toys/gps/docs/source/math/convex_polygon.cpp

#include "geo/private/math/convex_polygon.h"

#include <algorithm>

namespace ns
{
namespace geo
{

// 从下面的网址搬运过来修改的计算点集的外接多边形
// https://www.geeksforgeeks.org/convex-hull-set-1-jarviss-algorithm-or-wrapping/

// 此处小数点后的精确度必须精确到10位以后结果才会准确
// const double EPSION = 0.0000000000000001;
const double EPSION = std::numeric_limits<double>::min();
// A C++ program to find convex hull of a set of points. Refer
// https://www.geeksforgeeks.org/orientation-3-ordered-points/

// To find orientation of ordered triplet (p, q, r).
// The function returns following values
// 0 --> p, q and r are colinear
// 1 --> Clockwise
// 2 --> Counterclockwise
namespace
{
int orientation(const PointD& p, const PointD& q, const PointD& r)
{
    double val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
    if (std::abs(val) <= EPSION)
        return 0;                  // colinear 共线
    return (val > EPSION) ? 1 : 2; // clock or counterclock wise 顺时针或者逆时针方向
}

// 如果有重复点去除重复点
std::vector<PointD> repeatPoints(const std::vector<PointD>& points)
{
    std::vector<PointD> rePoints;
    for (size_t i = 0; i < points.size(); i++)
    {
        PointD tmpPoint(points[i].x, points[i].y, points[i].z);
        auto iter = std::find(rePoints.begin(), rePoints.end(), tmpPoint);
        if (iter == rePoints.end()) // 去除重复点
        {
            rePoints.emplace_back(tmpPoint);
        }
    }
    return rePoints;
}
} // namespace

// Prints convex hull of a set of n points.
std::vector<PointD> convexHull(const std::vector<PointD>& points)
{
    std::vector<PointD> rePoints = repeatPoints(points);
    // Initialize Result
    std::vector<PointD> hull;

    // There must be at least 3 points
    size_t n = rePoints.size();
    if (n < 3)
    {
        return hull;
    }

    // Find the leftmost point
    size_t l = 0;
    for (size_t i = 1; i < n; i++)
    {
        if (rePoints[i].x < rePoints[l].x)
        {
            l = i;
        }
    }

    // Start from leftmost point, keep moving counterclockwise
    // until reach the start point again. This loop runs O(h)
    // times where h is number of points in result or output.
    size_t p = l, q, count = 0;
    do
    {
        // Add current point to result
        hull.push_back(rePoints[p]);

        // Search for a point 'q' such that orientation(p, x,
        // q) is counterclockwise for all points 'x'. The idea
        // is to keep track of last visited most counterclock-
        // wise point in q. If any point 'i' is more counterclock-
        // wise than q, then update q.
        q = (p + 1) % n;
        for (size_t i = 0; i < n; i++)
        {
            // If i is more counterclockwise than current q, then
            // update q
            if (orientation(rePoints[p], rePoints[i], rePoints[q]) == 2) // 按照逆时针方向循环
            {
                q = i;
            }
        }
        // Now q is the most counterclockwise with respect to p
        // Set p as q for next iteration, so that q is added to
        // result 'hull'
        p = q;
        count++;
        if (count == n) // 最多遍历n次跳出循环,避免出现死循环的现象
        {
            p = l;
        }
    } while (p != l); // While we don't come to first point
    return hull;
}

// 下面这个判断一个点是否在多边形内的方法，比较复杂，想了解原理直接看下面的参考网址
// 参考网址：http://alienryderflex.com/polygon/
bool pointInPolygon(const std::vector<PointD>& points, const PointD& point)
{
    size_t j = points.size() - 1;
    bool oddNodes = false;
    for (size_t i = 0; i < points.size(); i++)
    {
        PointD tmpPointI = points[i];
        PointD tmpPointJ = points[j];
        if (((tmpPointI.y < point.y && tmpPointJ.y >= point.y) ||
             (tmpPointJ.y < point.y && tmpPointI.y >= point.y)) &&
            (tmpPointI.x <= point.x || tmpPointJ.x <= point.x))
        {
            oddNodes ^= (tmpPointI.x + (point.y - tmpPointI.y) / (tmpPointJ.y - tmpPointI.y) *
                                           (tmpPointJ.x - tmpPointI.x) <
                         point.x);
        }
        j = i;
    }
    return oddNodes;
}

} // namespace geo
} // namespace ns