sutherland-hodgman算法

Sutherland-Hodgman算法是一种计算多边形交集的算法。它的基本思想是将一个多边形沿着另一个多边形的边界进行裁剪，得到它们的交集。这个算法的主要优点是简单易懂，容易实现。它的缺点是可能会产生不必要的计算，导致效率较低。

相关问题

sutherland-hodgman算法vc++

Sutherland-Hodgman算法是一种计算多边形交集的算法，可以用于计算裁剪和填充等应用。下面是一个使用VC++实现Sutherland-Hodgman算法的示例代码：

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

struct Point {
    double x, y;
};

// 判断两个点是否在多边形的同一侧
bool SameSide(const Point& p1, const Point& p2, const Point& a, const Point& b) {
    double cp1 = (b.x - a.x) * (p1.y - a.y) - (b.y - a.y) * (p1.x - a.x);
    double cp2 = (b.x - a.x) * (p2.y - a.y) - (b.y - a.y) * (p2.x - a.x);
    return cp1 * cp2 >= 0;
}

// 计算两个点之间的交点
Point Intersect(const Point& p1, const Point& p2, const Point& a, const Point& b) {
    double u = ((a.y - b.y) * (p1.x - a.x) - (a.x - b.x) * (p1.y - a.y)) / ((b.x - a.x) * (p1.y - p2.y) - (b.y - a.y) * (p1.x - p2.x));
    return { p1.x + u * (p2.x - p1.x), p1.y + u * (p2.y - p1.y) };
}

// Sutherland-Hodgman算法
vector<Point> SutherlandHodgman(const vector<Point>& subjectPolygon, const vector<Point>& clipPolygon) {
    vector<Point> outputList = subjectPolygon;
    for (int i = 0; i < clipPolygon.size(); i++) {
        vector<Point> inputList = outputList;
        outputList.clear();
        Point S = clipPolygon[i];
        Point E = clipPolygon[(i + 1) % clipPolygon.size()];
        for (int j = 0; j < inputList.size(); j++) {
            Point P = inputList[j];
            Point Q = inputList[(j + 1) % inputList.size()];
            if (SameSide(P, S, E, Q)) {
                if (!SameSide(P, E, S, Q)) {
                    outputList.push_back(Intersect(P, Q, S, E));
                }
                outputList.push_back(Q);
            }
            else if (SameSide(P, E, S, Q)) {
                outputList.push_back(Intersect(P, Q, S, E));
            }
        }
    }
    return outputList;
}

int main() {
    vector<Point> subjectPolygon = { {0, 0}, {100, 0}, {100, 100}, {0, 100} };
    vector<Point> clipPolygon = { {50, 50}, {150, 50}, {150, 150}, {50, 150} };
    vector<Point> result = SutherlandHodgman(subjectPolygon, clipPolygon);
    for (int i = 0; i < result.size(); i++) {
        cout << "(" << result[i].x << ", " << result[i].y << ")" << endl;
    }
    return 0;
}

这个示例代码实现了一个计算矩形和正方形交集的例子。输入的两个多边形分别是`subjectPolygon`和`clipPolygon`，输出的多边形是`result`。程序的输出应该是一个四边形，表示矩形和正方形的交集。

写一个mfc的sutherland-hodgman算法

以下是一个简单的 MFC 实现 Sutherland-Hodgman 算法的代码：

// 定义多边形的点数
#define POLYGON_SIZE 4

// 定义两个点的结构体
struct Point {
    float x;
    float y;
};

// 定义多边形的结构体
struct Polygon {
    Point points[POLYGON_SIZE];
};

// Sutherland-Hodgman 算法
Polygon clipPolygon(Polygon subjectPolygon, Polygon clipPolygon) {
    Polygon outputPolygon = subjectPolygon;

    // 依次遍历裁剪多边形的边
    for (int i = 0; i < POLYGON_SIZE; i++) {
        Point clipStart = clipPolygon.points[i];
        Point clipEnd = clipPolygon.points[(i + 1) % POLYGON_SIZE];

