) * (y - o.y); return Point(nx, ny) + o; } Point rot90() const { return Point(-y, x); } Point unit() { return *this / abs(); } void read() { scanf("%lf%lf", &x, &y); } - double abs() { return hypot(x, y); } - double abs2() { return x * x + y * y; } + T abs() { return hypot(x, y); } + T abs2() { return x * x + y * y; } void write() { cout << "(" << x << "," << y << ")" << endl; } }; #define cross(p1, p2, p3) ((p2.x - p1.x) * (p3.y - p1.y) - (p3.x - p1.x) * (p2.y - p1.y)) #define crossOp(p1, p2, p3) sign(cross(p1, p2, p3)) Point isSS(Point p1, Point p2, Point q1, Point q2) { - double a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2); + T a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2); return (p1 * a2 + p2 * a1) / (a1 + a2); } struct Border { Point p1, p2; - double alpha; + T alpha; void setAlpha() { alpha = atan2(p2.y - p1.y, p2.x - p1.x); } void read() { p1.read(); @@ -88,7 +89,7 @@ bool operator<(const Border &a, const Border &b) { bool operator==(const Border &a, const Border &b) { return sign(a.alpha - b.alpha) == 0; } -void add(double x, double y, double nx, double ny) { +void add(T x, T y, T nx, T ny) { border[n].p1 = Point(x, y); border[n].p2 = Point(nx, ny); border[n].setAlpha(); @@ -123,7 +124,7 @@ void convexIntersection() { ++qh; } -double calcArea() { +T calcArea() { static Point ps[MAX_N_BORDER]; int cnt = 0; @@ -136,7 +137,7 @@ double calcArea() { ps[cnt++] = isBorder(que[i], que[next]); } - double area = 0; + T area = 0; for (int i = 0; i < cnt; ++i) { area += ps[i].det(ps[(i + 1) % cnt]); } @@ -145,7 +146,7 @@ double calcArea() { return area; } -double halfPlaneIntersection(vector cur) { +T halfPlaneIntersection(vector cur) { n = 0; for (auto i: cur) add(i[0].x, i[0].y, i[1].x, i[1].y); @@ -202,7 +203,7 @@ void testEmpty() { assert(sz(res) == 0); } void testRandom() { - int lim = 10; + int lim = 1e2; for (int i = 0; i < 1000; i++) { vector t; for (int i = 0; i < 6; i++) { @@ -227,6 +228,9 @@ void testRandom() { assert(diff < EPS); } } +void testConvex() { + +} int main() { test1(); @@ -235,7 +239,7 @@ int main() { testPoint(); testEmpty(); testRandom(); - // Failure case for MIT + // Failure case for MIT's half plane code // vector t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // addInf(t); // cout << polygonArea2(halfPlaneIntersection(t)) << endl; diff --git a/fuzz-tests/utils/genConvex.h b/fuzz-tests/utils/genConvex.h new file mode 100644 index 000000000..e69de29bb From cbd17e8c0f3b1472fdb93d68aff6ca50ffd945b6 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 01:47:50 -0400 Subject: [PATCH 21/44] Abstracted away the angle comparison --- content/geometry/HalfPlane.h | 8 +++++--- fuzz-tests/geometry/HalfPlane.cpp | 16 +++++++++++----- 2 files changed, 16 insertions(+), 8 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 2adff4cff..71dca543e 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -19,18 +19,20 @@ typedef Point P; typedef array Line; #define sp(a) a[0], a[1] #define ang(a) atan2((a[1] - a[0]).y, (a[1] - a[0]).x) + +int angDiff(Line a, Line b) { return sgn(ang(a) - ang(b)); } bool cmp(Line a, Line b) { - auto s = ang(a) - ang(b); + auto s = angDiff(a, b); return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; } vector

halfPlaneIntersection(vector vs) { sort(all(vs), cmp); vector deq(sz(vs) + 5); vector

ans(sz(vs) + 5); - int dh = 0, dt = 1, ah = 0, at = 0; deq[0] = vs[0]; + int dh = 0, dt = 1, ah = 0, at = 0; for (int i = 1; i < sz(vs); ++i) { - if (ang(vs[i]) - ang(vs[i - 1]) == 0) continue; + if (angDiff(vs[i], vs[i - 1]) == 0) continue; while (ah vi; #include "../../content/geometry/HalfPlane.h" #include "../../content/geometry/PolygonArea.h" -typedef Point P; ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } @@ -203,8 +202,8 @@ void testEmpty() { assert(sz(res) == 0); } void testRandom() { - int lim = 1e2; - for (int i = 0; i < 1000; i++) { + int lim = 1e1; + for (int i = 0; i < 10000; i++) { vector t; for (int i = 0; i < 6; i++) { Line cand{P(0, 0), P(0, 0)}; @@ -228,8 +227,8 @@ void testRandom() { assert(diff < EPS); } } -void testConvex() { - +void testSelf() { + int lim = 1e2; } int main() { @@ -239,6 +238,13 @@ int main() { testPoint(); testEmpty(); testRandom(); + vector t({{P(0,0), P(5,0)}, {P(0,1), P(5,1)}}); + reverse(all(t)); + addInf(t); + + auto res = halfPlaneIntersection(t); + for (auto i: res) cout< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // addInf(t); From 2eee5c119161f138e0b5067997afe2e045cbc8b8 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 01:51:54 -0400 Subject: [PATCH 22/44] Added newline --- content/geometry/HalfPlane.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 71dca543e..a5e1c4178 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -43,4 +43,4 @@ vector

halfPlaneIntersection(vector vs) { if (dt - dh <= 2) return {}; ans[at++] = lineInter(sp(deq[dh]), sp(deq[dt - 1])).second; return {ans.begin() + ah, ans.begin() + at}; -} \ No newline at end of file +} From a1d85bb5c9ae8cc2db1c0d29576eda3a859f7b58 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 06:07:46 -0400 Subject: [PATCH 23/44] Updated header --- content/geometry/HalfPlane.h | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index a5e1c4178..b0a4f8025 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -1,12 +1,12 @@ /** - * Author: - * Date: - * License: - * Source: - * Description: - * Time: - * Status: + * Author: chilli + * Date: 2019-05-05 + * License: CC0 + * Source: https://github.com/zimpha/algorithmic-library/blob/master/computational-geometry/polygon.cc + * Description: Computes the intersection of a set of half-planes. + * Time: O(n \log n) + * Status: fuzz-tested, submitted on https://maps19.kattis.com/problems/marshlandrescues * Usage: */ #pragma once From b0b03a9809a888b2400ebec1093712b30fe33d6d Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 12:34:11 -0400 Subject: [PATCH 24/44] Responded to comments and tried a macro --- content/geometry/HalfPlane.h | 9 ++++----- content/geometry/PolygonCut.h | 6 ++---- content/geometry/lineIntersection.h | 20 ++++++++++---------- fuzz-tests/geometry/HalfPlane | Bin 0 -> 554872 bytes fuzz-tests/geometry/HalfPlane.cpp | 10 ---------- 5 files changed, 16 insertions(+), 29 deletions(-) create mode 100755 fuzz-tests/geometry/HalfPlane diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index b0a4f8025..a6b4f0754 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -31,16 +31,15 @@ vector

halfPlaneIntersection(vector vs) { vector

ans(sz(vs) + 5); deq[0] = vs[0]; int dh = 0, dt = 1, ah = 0, at = 0; + #define upd(l, pt, op) while (ah < at && sideOf(sp(l), ans[pt]) < 0) op; for (int i = 1; i < sz(vs); ++i) { if (angDiff(vs[i], vs[i - 1]) == 0) continue; - while (ah polygonCut(const vector

& poly, P s, P e) { rep(i,0,sz(poly)) { P cur = poly[i], prev = i ? poly[i-1] : poly.back(); bool side = s.cross(e, cur) < 0; - if (side != (s.cross(e, prev) < 0)) { - res.emplace_back(); - lineIntersection(s, e, cur, prev, res.back()); - } + if (side != (s.cross(e, prev) < 0)) + res.push_back(lineInter(s, e, cur, prev).second); if (side) res.push_back(cur); } diff --git a/content/geometry/lineIntersection.h b/content/geometry/lineIntersection.h index 9b277312c..8dda44ebf 100644 --- a/content/geometry/lineIntersection.h +++ b/content/geometry/lineIntersection.h @@ -1,20 +1,20 @@ /** - * Author: Ulf Lundstrom - * Date: 2009-03-21 + * Author: Victor Lecomte, chilli + * Date: 2019-05-05 * License: CC0 - * Source: + * Source: https://vlecomte.github.io/cp-geo.pdf * Description:\\ \begin{minipage}{75mm} -If a unique intersection point of the lines going through s1,e1 and s2,e2 exists r is set to this point and 1 is returned. If no intersection point exists 0 is returned and if infinitely many exists -1 is returned. If s1==e1 or s2==e2 -1 is returned. The wrong position will be returned if P is Point and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. +If a unique intersection point of the lines going through s1,e1 and s2,e2 exists {1, point} is returned. If no intersection point exists {0, (0,0)} is returned and if infinitely many exists {-1, (0,0)} is returned. The wrong position will be returned if P is Point and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. \end{minipage} \begin{minipage}{15mm} \includegraphics[width=\textwidth]{content/geometry/lineIntersection} \end{minipage} - * Status: tested + * Status: tested through half-plane tests * Usage: - * point intersection; - * if (1 == LineIntersection(s1,e1,s2,e2,intersection)) - * cout << "intersection point at " << intersection << endl; + * auto res = lineInter(s1,e1,s2,e2); + * if (res.first == 1) + * cout << "intersection point at " << res.second << endl; */ #pragma once @@ -24,7 +24,7 @@ template pair lineInter(P s1, P e1, P s2, P e2) { auto d = (e1-s1).cross(e2-s2); if (d == 0) //if parallel - return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; + return {-(s1.cross(e1, s2)==0 || s2==e2), P(0,0)}; else - return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; + return {1, s2-(e2-s2)*s1.cross(e1, s2)/d}; } diff --git a/fuzz-tests/geometry/HalfPlane 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ZW;?huf4Z%Va literal 0 HcmV?d00001 diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index cf22443b3..f230fa60b 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -227,9 +227,6 @@ void testRandom() { assert(diff < EPS); } } -void testSelf() { - int lim = 1e2; -} int main() { test1(); @@ -238,13 +235,6 @@ int main() { testPoint(); testEmpty(); testRandom(); - vector t({{P(0,0), P(5,0)}, {P(0,1), P(5,1)}}); - reverse(all(t)); - addInf(t); - - auto res = halfPlaneIntersection(t); - for (auto i: res) cout< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // addInf(t); From 81f9cd3abfa588928661c32229de4b6a8369230b Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 13:01:49 -0400 Subject: [PATCH 25/44] removed extraneous deque variables --- content/geometry/HalfPlane.h | 16 ++++++++-------- fuzz-tests/geometry/HalfPlane | Bin 554872 -> 0 bytes fuzz-tests/geometry/HalfPlane.cpp | 10 +++++----- 3 files changed, 13 insertions(+), 13 deletions(-) delete mode 100755 fuzz-tests/geometry/HalfPlane diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index a6b4f0754..931f3376d 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -30,16 +30,16 @@ vector

