以下是在C++中使用分离轴定理实现的`doPolygonsIntersect`函数的完整代码：
```cpp
#include <iostream>
#include <vector>
#include <algorithm>
// Define a point
struct Point {
double x, y;
};
// Define a polygon using a vector of points
using Polygon = std::vector<Point>;
// Compute the projection of a polygon onto an axis
std::pair<double, double> projectPolygonOnAxis(const Polygon& polygon, const Point& axis) {
double minProj = polygon.front().x * axis.x + polygon.front().y * axis.y;
double maxProj = minProj;
for (const auto& vertex : polygon) {
double proj = vertex.x * axis.x + vertex.y * axis.y;
minProj = std::min(minProj, proj);
maxProj = std::max(maxProj, proj);
}
return {minProj, maxProj};
}
// Check if two projections overlap
bool doProjectionsOverlap(const std::pair<double, double>& proj1, const std::pair<double, double>& proj2) {
return std::max(proj1.first, proj2.first) <= std::min(proj1.second, proj2.second);
}
// Generate all edge normals for a polygon
std::vector<Point> generateEdgeNormals(const Polygon& polygon) {
std::vector<Point> normals;
for (size_t i = 0; i < polygon.size(); ++i) {
Point edge = {polygon[(i + 1) % polygon.size()].x - polygon.x,
polygon[(i + 1) % polygon.size()].y - polygon.y};
double length = std::sqrt(edge.x * edge.x + edge.y * edge.y);
Point normal = {-edge.y / length, edge.x / length};
normals.push_back(normal);
}
return normals;
}
// Check if two polygons intersect using the Separating Axis Theorem
bool doPolygonsIntersect(const Polygon& poly1, const Polygon& poly2) {
auto normals1 = generateEdgeNormals(poly1);
auto normals2 = generateEdgeNormals(poly2);
for (const auto& n : normals1) {
auto proj1 = projectPolygonOnAxis(poly1, n);
auto proj2 = projectPolygonOnAxis(poly2, n);
if (!doProjectionsOverlap(proj1, proj2)) {
return false;
}
}
for (const auto& n : normals2) {
auto proj1 = projectPolygonOnAxis(poly1, n);
auto proj2 = projectPolygonOnAxis(poly2, n);
if (!doProjectionsOverlap(proj1, proj2)) {
return false;
}
}
return true;
}
int main() {
// Example polygons
Polygon poly1 = {{0, 0}, {4, 0}, {4, 4}, {0, 4}};
Polygon poly2 = {{3, 3}, {6, 3}, {6, 6}, {3, 6}};
bool intersect = doPolygonsIntersect(poly1, poly2);
std::cout << "Do the polygons intersect? " << (intersect ? "Yes" : "No") << std::endl;
return 0;
}
```
在这个代码中，`projectPolygonOnAxis`函数计算多边形在指定轴上的投影，`doProjectionsOverlap`函数检查两个投影是否重叠，`generateEdgeNormals`函数生成多边形所有边的法线向量。`doPolygonsIntersect`函数首先为每个多边形生成其所有边的法线，然后对每个法线进行投影并检查投影是否重叠。如果在所有法线中都找不到分离轴，则认为两个多边形相交。
请注意，此代码假设输入的多边形是凸的。如果多边形是非凸的，那么你可能需要使用更复杂的算法，例如将非凸多边形分解成凸多边形，然后分别检查每个凸多边形对之间是否相交。
页:
[1]