        Polygon inputPolygon = outputPolygon;
        outputPolygon = {};

        // 依次遍历多边形的边
        for (int j = 0; j < POLYGON_SIZE; j++) {
            Point subjectStart = inputPolygon.points[j];
            Point subjectEnd = inputPolygon.points[(j + 1) % POLYGON_SIZE];

            float startLocation = (clipEnd.x - clipStart.x) * (subjectStart.y - clipStart.y) - (clipEnd.y - clipStart.y) * (subjectStart.x - clipStart.x);
            float endLocation = (clipEnd.x - clipStart.x) * (subjectEnd.y - clipStart.y) - (clipEnd.y - clipStart.y) * (subjectEnd.x - clipStart.x);

            // 判断起点位置
            if (startLocation >= 0) {
                outputPolygon.points[outputPolygonSize++] = subjectStart;
            }

            // 判断起点和终点位置
            if (startLocation * endLocation < 0) {
                float intersectionX = (clipEnd.x - clipStart.x) * (subjectStart.y - clipStart.y) - (clipEnd.y - clipStart.y) * (subjectStart.x - clipStart.x);
                float intersectionY = (clipEnd.y - clipStart.y) * (subjectEnd.x - clipStart.x) - (clipEnd.x - clipStart.x) * (subjectEnd.y - clipStart.y);

                intersectionX /= (subjectEnd.y - subjectStart.y) * (clipEnd.x - clipStart.x) - (subjectEnd.x - subjectStart.x) * (clipEnd.y - clipStart.y);
                intersectionY /= (subjectEnd.y - subjectStart.y) * (clipEnd.x - clipStart.x) - (subjectEnd.x - subjectStart.x) * (clipEnd.y - clipStart.y);

                Point intersection = { intersectionX, intersectionY };
                outputPolygon.points[outputPolygonSize++] = intersection;
            }
        }
    }

    return outputPolygon;
}

// 绘制多边形
void drawPolygon(CDC* pDC, Polygon polygon) {
    CPoint points[POLYGON_SIZE];
    for (int i = 0; i < POLYGON_SIZE; i++) {
        points[i] = CPoint(polygon.points[i].x, polygon.points[i].y);
    }
    pDC->Polygon(points, POLYGON_SIZE);
}

// 绘制裁剪框
void drawClipRectangle(CDC* pDC, Polygon clipPolygon) {
    CPoint points[POLYGON_SIZE];
    for (int i = 0; i < POLYGON_SIZE; i++) {
        points[i] = CPoint(clipPolygon.points[i].x, clipPolygon.points[i].y);
    }
    pDC->Polyline(points, POLYGON_SIZE);
}

// 绘制函数
void CMyView::OnDraw(CDC* pDC)
{
    CMyDoc* pDoc = GetDocument();
    ASSERT_VALID(pDoc);

    // 定义多边形和裁剪框
    Polygon subjectPolygon = { { { 100, 100 }, { 200, 100 }, { 200, 200 }, { 100, 200 } } };
    Polygon clipPolygon = { { { 150, 150 }, { 250, 150 }, { 250, 250 }, { 150, 250 } } };

    // 绘制多边形和裁剪框
    drawPolygon(pDC, subjectPolygon);
    drawClipRectangle(pDC, clipPolygon);

    // 裁剪多边形
    Polygon outputPolygon = clipPolygon(subjectPolygon, clipPolygon);

    // 绘制裁剪后的多边形
    drawPolygon(pDC, outputPolygon);
}

在该代码中，我们定义了结构体 Point 和 Polygon 表示点和多边形，clipPolygon 函数接收两个多边形作为参数，返回裁剪后的多边形。我们使用 MFC 的 CDC 绘制多边形和裁剪框，并使用 drawPolygon 函数绘制多边形，使用 drawClipRectangle 函数绘制裁剪框。最后，在 OnDraw 函数中调用 clipPolygon 函数对多边形进行裁剪，并使用 drawPolygon 函数绘制裁剪后的多边形。