halfPlaneIntersection(vector vs) { vector deq(sz(vs) + 5); vector

ans(sz(vs) + 5); deq[0] = vs[0]; - int dh = 0, dt = 1, ah = 0, at = 0; - #define upd(l, pt, op) while (ah < at && sideOf(sp(l), ans[pt]) < 0) op; + int ah = 0, at = 0; for (int i = 1; i < sz(vs); ++i) { if (angDiff(vs[i], vs[i - 1]) == 0) continue; - upd(vs[i], at-1, (at--,dt--)) upd(vs[i], ah, (ah++,dh++)); - ans[at++] = lineInter(sp(deq[dt - 1]), sp(vs[i])).second; - deq[dt++] = vs[i]; + while (ah=;bQzUe|mhXM<`|Nz(r|Q(H zQ>RXyI<<85!*l#NrMA|XM_*V?r)KuS>{XO!ZUPeVaD-V(lck3^?HCEZ)z z6e*o+0Xqjtcm?|ABi(F#NJ`)6Yz|GN09;eX-X#TOxkw$9uUgJmE$369QP!6N6@8LU z=-wu$w}dH3qf3EAOIPL@dp?CtQ(5#+aHXtx1uFUOMLv@AKfM&SkCw}8O)pup{0fwd z=lT`Rm^v`JUr~Oaq8YPG7WG*aJFw5d=)Uvk^zF~;P3B4}O&>Lm>lSfq%b@L_*S}S0 z?$9&2@y3RwuZ$gX|Z#)2IZ?6EWE%+HycJHH^>I(vpaB`S3RmAYtAPI1A!`EzFH7R|6P&RG!2i02F_ zF0rTPQF!DSdrY2vadCk)FEwfam@k}>Uoaa*%&-%O`|^u235>Bv4a~`zGv7Y1Aa|A` zKpwDBdDC;}<=E%t&alr13rJ*-8UQh7K z-!kwDVxK;5&O+2SKPNADzFih@P)<%0KDVf7P97!vNj1rmYVsE4=1eQeotK|8ub`*^ zdIRn3g|jG!uTEm~=SV6cb>%c=%FUZwGGiWP8e@;nn^R(EMa_vREGn5l9h!py%#zwZ 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ZW;?huf4Z%Va diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index f230fa60b..40cc8346d 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -229,12 +229,12 @@ void testRandom() { } int main() { - test1(); - testInf(); - testLine(); + // test1(); + // testInf(); + // testLine(); testPoint(); - testEmpty(); - testRandom(); + // testEmpty(); + // testRandom(); // Failure case for MIT's half plane code // vector t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // addInf(t); From d2832674b4546f20977c62f9205cf92ea75a322e Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 13:25:40 -0400 Subject: [PATCH 26/44] Updated description and such --- content/geometry/HalfPlane.h | 4 +++- fuzz-tests/geometry/HalfPlane.cpp | 12 ++++++------ 2 files changed, 9 insertions(+), 7 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 931f3376d..e8943a8a3 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -4,7 +4,8 @@ * Date: 2019-05-05 * License: CC0 * Source: https://github.com/zimpha/algorithmic-library/blob/master/computational-geometry/polygon.cc - * Description: Computes the intersection of a set of half-planes. + * Description: Computes the intersection of a set of half-planes. Input is given as a set of planes, facing left. + * Output is the convex polygon representing the intersection. The points may have duplicates and be collinear. * Time: O(n \log n) * Status: fuzz-tested, submitted on https://maps19.kattis.com/problems/marshlandrescues * Usage: @@ -41,5 +42,6 @@ vector

halfPlaneIntersection(vector vs) { while (ah t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // addInf(t); // cout << polygonArea2(halfPlaneIntersection(t)) << endl; From 8c6bb7cc0c52fa4b8aca20273f9024696999c7f3 Mon Sep 17 00:00:00 2001 From: Horace He Date: Sun, 5 May 2019 14:25:57 -0400 Subject: [PATCH 27/44] Shortened half plane through macros --- content/geometry/HalfPlane.h | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index e8943a8a3..be8e3030d 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -32,16 +32,15 @@ vector

halfPlaneIntersection(vector vs) { vector

ans(sz(vs) + 5); deq[0] = vs[0]; int ah = 0, at = 0; - for (int i = 1; i < sz(vs); ++i) { +#define fix(a, b) \ +while (ah Date: Sun, 5 May 2019 15:06:15 -0400 Subject: [PATCH 28/44] Shortened half plane a bit --- content/geometry/HalfPlane.h | 16 +++++++--------- 1 file changed, 7 insertions(+), 9 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index be8e3030d..7b271e5f2 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -1,4 +1,3 @@ - /** * Author: chilli * Date: 2019-05-05 @@ -31,16 +30,15 @@ vector

halfPlaneIntersection(vector vs) { vector deq(sz(vs) + 5); vector

ans(sz(vs) + 5); deq[0] = vs[0]; - int ah = 0, at = 0; -#define fix(a, b) \ -while (ah Date: Mon, 6 May 2019 05:03:06 -0400 Subject: [PATCH 29/44] Started fixing the bugs --- content/geometry/HalfPlane.h | 8 +++++++- content/geometry/lineIntersection.h | 5 +++++ fuzz-tests/geometry/HalfPlane.cpp | 17 ++++++++++++----- 3 files changed, 24 insertions(+), 6 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 7b271e5f2..523946368 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -36,7 +36,13 @@ vector

halfPlaneIntersection(vector vs) { if (angDiff(vs[i], vs[i - 1]) == 0) continue; while (ah lineInter(P s1, P e1, P s2, P e2) { else return {1, s2-(e2-s2)*s1.cross(e1, s2)/d}; } +template P lineInter2(P p1, P p2, P q1, P q2) { + double a1 = q1.cross(q2, p1), a2 = -q1.cross(q2, p2); + auto res = (p1 * a2 + p2 * a1) / (a1 + a2); + return res; +} diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 08306c100..9473cad3f 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -10,10 +10,11 @@ typedef long long ll; typedef pair pii; typedef vector vi; -#include "../../content/geometry/HalfPlane.h" #include "../../content/geometry/PolygonArea.h" - +typedef Point P; ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } +#include "../../content/geometry/HalfPlane.h" + namespace sjtu { typedef double T; @@ -203,7 +204,7 @@ void testEmpty() { } void testRandom() { int lim = 1e1; - for (int i = 0; i < 10000; i++) { + for (int i = 0; i < 10000000; i++) { vector t; for (int i = 0; i < 6; i++) { Line cand{P(0, 0), P(0, 0)}; @@ -214,9 +215,11 @@ void testRandom() { addInf(t, lim); auto res = halfPlaneIntersection(t); double area = sjtu::halfPlaneIntersection(t); - double diff = abs(2 * area - polygonArea2(res)); + double resArea = polygonArea2(res)/2; + if (isnan(resArea)) resArea = 0; + double diff = abs(area - resArea); if (diff > EPS) { - cout << diff << ' ' << area << ' ' << endl; + cout << diff << ' ' << area << ' ' <" << i[1] << ' '; cout << endl; @@ -237,6 +240,10 @@ int main() { testRandom(); // Failure case for MIT's half plane cod // vector t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); + // Failure case for old code. + // vector t({{P(3,0),P(3,3)},{P(5,3), P(5,0)}, {P(4,-2), P(0,1)}, {P(3,-1), P(0,-1)}}); + // addInf(t); + // cout << polygonArea2(halfPlaneIntersection(t)) << endl; // addInf(t); // cout << polygonArea2(halfPlaneIntersection(t)) << endl; // cout << MIT::Intersection_Area(convert(t)) << endl; From 1aa4b39501dc70e61de9d2ed4ce7b266d491d49e Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 6 May 2019 05:12:56 -0400 Subject: [PATCH 30/44] Fixed bugs/found bugs --- content/geometry/HalfPlane.h | 4 ---- content/geometry/lineIntersection.h | 1 + fuzz-tests/geometry/HalfPlane.cpp | 11 +++++++++-- 3 files changed, 10 insertions(+), 6 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 523946368..e9b113489 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -37,10 +37,6 @@ vector

