写一个效率最高的求三角形内所有坐标的算法
时间: 2024-03-06 16:49:06 浏览: 16
一种高效的算法是扫描线算法。具体步骤如下:
1. 找出三角形的最小包围矩形,确定扫描线的范围。
2. 从最小包围矩形的上边界开始,向下沿着扫描线扫描。
3. 对于每条扫描线,计算出与三角形的交点,并将这些交点按照x坐标排序。
4. 根据相邻两个交点之间的距离和扫描线间距,计算出每个像素点的y坐标,并将其加入到像素集合中。
下面是C++代码实现:
```c++
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
struct Point {
int x;
int y;
};
void drawLine(Point p1, Point p2, vector<Point>& points) {
int x1 = p1.x;
int y1 = p1.y;
int x2 = p2.x;
int y2 = p2.y;
int dx = abs(x2 - x1);
int dy = abs(y2 - y1);
int sx = x1 < x2 ? 1 : -1;
int sy = y1 < y2 ? 1 : -1;
int err = dx - dy;
while (true) {
points.push_back({x1, y1});
if (x1 == x2 && y1 == y2) break;
int e2 = 2 * err;
if (e2 > -dy) {
err -= dy;
x1 += sx;
}
if (e2 < dx) {
err += dx;
y1 += sy;
}
}
}
void drawTriangle(Point p1, Point p2, Point p3, vector<Point>& points) {
drawLine(p1, p2, points);
drawLine(p2, p3, points);
drawLine(p3, p1, points);
}
void getBoundingBox(Point p1, Point p2, Point p3, Point& minP, Point& maxP) {
minP = {min({p1.x, p2.x, p3.x}), min({p1.y, p2.y, p3.y})};
maxP = {max({p1.x, p2.x, p3.x}), max({p1.y, p2.y, p3.y})};
}
void scanTriangle(Point p1, Point p2, Point p3, vector<Point>& points) {
Point minP, maxP;
getBoundingBox(p1, p2, p3, minP, maxP);
for (int y = minP.y; y <= maxP.y; y++) {
vector<double> intersections;
if (y >= p1.y && y < p2.y) {
intersections.push_back(p1.x + (double)(p2.x - p1.x) * (double)(y - p1.y) / (double)(p2.y - p1.y));
}
if (y >= p1.y && y < p3.y) {
intersections.push_back(p1.x + (double)(p3.x - p1.x) * (double)(y - p1.y) / (double)(p3.y - p1.y));
}
if (y >= p2.y && y < p3.y) {
intersections.push_back(p2.x + (double)(p3.x - p2.x) * (double)(y - p2.y) / (double)(p3.y - p2.y));
}
sort(intersections.begin(), intersections.end());
for (int i = 0; i < (int)intersections.size() - 1; i++) {
int x1 = (int)intersections[i];
int x2 = (int)intersections[i + 1];
for (int x = x1; x <= x2; x++) {
points.push_back({x, y});
}
}
}
}
int main() {
Point p1 = {0, 0};
Point p2 = {5, 10};
Point p3 = {10, 5};
vector<Point> points;
scanTriangle(p1, p2, p3, points);
for (auto p : points) {
cout << "(" << p.x << ", " << p.y << ")" << endl;
}
return 0;
}
```
在这个例子中,我们定义了一个getBoundingBox函数来获取三角形的最小包围矩形,定义了一个scanTriangle函数来实现扫描线算法,将计算出来的像素点加入到points向量中。在scanTriangle函数中,对于每条扫描线,我们计算出与三角形的交点,并将这些交点按照x坐标排序,然后根据相邻两个交点之间的距离和扫描线间距,计算出每个像素点的y坐标,并将其加入到像素集合中。最后,在main函数中,我们使用scanTriangle函数来画出三角形,并输出所有的像素点坐标。