Add PlaneDistance and sideOfPlane (#49)

* Add `PlaneDistance` and `sideOfPlane`

* Fix indentation

content/geometry/PlaneDistance.h

@@ -0,0 +1,19 @@
+/**
+ * Author: Iván Renison
+ * Date: 2024-08-29
+ * License: CC0
+ * Source: notebook el vasito
+ * Description:
+ * Returns the signed distance between point $p$ and the plane containing points $a$, $b$ and $c$.
+ * $a$, $b$ and $c$ must not be collinear.
+ * Status: untested
+ */
+#pragma once
+
+#include "Point3D.h"
+
+template<class P>
+double planeDist(P a, P b, P c, P p) {
+	P n = (b-a).cross(c-a);
+	return (double)n.dot(p-a) / n.dist();
+}

content/geometry/chapter.tex

@@ -42,5 +42,7 @@ \section{Misc. Point Set Problems}
 \section{3D}
 	\kactlimport{PolyhedronVolume.h}
 	\kactlimport{Point3D.h}
+	\kactlimport{PlaneDistance.h}
+	\kactlimport{sideOfPlane.h}
 	\kactlimport{3dHull.h}
 	\kactlimport{sphericalDistance.h}

content/geometry/sideOfPlane.h

@@ -0,0 +1,19 @@
+/**
+ * Author: Iván Renison
+ * Date: 2024-08-29
+ * License: CC0
+ * Source: notebook el vasito
+ * Description: Returns at witch side of the plane defined by $a$, $b$ and $c$ the point $p$ is.
+ * If the point is on the plane 0 is returned, else 1 or -1.
+ * $a$, $b$ and $c$ must not be collinear. For double add epsilon checks.
+ * Status: Problem tested
+ */
+#pragma once
+
+#include "Point.h"
+
+template<class P>
+ll sideOf(P a, P b, P c, P p) {
+	ll x = (b-a).cross(c-a).dot(p-a);
+	return (x > 0) - (x < 0);
+}

test-problems/geometry/sideOfPlane.cpp

@@ -0,0 +1,94 @@
+// Problem: https://codeforces.com/gym/105321/problem/C
+// Status: Accepted
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fst first
+#define snd second
+#define pb push_back
+#define fore(i, a, b) for (ll i = a, gmat = b; i < gmat; i++)
+#define ALL(x) begin(x), end(x)
+#define SZ(x) (ll)(x).size()
+#define mset(a, v) memset((a), (v), sizeof(a))
+typedef long long ll;
+typedef pair<ll, ll> ii;
+typedef vector<ll> vi;
+
+/// content/geometry/Point3D.h
+template<class T> struct Point3D {
+	typedef Point3D P;
+	typedef const P& R;
+	T x, y, z;
+	explicit Point3D(T x=0, T y=0, T z=0) : x(x), y(y), z(z) {}
+	bool operator<(R p) const {
+		return tie(x, y, z) < tie(p.x, p.y, p.z); }
+	bool operator==(R p) const {
+		return tie(x, y, z) == tie(p.x, p.y, p.z); }
+	P operator+(R p) const { return P(x+p.x, y+p.y, z+p.z); }
+	P operator-(R p) const { return P(x-p.x, y-p.y, z-p.z); }
+	P operator*(T d) const { return P(x*d, y*d, z*d); }
+	P operator/(T d) const { return P(x/d, y/d, z/d); }
+	T dot(R p) const { return x*p.x + y*p.y + z*p.z; }
+	P cross(R p) const {
+		return P(y*p.z - z*p.y, z*p.x - x*p.z, x*p.y - y*p.x);
+	}
+	T dist2() const { return x*x + y*y + z*z; }
+	double dist() const { return sqrt((double)dist2()); }
+	//Azimuthal angle (longitude) to x-axis in interval [-pi, pi]
+	double phi() const { return atan2(y, x); }
+	//Zenith angle (latitude) to the z-axis in interval [0, pi]
+	double theta() const { return atan2(sqrt(x*x+y*y),z); }
+	P unit() const { return *this/(T)dist(); } //makes dist()=1
+	//returns unit vector normal to *this and p
+	P normal(P p) const { return cross(p).unit(); }
+	//returns point rotated 'angle' radians ccw around axis
+	P rotate(double angle, P axis) const {
+		double s = sin(angle), c = cos(angle); P u = axis.unit();
+		return u*dot(u)*(1-c) + (*this)*c - cross(u)*s;
+	}
+};
+/// END content
+
+/// content/geometry/sideOfPlane.h
+template<class P>
+ll sideOf(P a, P b, P c, P p) {
+	ll x = (b-a).cross(c-a).dot(p-a);
+	return (x > 0) - (x < 0);
+}
+/// END content
+
+bool solve(Point3D<ll> cus, Point3D<ll> sun,const vector<Point3D<ll>>& poly) {
+	ll N = poly.size();
+
+	fore(i, 0, N) {
+		Point3D<ll> p = poly[i], q = poly[(i + 1) % N];
+		if (sideOf(p, q, cus, sun) == 1) {
+			return true;
+		}
+	}
+
+	return false;
+}
+
+int main() {
+	cin.tie(0)->sync_with_stdio(0);
+
+	ll N;
+	cin >> N;
+
+	Point3D<ll> cus, sun;
+	cin >> cus.x >> cus.y >> cus.z >> sun.x >> sun.y >> sun.z;
+
+	vector<Point3D<ll>> poly(N);
+	for (auto& [X, Y, Z] : poly) {
+		cin >> X >> Y;
+	}
+
+	bool ans = solve(cus, sun, poly);
+
+	if (ans) {
+		cout << "S\n";
+	} else {
+		cout << "N\n";
+	}
+}