halfPlaneIntersection(vector vs) { while (ah lineInter(P s1, P e1, P s2, P e2) { else return {1, s2-(e2-s2)*s1.cross(e1, s2)/d}; } + template P lineInter2(P p1, P p2, P q1, P q2) { double a1 = q1.cross(q2, p1), a2 = -q1.cross(q2, p2); auto res = (p1 * a2 + p2 * a1) / (a1 + a2); diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 9473cad3f..c6e20481f 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -223,6 +223,9 @@ void testRandom() { for (auto i : t) cout << i[0] << "->" << i[1] << ' '; cout << endl; + for (auto i : t) + cout << "{P"< t({{P(8,9),P(8,2)},{P(3,9),P(5,2)},{P(8,2),P(8,3)},{P(7,2),P(1,7)},{P(1,0),P(7,1)},{P(9,2),P(5,6)},{P(10,10),P(-10,10)},{P(-10,10),P(-10,-10)},{P(-10,-10),P(10,-10)},{P(10,-10),P(10,10)}}); + auto res = halfPlaneIntersection(t); + cout< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // Failure case for old code. @@ -246,6 +254,5 @@ int main() { // cout << polygonArea2(halfPlaneIntersection(t)) << endl; // addInf(t); // cout << polygonArea2(halfPlaneIntersection(t)) << endl; - // cout << MIT::Intersection_Area(convert(t)) << endl; cout << "Tests passed!" << endl; } From e61acd57ea5e8dd042be9d6b92f5600868121255 Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 6 May 2019 05:45:30 -0400 Subject: [PATCH 31/44] Doing some precision analysis --- content/geometry/HalfPlane.h | 8 +- fuzz-tests/geometry/HalfPlane.cpp | 148 ++++++++++++++++++++++++++---- 2 files changed, 137 insertions(+), 19 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index e9b113489..eeda330f9 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -14,6 +14,7 @@ #include "Point.h" #include "sideOf.h" #include "lineIntersection.h" +#include "lineDistance.h" typedef Point P; typedef array Line; @@ -25,6 +26,7 @@ bool cmp(Line a, Line b) { auto s = angDiff(a, b); return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; } +double mxErr1 = 0, mxErr2 = 0; vector

halfPlaneIntersection(vector vs) { sort(all(vs), cmp); vector deq(sz(vs) + 5); @@ -38,7 +40,11 @@ vector

halfPlaneIntersection(vector vs) { while (i!=n && ah P; ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } #include "../../content/geometry/HalfPlane.h" - namespace sjtu { typedef double T; const T EPS = 1e-8; @@ -148,12 +147,112 @@ T calcArea() { T halfPlaneIntersection(vector cur) { n = 0; - for (auto i: cur) + for (auto i : cur) add(i[0].x, i[0].y, i[1].x, i[1].y); convexIntersection(); return calcArea(); } +#undef cross } // namespace sjtu +namespace mit { +#define eps 1e-8 +typedef Point P; + +template pair lineIntersection(P s1, P e1, P s2, P e2) { + auto d = (e1 - s1).cross(e2 - s2); + if (d == 0) // if parallel + return {-((e1 - s1).cross(s2 - s1) == 0 || s2 == e2), P(0, 0)}; + else + return {1, s2 - (e2 - s2) * (e1 - s1).cross(s2 - s1) / d}; +} + +struct Line { + P P1, P2; + // Right hand side of the ray P1 -> P2 + explicit Line(P a = P(), P b = P()) : P1(a), P2(b){}; + P intpo(Line y) { + auto res = lineIntersection(P1, P2, y.P1, y.P2); + assert(res.first == 1); + return res.second; + } + P dir() { return P2 - P1; } + bool contains(P x) { return (P2 - P1).cross(x - P1) < eps; } + bool out(P x) { return !contains(x); } +}; + +template bool mycmp(Point a, Point b) { + // return atan2(a.y, a.x) < atan2(b.y, b.x); + if (a.x * b.x < 0) + return a.x < 0; + if (abs(a.x) < eps) { + if (abs(b.x) < eps) + return a.y > 0 && b.y < 0; + if (b.x < 0) + return a.y > 0; + if (b.x > 0) + return true; + } + if (abs(b.x) < eps) { + if (a.x < 0) + return b.y < 0; + if (a.x > 0) + return false; + } + return a.cross(b) > 0; +} + +bool cmp(Line a, Line b) { return mycmp(a.dir(), b.dir()); } + +double Intersection_Area(vector b) { + sort(b.begin(), b.end(), cmp); + int n = b.size(); + int q = 1, h = 0, i; + vector ca(b.size() + 10); + for (i = 0; i < n; i++) { + while (q < h && b[i].out(ca[h].intpo(ca[h - 1]))) + h--; + while (q < h && b[i].out(ca[q].intpo(ca[q + 1]))) + q++; + ca[++h] = b[i]; + if (q < h && abs(ca[h].dir().cross(ca[h - 1].dir())) < eps) { + if (ca[h].dir().dot(ca[h - 1].dir()) > 0) { + h--; + if (b[i].out(ca[h].P1)) + ca[h] = b[i]; + } else { + // The area is either 0 or infinite. + // If you have a bounding box, then the area is definitely 0. + return 0; + } + } + } + while (q < h - 1 && ca[q].out(ca[h].intpo(ca[h - 1]))) + h--; + while (q < h - 1 && ca[h].out(ca[q].intpo(ca[q + 1]))) + q++; + // Intersection is empty. This is sometimes different from the case when + // the intersection area is 0. + if (h - q <= 1) + return 0; + ca[h + 1] = ca[q]; + vector

s; + for (i = q; i <= h; i++) + s.push_back(ca[i].intpo(ca[i + 1])); + s.push_back(s[0]); + // for (auto i: s) cout< convert(vector x) { + vector res; + for (auto i : x) + res.push_back(mit::Line(i[1], i[0])); + return res; +} const double INF = 100; const double EPS = 1e-8; @@ -203,8 +302,8 @@ void testEmpty() { assert(sz(res) == 0); } void testRandom() { - int lim = 1e1; - for (int i = 0; i < 10000000; i++) { + int lim = 3; + for (int i = 0; i < 1000000; i++) { vector t; for (int i = 0; i < 6; i++) { Line cand{P(0, 0), P(0, 0)}; @@ -215,16 +314,17 @@ void testRandom() { addInf(t, lim); auto res = halfPlaneIntersection(t); double area = sjtu::halfPlaneIntersection(t); - double resArea = polygonArea2(res)/2; - if (isnan(resArea)) resArea = 0; + // double resArea = polygonArea2(res)/2; + double resArea = mit::Intersection_Area(convert(t)); double diff = abs(area - resArea); if (diff > EPS) { - cout << diff << ' ' << area << ' ' <" << i[1] << ' '; cout << endl; for (auto i : t) - cout << "{P"< t({{P(8,9),P(8,2)},{P(3,9),P(5,2)},{P(8,2),P(8,3)},{P(7,2),P(1,7)},{P(1,0),P(7,1)},{P(9,2),P(5,6)},{P(10,10),P(-10,10)},{P(-10,10),P(-10,-10)},{P(-10,-10),P(10,-10)},{P(10,-10),P(10,10)}}); + vector t({{P(8, 9), P(8, 2)}, + {P(3, 9), P(5, 2)}, + {P(8, 2), P(8, 3)}, + {P(7, 2), P(1, 7)}, + {P(1, 0), P(7, 1)}, + {P(9, 2), P(5, 6)}, + {P(10, 10), P(-10, 10)}, + {P(-10, 10), P(-10, -10)}, + {P(-10, -10), P(10, -10)}, + {P(10, -10), P(10, 10)}}); auto res = halfPlaneIntersection(t); - cout< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // Failure case for old code. // vector t({{P(3,0),P(3,3)},{P(5,3), P(5,0)}, {P(4,-2), P(0,1)}, {P(3,-1), P(0,-1)}}); From 4cb642a401794b03f96a7ce999c15539cd7b66d1 Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 6 May 2019 05:49:22 -0400 Subject: [PATCH 32/44] Updated with current version --- content/geometry/HalfPlane.h | 6 +----- content/geometry/lineDistance.h | 2 +- content/geometry/lineIntersection.h | 26 ++++++++++++-------------- fuzz-tests/geometry/HalfPlane | Bin 0 -> 740960 bytes fuzz-tests/geometry/HalfPlane.cpp | 11 +++++------ 5 files changed, 19 insertions(+), 26 deletions(-) create mode 100755 fuzz-tests/geometry/HalfPlane diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index eeda330f9..1cb6f3ef9 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -40,11 +40,7 @@ vector

halfPlaneIntersection(vector vs) { while (i!=n && ah and the intersection point does not have integer coordinates. Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long. -\end{minipage} +If a unique intersection point of the lines going through s1,e1 and s2,e2 exists {1, point} is returned. If no +intersection point exists {0, (0,0)} is returned and if infinitely many exists {-1, (0,0)} is returned. The wrong +position will be returned if P is Point and the intersection point does not have integer coordinates. Products of +three coordinates are used in intermediate steps so watch out for overflow if using int or long long. \end{minipage} \begin{minipage}{15mm} \includegraphics[width=\textwidth]{content/geometry/lineIntersection} \end{minipage} @@ -20,17 +22,13 @@ If a unique intersection point of the lines going through s1,e1 and s2,e2 exists #include "Point.h" -template -pair lineInter(P s1, P e1, P s2, P e2) { - auto d = (e1-s1).cross(e2-s2); - if (d == 0) //if parallel - return {-(s1.cross(e1, s2)==0 || s2==e2), P(0,0)}; - else - return {1, s2-(e2-s2)*s1.cross(e1, s2)/d}; -} +template pair lineInter(P s1, P e1, P s2, P e2) { + auto d = (e1 - s1).cross(e2 - s2); + if (d == 0) // if parallel + return {-(s1.cross(e1, s2) == 0 || s2 == e2), P(0, 0)}; + else { -template P lineInter2(P p1, P p2, P q1, P q2) { - double a1 = q1.cross(q2, p1), a2 = -q1.cross(q2, p2); - auto res = (p1 * a2 + p2 * a1) / (a1 + a2); - return res; + double a1 = s2.cross(e2, s1), a2 = -s2.cross(e2, e1); + return {1, (s1 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literal 0 HcmV?d00001 diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 0fa7abca6..2b3bd22c1 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -335,12 +335,11 @@ void testRandom() { } int main() { - // test1(); - // testInf(); - // testLine(); - // testPoint(); - // testEmpty(); - srand(time(0)); + test1(); + testInf(); + testLine(); + testPoint(); + testEmpty(); testRandom(); // Case that messes with precision vector t({{P(8, 9), P(8, 2)}, From 50a3915230e07b90a30e90b95b63ee518fac50d4 Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 6 May 2019 19:48:45 -0400 Subject: [PATCH 33/44] Shortened a bit --- content/geometry/HalfPlane.h | 3 +-- content/geometry/lineIntersection.h | 1 - 2 files changed, 1 insertion(+), 3 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 1cb6f3ef9..ad7ca3ba0 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -40,8 +40,7 @@ vector

halfPlaneIntersection(vector vs) { while (i!=n && ah pair lineInter(P s1, P e1, P s2, P e2) { if (d == 0) // if parallel return {-(s1.cross(e1, s2) == 0 || s2 == e2), P(0, 0)}; else { - double a1 = s2.cross(e2, s1), a2 = -s2.cross(e2, e1); return {1, (s1 * a2 + e1 * a1) / (a1 + a2)}; } From 3d7e6f047ad10992fdbe3a8bf36ff89a9573faa8 Mon Sep 17 00:00:00 2001 From: Horace He Date: Wed, 8 May 2019 23:06:42 -0400 Subject: [PATCH 34/44] removed binary --- fuzz-tests/geometry/HalfPlane | Bin 740960 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100755 fuzz-tests/geometry/HalfPlane diff --git a/fuzz-tests/geometry/HalfPlane b/fuzz-tests/geometry/HalfPlane deleted file mode 100755 index 4735ffbdcfb647401dd5e86b19b7db02bc1ddd4e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 740960 zcmeFa33wD$);?a9bd!b(sg8n1L}|3q1O*Z{6Cs!ts-c5XKta%e3ERjLNe3bdM3W$G zXhaA1Wf+H1#=((s8+A|G%JZ|Mxu8&r@~o 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From a8b3ec7943fe21895e33a84bf8bffa6494dcd75f Mon Sep 17 00:00:00 2001 From: Horace He Date: Mon, 13 May 2019 20:01:44 -0400 Subject: [PATCH 35/44] Removed some debug code --- content/geometry/HalfPlane.h | 2 -- 1 file changed, 2 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index ad7ca3ba0..5fdb1c273 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -14,7 +14,6 @@ #include "Point.h" #include "sideOf.h" #include "lineIntersection.h" -#include "lineDistance.h" typedef Point P; typedef array Line; @@ -26,7 +25,6 @@ bool cmp(Line a, Line b) { auto s = angDiff(a, b); return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; } -double mxErr1 = 0, mxErr2 = 0; vector

halfPlaneIntersection(vector vs) { sort(all(vs), cmp); vector deq(sz(vs) + 5); From 8971c0322b70739c58d7c3fdc7d23df3948ab73b Mon Sep 17 00:00:00 2001 From: Horace He Date: Sat, 26 Oct 2019 12:06:30 -0400 Subject: [PATCH 36/44] some debugging stuff --- content/geometry/HalfPlane.h | 30 +++++- content/geometry/PolygonArea.h | 4 +- content/geometry/lineIntersection.h | 19 +++- content/geometry/sideOf.h | 8 +- content/strings/Hashing.h | 10 +- fuzz-tests/geometry/HalfPlane | Bin 0 -> 1026576 bytes fuzz-tests/geometry/HalfPlane.cpp | 156 +++++++++++++++++++++++----- fuzz-tests/geometry/t | 50 +++++++++ fuzz-tests/geometry/t2 | 53 ++++++++++ fuzz-tests/graph/MaximumClique | Bin 0 -> 410448 bytes 10 files changed, 287 insertions(+), 43 deletions(-) create mode 100755 fuzz-tests/geometry/HalfPlane create mode 100644 fuzz-tests/geometry/t create mode 100644 fuzz-tests/geometry/t2 create mode 100755 fuzz-tests/graph/MaximumClique diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 5fdb1c273..29ccfb9de 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -27,18 +27,40 @@ bool cmp(Line a, Line b) { } vector

halfPlaneIntersection(vector vs) { sort(all(vs), cmp); + // for (auto l: vs) { + // cout< "< deq(sz(vs) + 5); vector

ans(sz(vs) + 5); deq[0] = vs[0]; int ah = 0, at = 0, n = sz(vs); rep(i,1,n+1) { if (i == n) vs.push_back(deq[ah]); - if (angDiff(vs[i], vs[i - 1]) == 0) continue; - while (ah "< T polygonArea2(vector> v) { if (sz(v) < 3) return 0; T a = v.back().cross(v[0]); - rep(i,0,sz(v)-1) a += v[i].cross(v[i+1]); + rep(i,0,sz(v)-1) { + a += v[i].cross(v[i+1]); + } return a; } diff --git a/content/geometry/lineIntersection.h b/content/geometry/lineIntersection.h index c5dce95d9..b40d850d3 100644 --- a/content/geometry/lineIntersection.h +++ b/content/geometry/lineIntersection.h @@ -25,9 +25,18 @@ Products of three coordinates are used in intermediate steps so watch out for ov template pair lineInter(P s1, P e1, P s2, P e2) { - auto d = (e1 - s1).cross(e2 - s2); - if (d == 0) // if parallel - return {-(s1.cross(e1, s2) == 0), P(0, 0)}; - auto p = s2.cross(e1, e2), q = s2.cross(e2, s1); - return {1, (s1 * p + e1 * q) / d}; + auto d = (e1-s1).cross(e2-s2); + if (d == 0) //if parallel + return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; + else + return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; } + +// template +// pair lineInter(P s1, P e1, P s2, P e2) { +// auto d = (e1 - s1).cross(e2 - s2); +// if (d == 0) // if parallel +// return {-(s1.cross(e1, s2) == 0), P(0, 0)}; +// auto p = s2.cross(e1, e2), q = s2.cross(e2, s1); +// return {1, (s1 * p + e1 * q) / d}; +// } diff --git a/content/geometry/sideOf.h b/content/geometry/sideOf.h index 61b40eaae..dd342658e 100644 --- a/content/geometry/sideOf.h +++ b/content/geometry/sideOf.h @@ -19,5 +19,11 @@ template int sideOf(const P& s, const P& e, const P& p, double eps) { auto a = (e-s).cross(p-s); double l = (e-s).dist()*eps; - return (a > l) - (a < -l); + if (a<=l && a>=-l) { + return 0; + } else if (a > l) { + return 1; + } else { + return -1; + } } diff --git a/content/strings/Hashing.h b/content/strings/Hashing.h index 516f7c6fc..b91316387 100644 --- a/content/strings/Hashing.h +++ b/content/strings/Hashing.h @@ -16,10 +16,12 @@ struct H { typedef uint64_t ull; ull x; H(ull x=0) : x(x) {} -#define OP(O,A,B) H operator O(H o) { ull r = x; asm \ - (A "addq %%rdx, %0\n adcq $0,%0" : "+a"(r) : B); return r; } - OP(+,,"d"(o.x)) OP(*,"mul %1\n", "r"(o.x) : "rdx") - H operator-(H o) { return *this + ~o.x; } + H operator+(H o) { return x + o.x + (x + o.x < x); } + H operator*(H o) { + ull r = x; + asm("mul %1\n addq %%rdx, %0\n adcq $0,%0" : "+a"(r) : "r"(o.x) : "rdx"); + return r; + } H operator-(H o) { return *this + ~o.x; } ull get() const { return x + !~x; } bool operator==(H o) const { return get() == o.get(); } bool operator<(H o) const { return get() < o.get(); } diff --git a/fuzz-tests/geometry/HalfPlane b/fuzz-tests/geometry/HalfPlane new file mode 100755 index 0000000000000000000000000000000000000000..ef086151d1478d5592074302abe6bf846002eb24 GIT binary patch literal 1026576 zcmeFa3w%`7xi-Eh$-oF?_C%q^`>3NPppYO`f}jZ`um>g@xdsU)m;}KBiOGZ@qQoXa 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C!GeMX=^pbv*A@Jw(mc%^+rdii@lu_UX^(L5cg~ zbAONP{mJ^BqHSNN<F>|nDOb){{H~}himly_`E7{41_&@{n1?zpZ=F=n->Bf^Lrmwn?Im8Khyub zT+{!&k2ll(3*kpxCJHX()k@*d=N5@0mZV2ZrAO;E!k^F663wT(WSd&2TIMk#FGbd0 zt;Jg4;$VfbGk>tuI=ztY&*yWA2Md2$zk7v0pW`LA>d)EJ|2Y1%ZPW|t@%g+ju}Q=i z!=b#7(e)!7{x+l`crJL|170g!Z^kFSraAgijKH7I4{v}!d7hT{$2Re8ZS&?HH&Z@m zypi#dKj$a?I1V3aU$0N}=kv&|ztKkhS8O2om;S_0^_q15;JM|E#^uGp(=5=B=smxZ z?$75`UW7llGs@79?R@R**_c0{mw6xlgQv88cDay_!0w1I`$>QO_(_{TFIVr6xIO%h zHT7@oA+x-NM641`wWq`XFPn_R>h9cgnYQ#VcK9!P+W4&$^I!TO;_&bHy78a#6cTsj ze-!*>{VLa+8MkRv+YN~EiQaRGTuzU)*E?pUuf4MU{?ByyZ#vi8DwTTwlXTT^EH8H3 z3=Mz7d~d5%!S@mN(91{a|2h9SFZJVvskx_@`S;>Q#{VMkppo_``|8cFVD6^zl532A Kop2CM_5T1bL`qcv literal 0 HcmV?d00001 diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 1756e80ab..8e07ab83c 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -302,22 +302,37 @@ void testEmpty() { assert(sz(res) == 0); } void testRandom() { - int lim = 3; - for (int i = 0; i < 1000000; i++) { + int lim = 5; + for (int i = 0; i < 10000000; i++) { vector t; - for (int i = 0; i < 6; i++) { + for (int i = 0; i < 4; i++) { Line cand{P(0, 0), P(0, 0)}; while (cand[0] == cand[1]) cand = {randPt(lim), randPt(lim)}; + Point s1 = Point(cand[0].x, cand[0].y); + Point e1 = Point(cand[1].x, cand[1].y); + bool fail = false; + for (auto j: t) { + Point s2 = Point(j[0].x, j[0].y); + Point e2 = Point(j[1].x, j[1].y); + if (lineInter(s1, e1, s2, e2).first == -1) { + fail = false; + break; + } + } + if (fail) { + i--; + continue; + } t.push_back(cand); } addInf(t, lim); auto res = halfPlaneIntersection(t); double area = sjtu::halfPlaneIntersection(t); - // double resArea = polygonArea2(res)/2; - double resArea = mit::Intersection_Area(convert(t)); + double resArea = abs(polygonArea2(res) / 2); + // double resArea = mit::Intersection_Area(convert(t)); double diff = abs(area - resArea); - if (diff > EPS) { + if (diff > EPS || isnan(diff)) { cout << diff << ' ' << area << ' ' << resArea << endl; for (auto i : t) cout << i[0] << "->" << i[1] << ' '; @@ -330,36 +345,121 @@ void testRandom() { cout << i << ','; cout << endl; } - assert(diff < EPS); + assert(diff <= EPS); } } +vector

convexHull(vector

pts) { + if (sz(pts) <= 1) return pts; + sort(all(pts)); + vector

h(sz(pts)+1); + int s = 0, t = 0; + for (int it = 2; it--; s = --t, reverse(all(pts))) + trav(p, pts) { + while (t >= s + 2 && h[t-2].cross(h[t-1], p) <= 0) t--; + h[t++] = p; + } + return {h.begin(), h.begin() + t - (t == 2 && h[0] == h[1])}; +} + int main() { - test1(); - testInf(); - testLine(); - testPoint(); - testEmpty(); - testRandom(); + // test1(); + // testInf(); + // testLine(); + // testPoint(); + // testRandom(); + // return 0; + // testEmpty(); // Case that messes with precision - vector t({{P(8, 9), P(8, 2)}, - {P(3, 9), P(5, 2)}, - {P(8, 2), P(8, 3)}, - {P(7, 2), P(1, 7)}, - {P(1, 0), P(7, 1)}, - {P(9, 2), P(5, 6)}, - {P(10, 10), P(-10, 10)}, - {P(-10, 10), P(-10, -10)}, - {P(-10, -10), P(10, -10)}, - {P(10, -10), P(10, 10)}}); - auto res = halfPlaneIntersection(t); - cout << polygonArea2(res) << endl; - cout << sjtu::halfPlaneIntersection(t) << endl; - cout << mit::Intersection_Area(convert(t))< cases({{P(1,0),P(0,2)},{P(0,1),P(2,0)},{P(0,0),P(1,1)},{P(2,2),P(1,1)},{P(3,3),P(-3,3)},{P(-3,3),P(-3,-3)},{P(-3,-3),P(3,-3)},{P(3,-3),P(3,3)}}); + + // auto pts = halfPlaneIntersection(cases); + // for (auto p: pts) { + // cout< mn = {1e6, 1e6, 10}; + for (int i = 0; i < 10000000; i++) { + ll offset = rand() % ll(1e9); + ll mul = rand() % ll(1e9); + vector>> cases; + + cases.push_back({10, + {{P(offset + mul * 8, offset + mul * 9), P(offset + mul * 8, offset + mul * 2)}, + {P(offset + mul * 3, offset + mul * 9), P(offset + mul * 5, offset + mul * 2)}, + {P(offset + mul * 8, offset + mul * 2), P(offset + mul * 8, offset + mul * 3)}, + {P(offset + mul * 7, offset + mul * 2), P(offset + mul * 1, offset + mul * 7)}, + {P(offset + mul * 1, offset + mul * 0), P(offset + mul * 7, offset + mul * 1)}, + {P(offset + mul * 9, offset + mul * 2), P(offset + mul * 5, offset + mul * 6)}, + {P(offset + mul * 10, offset + mul * 10), P(offset + mul * -10, offset + mul * 10)}, + {P(offset + mul * -10, offset + mul * 10), P(offset + mul * -10, offset + mul * -10)}, + {P(offset + mul * -10, offset + mul * -10), P(offset + mul * 10, offset + mul * -10)}, + {P(offset + mul * 10, offset + mul * -10), P(offset + mul * 10, offset + mul * 10)}}}); + cases.push_back({5, + {{P(offset + mul * 0, offset + mul * 1), P(offset + mul * 4, offset + mul * 0)}, + {P(offset + mul * 0, offset + mul * 2), P(offset + mul * 2, offset + mul * 0)}, + {P(offset + mul * 1, offset + mul * 0), P(offset + mul * 3, offset + mul * 4)}, + {P(offset + mul * 4, offset + mul * 2), P(offset + mul * 0, offset + mul * 0)}, + {P(offset + mul * 4, offset + mul * 2), P(offset + mul * 2, offset + mul * 2)}, + {P(offset + mul * 0, offset + mul * 3), P(offset + mul * 1, offset + mul * 1)}, + {P(offset + mul * 5, offset + mul * 5), P(offset + mul * -5, offset + mul * 5)}, + {P(offset + mul * -5, offset + mul * 5), P(offset + mul * -5, offset + mul * -5)}, + {P(offset + mul * -5, offset + mul * -5), P(offset + mul * 5, offset + mul * -5)}, + {P(offset + mul * 5, offset + mul * -5), P(offset + mul * 5, offset + mul * 5)}}}); + cases.push_back({20, + {{P(offset + mul * 10, offset + mul * 12), P(offset + mul * 16, offset + mul * 5)}, + {P(offset + mul * 10, offset + mul * 12), P(offset + mul * 4, offset + mul * 19)}, + {P(offset + mul * 18, offset + mul * 15), P(offset + mul * 17, offset + mul * 7)}, + {P(offset + mul * 12, offset + mul * 13), P(offset + mul * 14, offset + mul * 6)}, + {P(offset + mul * 16, offset + mul * 3), P(offset + mul * 4, offset + mul * 11)}, + {P(offset + mul * 12, offset + mul * 8), P(offset + mul * 9, offset + mul * 0)}, + {P(offset + mul * 20, offset + mul * 20), P(offset + mul * -20, offset + mul * 20)}, + {P(offset + mul * -20, offset + mul * 20), P(offset + mul * -20, offset + mul * -20)}, + {P(offset + mul * -20, offset + mul * -20), P(offset + mul * 20, offset + mul * -20)}, + {P(offset + mul * 20, offset + mul * -20), P(offset + mul * 20, offset + mul * 20)}}}); + // {P(5,8),P(4,9)},{P(9,1),P(5,8)},{P(9,7),P(7,6)},{P(3,7),P(8,5)},{P(6,6),P(8,4)},{P(6,1),P(7,2)},{P(10,10),P(-10,10)},{P(-10,10),P(-10,-10)},{P(-10,-10),P(10,-10)},{P(10,-10),P(10,10)}, + int idx = 0; + for (auto tmp : cases) { + auto t = tmp.second; + auto lim = tmp.first; + auto res = halfPlaneIntersection(t); + auto ours = polygonArea2(res); + if (abs(ours) > 1e-3) { + if (mn[0] + mn[1] * mn[2] >= offset + mul * tmp.first) { + cout << "case: " << idx << endl; + cout << offset << ' ' << mul << ' ' << offset + mul * tmp.first << endl; + cout << ours << ' ' << sjtu::halfPlaneIntersection(t) << endl; + + double mx = 0; + for (auto i: res) { + for (auto j: res) + mx = max(mx, (i - j).dist()); + } + cout<<"mx: "< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); // Failure case for old code. - // vector t({{P(3,0),P(3,3)},{P(5,3), P(5,0)}, {P(4,-2), P(0,1)}, {P(3,-1), P(0,-1)}}); // addInf(t); // cout << polygonArea2(halfPlaneIntersection(t)) << endl; // addInf(t); diff --git a/fuzz-tests/geometry/t b/fuzz-tests/geometry/t new file mode 100644 index 000000000..6d7744604 --- /dev/null +++ b/fuzz-tests/geometry/t @@ -0,0 +1,50 @@ +(2,2) -> (1,1) +(-3,3) -> (-3,-3) +(0,1) -> (2,0) +(-3,-3) -> (3,-3) +(0,0) -> (1,1) +(3,-3) -> (3,3) +(1,0) -> (0,2) +(3,3) -> (-3,3) +i: 1 +ans: 0 1 +(-3,-3) +deq: (2,2)-> (1,1) (-3,3)-> (-3,-3) + +i: 2 +ans: 0 1 +(0.666667,0.666667) +deq: (2,2)-> (1,1) (0,1)-> (2,0) + +i: 3 +ans: 0 2 +(0.666667,0.666667) (8,-3) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (-3,-3)-> (3,-3) + +i: 4 +ans: 0 2 +(0.666667,0.666667) (0.666667,0.666667) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) + +i: 5 +ans: 0 3 +(0.666667,0.666667) (0.666667,0.666667) (3,3) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (3,-3)-> (3,3) + +i: 6 +ans: 1 3 +(0.666667,0.666667) (0.666667,0.666667) +deq: (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) + +i: 7 +ans: 1 4 +(0.666667,0.666667) (0.666667,0.666667) (-0.5,3) +deq: (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (3,3)-> (-3,3) + +i: 8 +ans: 1 5 +(0.666667,0.666667) (0.666667,0.666667) (-0.5,3) (-4,3) +deq: (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (3,3)-> (-3,3) (0,1)-> (2,0) + +(0.666667,0.666667) (0.666667,0.666667) (-0.5,3) (-4,3) +8.16667 diff --git a/fuzz-tests/geometry/t2 b/fuzz-tests/geometry/t2 new file mode 100644 index 000000000..1e26596c9 --- /dev/null +++ b/fuzz-tests/geometry/t2 @@ -0,0 +1,53 @@ +(2,2) -> (1,1) +(-3,3) -> (-3,-3) +(0,1) -> (2,0) +(-3,-3) -> (3,-3) +(0,0) -> (1,1) +(3,-3) -> (3,3) +(1,0) -> (0,2) +(3,3) -> (-3,3) +i: 1 +ans: 0 1 +(-3,-3) +deq: (2,2)-> (1,1) (-3,3)-> (-3,-3) + +i: 2 +ans: 0 1 +(0.666667,0.666667) +deq: (2,2)-> (1,1) (0,1)-> (2,0) + +i: 3 +ans: 0 2 +(0.666667,0.666667) (8,-3) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (-3,-3)-> (3,-3) + +i: 4 +ans: 0 2 +(0.666667,0.666667) (0.666667,0.666667) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) + +i: 5 +ans: 0 3 +(0.666667,0.666667) (0.666667,0.666667) (3,3) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (3,-3)-> (3,3) + +i: 6 +ans: 0 3 +(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) + +i: 7 +ans: 0 4 +(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) (-0.5,3) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (3,3)-> (-3,3) + +i: 8 +ans: 0 4 +(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) +deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (2,2)-> (1,1) + +(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) +0 +0 +0 +0 diff --git a/fuzz-tests/graph/MaximumClique b/fuzz-tests/graph/MaximumClique new file mode 100755 index 0000000000000000000000000000000000000000..7d6f9a405869058d8752e763d81e9b9353b99672 GIT binary patch literal 410448 zcmeFad3;RQ8wY&Oo#jq)BNGv!s6@mPVhMt=CX&b<#!jg%B4S@-QWT|4f-!<_N_Ejq zs~g>Q(}Y^8t+l19t)*I%qE%|AdB4xOOD4*@eBOWF&-?k!=X2*d=RDu%InQ~{e(srM 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z_))#NZLhyun>v5Dy%6fp_-&;}ZV^{Xfo0mXc<)cbf%~(U%cU-Nb%Op!p9p9CYfh=I zZ+%y0IOHF=e>h?;#r=Z)L_A;qvEQ;^%H_kT?}eJ--|g+8{+}(O?4#>yn}>b3jAm}e L0eC=<4{1@T literal 0 HcmV?d00001 From 5f4ff5ab5c672726286a89d3d6fdfde58a1b0b48 Mon Sep 17 00:00:00 2001 From: Horace He Date: Thu, 31 Oct 2019 12:00:09 -0400 Subject: [PATCH 37/44] Added some experimentation code --- content/geometry/HalfPlane.h | 14 +++++++++----- content/geometry/lineIntersection.h | 28 ++++++++++++++-------------- fuzz-tests/geometry/HalfPlane.cpp | 20 +++++++++++++------- 3 files changed, 36 insertions(+), 26 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 29ccfb9de..abf62e7f1 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -25,7 +25,9 @@ bool cmp(Line a, Line b) { auto s = angDiff(a, b); return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; } -vector

halfPlaneIntersection(vector vs) { +std::random_device rd; +std::mt19937 e2(rd()); +vector

halfPlaneIntersection(vector vs, const double EPS=1e-8) { sort(all(vs), cmp); // for (auto l: vs) { // cout< "< halfPlaneIntersection(vector vs) { if (angDiff(vs[i], vs[i - 1]) == 0) { continue; } - - while (ah dist(-EPS, EPS); +while (ah -pair lineInter(P s1, P e1, P s2, P e2) { - auto d = (e1-s1).cross(e2-s2); - if (d == 0) //if parallel - return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; - else - return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; -} - // template // pair lineInter(P s1, P e1, P s2, P e2) { -// auto d = (e1 - s1).cross(e2 - s2); -// if (d == 0) // if parallel -// return {-(s1.cross(e1, s2) == 0), P(0, 0)}; -// auto p = s2.cross(e1, e2), q = s2.cross(e2, s1); -// return {1, (s1 * p + e1 * q) / d}; +// auto d = (e1-s1).cross(e2-s2); +// if (d == 0) //if parallel +// return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; +// else +// return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; // } + +template +pair lineInter(P s1, P e1, P s2, P e2) { + auto d = (e1 - s1).cross(e2 - s2); + if (d == 0) // if parallel + return {-(s1.cross(e1, s2) == 0), P(0, 0)}; + auto p = s2.cross(e1, e2), q = s2.cross(e2, s1); + return {1, (s1 * p + e1 * q) / d}; +} diff --git a/fuzz-tests/geometry/HalfPlane.cpp b/fuzz-tests/geometry/HalfPlane.cpp index 8e07ab83c..ca43d3319 100644 --- a/fuzz-tests/geometry/HalfPlane.cpp +++ b/fuzz-tests/geometry/HalfPlane.cpp @@ -301,8 +301,9 @@ void testEmpty() { auto res = halfPlaneIntersection(t); assert(sz(res) == 0); } -void testRandom() { - int lim = 5; +void testRandom(const double EPS) { + int lim = 3; + double mxDiff = 0; for (int i = 0; i < 10000000; i++) { vector t; for (int i = 0; i < 4; i++) { @@ -327,12 +328,14 @@ void testRandom() { t.push_back(cand); } addInf(t, lim); - auto res = halfPlaneIntersection(t); + auto res = halfPlaneIntersection(t, EPS); double area = sjtu::halfPlaneIntersection(t); double resArea = abs(polygonArea2(res) / 2); // double resArea = mit::Intersection_Area(convert(t)); double diff = abs(area - resArea); - if (diff > EPS || isnan(diff)) { + mxDiff = max(diff, mxDiff); + continue; + if (diff > .1 || isnan(diff)) { cout << diff << ' ' << area << ' ' << resArea << endl; for (auto i : t) cout << i[0] << "->" << i[1] << ' '; @@ -344,9 +347,11 @@ void testRandom() { for (auto i : res) cout << i << ','; cout << endl; + assert(false); } - assert(diff <= EPS); } + cout<<"eps: "< convexHull(vector

pts) { if (sz(pts) <= 1) return pts; @@ -367,8 +372,9 @@ int main() { // testInf(); // testLine(); // testPoint(); - // testRandom(); - // return 0; + for (double e : {1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2}) + testRandom(e); + return 0; // testEmpty(); // Case that messes with precision // vector cases({{P(1,0),P(0,2)},{P(0,1),P(2,0)},{P(0,0),P(1,1)},{P(2,2),P(1,1)},{P(3,3),P(-3,3)},{P(-3,3),P(-3,-3)},{P(-3,-3),P(3,-3)},{P(3,-3),P(3,3)}}); From 74faa81417d07333d2f564429940d2a8493d2795 Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Jun 2020 01:55:19 -0700 Subject: [PATCH 38/44] remove unintended --- stress-tests/geometry/HalfPlane | Bin 1026576 -> 0 bytes stress-tests/graph/MaximumClique | Bin 410448 -> 0 bytes stress-tests/utils/genConvex.h | 0 3 files changed, 0 insertions(+), 0 deletions(-) delete mode 100755 stress-tests/geometry/HalfPlane delete mode 100755 stress-tests/graph/MaximumClique delete mode 100644 stress-tests/utils/genConvex.h diff --git 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z_))#NZLhyun>v5Dy%6fp_-&;}ZV^{Xfo0mXc<)cbf%~(U%cU-Nb%Op!p9p9CYfh=I zZ+%y0IOHF=e>h?;#r=Z)L_A;qvEQ;^%H_kT?}eJ--|g+8{+}(O?4#>yn}>b3jAm}e L0eC=<4{1@T diff --git a/stress-tests/utils/genConvex.h b/stress-tests/utils/genConvex.h deleted file mode 100644 index e69de29bb..000000000 From f3916db0c81892a81f2920e32e71a05bada3fbf4 Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Jun 2020 02:01:36 -0700 Subject: [PATCH 39/44] removed test cases --- stress-tests/geometry/t | 50 ------------------------------------- stress-tests/geometry/t2 | 53 ---------------------------------------- 2 files changed, 103 deletions(-) delete mode 100644 stress-tests/geometry/t delete mode 100644 stress-tests/geometry/t2 diff --git a/stress-tests/geometry/t b/stress-tests/geometry/t deleted file mode 100644 index 6d7744604..000000000 --- a/stress-tests/geometry/t +++ /dev/null @@ -1,50 +0,0 @@ -(2,2) -> (1,1) -(-3,3) -> (-3,-3) -(0,1) -> (2,0) -(-3,-3) -> (3,-3) -(0,0) -> (1,1) -(3,-3) -> (3,3) -(1,0) -> (0,2) -(3,3) -> (-3,3) -i: 1 -ans: 0 1 -(-3,-3) -deq: (2,2)-> (1,1) (-3,3)-> (-3,-3) - -i: 2 -ans: 0 1 -(0.666667,0.666667) -deq: (2,2)-> (1,1) (0,1)-> (2,0) - -i: 3 -ans: 0 2 -(0.666667,0.666667) (8,-3) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (-3,-3)-> (3,-3) - -i: 4 -ans: 0 2 -(0.666667,0.666667) (0.666667,0.666667) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) - -i: 5 -ans: 0 3 -(0.666667,0.666667) (0.666667,0.666667) (3,3) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (3,-3)-> (3,3) - -i: 6 -ans: 1 3 -(0.666667,0.666667) (0.666667,0.666667) -deq: (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) - -i: 7 -ans: 1 4 -(0.666667,0.666667) (0.666667,0.666667) (-0.5,3) -deq: (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (3,3)-> (-3,3) - -i: 8 -ans: 1 5 -(0.666667,0.666667) (0.666667,0.666667) (-0.5,3) (-4,3) -deq: (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (3,3)-> (-3,3) (0,1)-> (2,0) - -(0.666667,0.666667) (0.666667,0.666667) (-0.5,3) (-4,3) -8.16667 diff --git a/stress-tests/geometry/t2 b/stress-tests/geometry/t2 deleted file mode 100644 index 1e26596c9..000000000 --- a/stress-tests/geometry/t2 +++ /dev/null @@ -1,53 +0,0 @@ -(2,2) -> (1,1) -(-3,3) -> (-3,-3) -(0,1) -> (2,0) -(-3,-3) -> (3,-3) -(0,0) -> (1,1) -(3,-3) -> (3,3) -(1,0) -> (0,2) -(3,3) -> (-3,3) -i: 1 -ans: 0 1 -(-3,-3) -deq: (2,2)-> (1,1) (-3,3)-> (-3,-3) - -i: 2 -ans: 0 1 -(0.666667,0.666667) -deq: (2,2)-> (1,1) (0,1)-> (2,0) - -i: 3 -ans: 0 2 -(0.666667,0.666667) (8,-3) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (-3,-3)-> (3,-3) - -i: 4 -ans: 0 2 -(0.666667,0.666667) (0.666667,0.666667) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) - -i: 5 -ans: 0 3 -(0.666667,0.666667) (0.666667,0.666667) (3,3) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (3,-3)-> (3,3) - -i: 6 -ans: 0 3 -(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) - -i: 7 -ans: 0 4 -(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) (-0.5,3) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (3,3)-> (-3,3) - -i: 8 -ans: 0 4 -(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) -deq: (2,2)-> (1,1) (0,1)-> (2,0) (0,0)-> (1,1) (1,0)-> (0,2) (2,2)-> (1,1) - -(0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) (0.666667,0.666667) -0 -0 -0 -0 From 43305613c24b8adf166ec33e2dc6d74c91194400 Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Jun 2020 03:40:43 -0700 Subject: [PATCH 40/44] removed test cases --- content/geometry/HalfPlane.h | 41 +++------- content/geometry/lineIntersection.h | 9 --- content/geometry/sideOf.h | 8 +- content/strings/Hashing.h | 10 +-- stress-tests/geometry/HalfPlane.cpp | 120 +++------------------------- 5 files changed, 24 insertions(+), 164 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index abf62e7f1..bd8b95175 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -25,46 +25,23 @@ bool cmp(Line a, Line b) { auto s = angDiff(a, b); return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; } -std::random_device rd; -std::mt19937 e2(rd()); -vector

halfPlaneIntersection(vector vs, const double EPS=1e-8) { +vector

halfPlaneIntersection(vector vs) { + const double EPS = sqrt(2) * 1e-8; sort(all(vs), cmp); - // for (auto l: vs) { - // cout< "< deq(sz(vs) + 5); vector

ans(sz(vs) + 5); deq[0] = vs[0]; int ah = 0, at = 0, n = sz(vs); rep(i,1,n+1) { if (i == n) vs.push_back(deq[ah]); - if (angDiff(vs[i], vs[i - 1]) == 0) { - continue; - } -const double mult = 1.414; -std::uniform_real_distribution<> dist(-EPS, EPS); -while (ah "< -// pair lineInter(P s1, P e1, P s2, P e2) { -// auto d = (e1-s1).cross(e2-s2); -// if (d == 0) //if parallel -// return {-((e1-s1).cross(s2-s1)==0 || s2==e2), P(0,0)}; -// else -// return {1, s2-(e2-s2)*(e1-s1).cross(s2-s1)/d}; -// } - template pair lineInter(P s1, P e1, P s2, P e2) { auto d = (e1 - s1).cross(e2 - s2); diff --git a/content/geometry/sideOf.h b/content/geometry/sideOf.h index dd342658e..61b40eaae 100644 --- a/content/geometry/sideOf.h +++ b/content/geometry/sideOf.h @@ -19,11 +19,5 @@ template int sideOf(const P& s, const P& e, const P& p, double eps) { auto a = (e-s).cross(p-s); double l = (e-s).dist()*eps; - if (a<=l && a>=-l) { - return 0; - } else if (a > l) { - return 1; - } else { - return -1; - } + return (a > l) - (a < -l); } diff --git a/content/strings/Hashing.h b/content/strings/Hashing.h index 7499a35be..c91746d06 100644 --- a/content/strings/Hashing.h +++ b/content/strings/Hashing.h @@ -16,12 +16,10 @@ struct H { typedef uint64_t ull; ull x; H(ull x=0) : x(x) {} - H operator+(H o) { return x + o.x + (x + o.x < x); } - H operator*(H o) { - ull r = x; - asm("mul %1\n addq %%rdx, %0\n adcq $0,%0" : "+a"(r) : "r"(o.x) : "rdx"); - return r; - } H operator-(H o) { return *this + ~o.x; } +#define OP(O,A,B) H operator O(H o) { ull r = x; asm \ + (A "addq %%rdx, %0\n adcq $0,%0" : "+a"(r) : B); return r; } + OP(+,,"d"(o.x)) OP(*,"mul %1\n", "r"(o.x) : "rdx") + H operator-(H o) { return *this + ~o.x; } ull get() const { return x + !~x; } bool operator==(H o) const { return get() == o.get(); } bool operator<(H o) const { return get() < o.get(); } diff --git a/stress-tests/geometry/HalfPlane.cpp b/stress-tests/geometry/HalfPlane.cpp index ca43d3319..66559c611 100644 --- a/stress-tests/geometry/HalfPlane.cpp +++ b/stress-tests/geometry/HalfPlane.cpp @@ -12,13 +12,13 @@ typedef vector vi; #include "../../content/geometry/PolygonArea.h" typedef Point P; -ostream &operator<<(ostream &os, P p) { return cout << "(" << p.x << "," << p.y << ")"; } + #include "../../content/geometry/HalfPlane.h" namespace sjtu { typedef double T; -const T EPS = 1e-8; -inline int sign(T a) { return a < -EPS ? -1 : a > EPS; } +const T sEPS = 1e-8; +inline int sign(T a) { return a < -sEPS ? -1 : a > sEPS; } struct Point { T x, y; Point() {} @@ -255,7 +255,6 @@ vector convert(vector x) { } const double INF = 100; -const double EPS = 1e-8; void addInf(vector &res, double INF = INF) { vector

infPts({P(INF, INF), P(-INF, INF), P(-INF, -INF), P(INF, -INF)}); for (int i = 0; i < 4; i++) @@ -301,7 +300,7 @@ void testEmpty() { auto res = halfPlaneIntersection(t); assert(sz(res) == 0); } -void testRandom(const double EPS) { +void testRandom() { int lim = 3; double mxDiff = 0; for (int i = 0; i < 10000000; i++) { @@ -328,13 +327,12 @@ void testRandom(const double EPS) { t.push_back(cand); } addInf(t, lim); - auto res = halfPlaneIntersection(t, EPS); + auto res = halfPlaneIntersection(t); double area = sjtu::halfPlaneIntersection(t); double resArea = abs(polygonArea2(res) / 2); // double resArea = mit::Intersection_Area(convert(t)); double diff = abs(area - resArea); mxDiff = max(diff, mxDiff); - continue; if (diff > .1 || isnan(diff)) { cout << diff << ' ' << area << ' ' << resArea << endl; for (auto i : t) @@ -350,8 +348,6 @@ void testRandom(const double EPS) { assert(false); } } - cout<<"eps: "< convexHull(vector

pts) { if (sz(pts) <= 1) return pts; @@ -368,107 +364,11 @@ vector

convexHull(vector

pts) { int main() { - // test1(); - // testInf(); - // testLine(); - // testPoint(); - for (double e : {1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2}) - testRandom(e); - return 0; - // testEmpty(); - // Case that messes with precision - // vector cases({{P(1,0),P(0,2)},{P(0,1),P(2,0)},{P(0,0),P(1,1)},{P(2,2),P(1,1)},{P(3,3),P(-3,3)},{P(-3,3),P(-3,-3)},{P(-3,-3),P(3,-3)},{P(3,-3),P(3,3)}}); - - // auto pts = halfPlaneIntersection(cases); - // for (auto p: pts) { - // cout< mn = {1e6, 1e6, 10}; - for (int i = 0; i < 10000000; i++) { - ll offset = rand() % ll(1e9); - ll mul = rand() % ll(1e9); - vector>> cases; + test1(); + testInf(); + testLine(); + testPoint(); + testRandom(); - cases.push_back({10, - {{P(offset + mul * 8, offset + mul * 9), P(offset + mul * 8, offset + mul * 2)}, - {P(offset + mul * 3, offset + mul * 9), P(offset + mul * 5, offset + mul * 2)}, - {P(offset + mul * 8, offset + mul * 2), P(offset + mul * 8, offset + mul * 3)}, - {P(offset + mul * 7, offset + mul * 2), P(offset + mul * 1, offset + mul * 7)}, - {P(offset + mul * 1, offset + mul * 0), P(offset + mul * 7, offset + mul * 1)}, - {P(offset + mul * 9, offset + mul * 2), P(offset + mul * 5, offset + mul * 6)}, - {P(offset + mul * 10, offset + mul * 10), P(offset + mul * -10, offset + mul * 10)}, - {P(offset + mul * -10, offset + mul * 10), P(offset + mul * -10, offset + mul * -10)}, - {P(offset + mul * -10, offset + mul * -10), P(offset + mul * 10, offset + mul * -10)}, - {P(offset + mul * 10, offset + mul * -10), P(offset + mul * 10, offset + mul * 10)}}}); - cases.push_back({5, - {{P(offset + mul * 0, offset + mul * 1), P(offset + mul * 4, offset + mul * 0)}, - {P(offset + mul * 0, offset + mul * 2), P(offset + mul * 2, offset + mul * 0)}, - {P(offset + mul * 1, offset + mul * 0), P(offset + mul * 3, offset + mul * 4)}, - {P(offset + mul * 4, offset + mul * 2), P(offset + mul * 0, offset + mul * 0)}, - {P(offset + mul * 4, offset + mul * 2), P(offset + mul * 2, offset + mul * 2)}, - {P(offset + mul * 0, offset + mul * 3), P(offset + mul * 1, offset + mul * 1)}, - {P(offset + mul * 5, offset + mul * 5), P(offset + mul * -5, offset + mul * 5)}, - {P(offset + mul * -5, offset + mul * 5), P(offset + mul * -5, offset + mul * -5)}, - {P(offset + mul * -5, offset + mul * -5), P(offset + mul * 5, offset + mul * -5)}, - {P(offset + mul * 5, offset + mul * -5), P(offset + mul * 5, offset + mul * 5)}}}); - cases.push_back({20, - {{P(offset + mul * 10, offset + mul * 12), P(offset + mul * 16, offset + mul * 5)}, - {P(offset + mul * 10, offset + mul * 12), P(offset + mul * 4, offset + mul * 19)}, - {P(offset + mul * 18, offset + mul * 15), P(offset + mul * 17, offset + mul * 7)}, - {P(offset + mul * 12, offset + mul * 13), P(offset + mul * 14, offset + mul * 6)}, - {P(offset + mul * 16, offset + mul * 3), P(offset + mul * 4, offset + mul * 11)}, - {P(offset + mul * 12, offset + mul * 8), P(offset + mul * 9, offset + mul * 0)}, - {P(offset + mul * 20, offset + mul * 20), P(offset + mul * -20, offset + mul * 20)}, - {P(offset + mul * -20, offset + mul * 20), P(offset + mul * -20, offset + mul * -20)}, - {P(offset + mul * -20, offset + mul * -20), P(offset + mul * 20, offset + mul * -20)}, - {P(offset + mul * 20, offset + mul * -20), P(offset + mul * 20, offset + mul * 20)}}}); - // {P(5,8),P(4,9)},{P(9,1),P(5,8)},{P(9,7),P(7,6)},{P(3,7),P(8,5)},{P(6,6),P(8,4)},{P(6,1),P(7,2)},{P(10,10),P(-10,10)},{P(-10,10),P(-10,-10)},{P(-10,-10),P(10,-10)},{P(10,-10),P(10,10)}, - int idx = 0; - for (auto tmp : cases) { - auto t = tmp.second; - auto lim = tmp.first; - auto res = halfPlaneIntersection(t); - auto ours = polygonArea2(res); - if (abs(ours) > 1e-3) { - if (mn[0] + mn[1] * mn[2] >= offset + mul * tmp.first) { - cout << "case: " << idx << endl; - cout << offset << ' ' << mul << ' ' << offset + mul * tmp.first << endl; - cout << ours << ' ' << sjtu::halfPlaneIntersection(t) << endl; - - double mx = 0; - for (auto i: res) { - for (auto j: res) - mx = max(mx, (i - j).dist()); - } - cout<<"mx: "< t({{P(9, 8), P(9, 1)}, {P(3, 3), P(3, 5)}, {P(7, 6), P(0, 8)}}); - // Failure case for old code. - // addInf(t); - // cout << polygonArea2(halfPlaneIntersection(t)) << endl; - // addInf(t); - // cout << polygonArea2(halfPlaneIntersection(t)) << endl; cout << "Tests passed!" << endl; } From 908a31385384984929c6787c02e884bc9316e368 Mon Sep 17 00:00:00 2001 From: Horace He Date: Fri, 26 Jun 2020 03:57:44 -0700 Subject: [PATCH 41/44] Added my current guess about the condition for failure --- content/geometry/HalfPlane.h | 2 ++ 1 file changed, 2 insertions(+) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index bd8b95175..6d71bf926 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -5,6 +5,8 @@ * Source: https://github.com/zimpha/algorithmic-library/blob/master/computational-geometry/polygon.cc * Description: Computes the intersection of a set of half-planes. Input is given as a set of planes, facing left. * Output is the convex polygon representing the intersection. The points may have duplicates and be collinear. + * Will not fail catastrophically if `eps > sqrt(2)(line intersection error)`. Likely to work for more ranges if + * 3 half planes are never guaranteed to intersect at the same point. * Time: O(n \log n) * Status: fuzz-tested, submitted on https://maps19.kattis.com/problems/marshlandrescues * Usage: From 34c550e40e6047d9a08316a96d36b7bac4886649 Mon Sep 17 00:00:00 2001 From: Simon Lindholm Date: Tue, 20 Oct 2020 18:16:01 +0200 Subject: [PATCH 42/44] Warning fixes --- stress-tests/geometry/HalfPlane.cpp | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/stress-tests/geometry/HalfPlane.cpp b/stress-tests/geometry/HalfPlane.cpp index 66559c611..4c6dfd117 100644 --- a/stress-tests/geometry/HalfPlane.cpp +++ b/stress-tests/geometry/HalfPlane.cpp @@ -108,7 +108,7 @@ bool check(const Border &a, const Border &b, const Border &me) { void convexIntersection() { qh = qt = 0; sort(border, border + n); - n = unique(border, border + n) - border; + n = (int)(unique(border, border + n) - border); for (int i = 0; i < n; ++i) { Border cur = border[i]; while (qh + 1 < qt && !check(que[qt - 2], que[qt - 1], cur)) @@ -141,7 +141,7 @@ T calcArea() { area += ps[i].det(ps[(i + 1) % cnt]); } area /= 2; - area = fabsl(area); + area = (T) fabsl(area); return area; } @@ -205,7 +205,7 @@ bool cmp(Line a, Line b) { return mycmp(a.dir(), b.dir()); } double Intersection_Area(vector b) { sort(b.begin(), b.end(), cmp); - int n = b.size(); + int n = (int) b.size(); int q = 1, h = 0, i; vector ca(b.size() + 10); for (i = 0; i < n; i++) { @@ -301,6 +301,9 @@ void testEmpty() { assert(sz(res) == 0); } void testRandom() { + auto toIntPoint = [&](P p) -> Point { + return Point((int)p.x, (int)p.y); + }; int lim = 3; double mxDiff = 0; for (int i = 0; i < 10000000; i++) { @@ -309,12 +312,12 @@ void testRandom() { Line cand{P(0, 0), P(0, 0)}; while (cand[0] == cand[1]) cand = {randPt(lim), randPt(lim)}; - Point s1 = Point(cand[0].x, cand[0].y); - Point e1 = Point(cand[1].x, cand[1].y); + Point s1 = toIntPoint(cand[0]); + Point e1 = toIntPoint(cand[1]); bool fail = false; for (auto j: t) { - Point s2 = Point(j[0].x, j[0].y); - Point e2 = Point(j[1].x, j[1].y); + Point s2 = toIntPoint(j[0]); + Point e2 = toIntPoint(j[1]); if (lineInter(s1, e1, s2, e2).first == -1) { fail = false; break; From 5fb4588eedac78b9fd3235a6507b30152c2adbb6 Mon Sep 17 00:00:00 2001 From: Simon Lindholm Date: Tue, 20 Oct 2020 18:23:11 +0200 Subject: [PATCH 43/44] Use .angle() --- content/geometry/HalfPlane.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 6d71bf926..3bf35cff4 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -20,7 +20,7 @@ typedef Point P; typedef array Line; #define sp(a) a[0], a[1] -#define ang(a) atan2((a[1] - a[0]).y, (a[1] - a[0]).x) +#define ang(a) (a[1] - a[0]).angle() int angDiff(Line a, Line b) { return sgn(ang(a) - ang(b)); } bool cmp(Line a, Line b) { From 26b50eefec24d6f4ce7fce274df36608e07f3a1c Mon Sep 17 00:00:00 2001 From: Simon Lindholm Date: Tue, 20 Oct 2020 18:35:53 +0200 Subject: [PATCH 44/44] Fix cmp to not say a < a --- content/geometry/HalfPlane.h | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/content/geometry/HalfPlane.h b/content/geometry/HalfPlane.h index 3bf35cff4..e3ee025e4 100644 --- a/content/geometry/HalfPlane.h +++ b/content/geometry/HalfPlane.h @@ -24,8 +24,8 @@ typedef array Line; int angDiff(Line a, Line b) { return sgn(ang(a) - ang(b)); } bool cmp(Line a, Line b) { - auto s = angDiff(a, b); - return s == 0 ? sideOf(sp(b), a[0]) >= 0 : s < 0; + int s = angDiff(a, b); + return (s ? s : sideOf(sp(a), b[0])) < 0; } vector

halfPlaneIntersection(vector vs) { const double EPS = sqrt(2) * 1e-8;