判断两条直线是否相交c语言,学习OpenCV3：判断两条直线相交，并计算交点和夹角...
一、问题
已知两条直线
和
，现希望判断
与
间是否相交。若相交，计算出两条直线的交点和夹角。
二、分析
1、直线方程
的直线方程：
的直线方程：
提示：
和
不能同时为0。若
和
同时为0，起点和终点重合，该直线实际上是一个点。
2、判断相交
当
垂直于
轴，
倾斜于
轴时，
与
相交：
b1==0 && b2!=0
当
倾斜于
轴，
垂直于
轴时，
与
相交：
b1!=0 && b2==0
当
与
都倾斜于
轴，且斜率不同时，
与
相交：
b1!=0 && b2!=0 && a1/b1!=a2/b2
3、计算交点
4、计算夹角
交点
、
的终点
和
的终点
组成一个三角形，则其各边边长为：
由余弦定理得：
三、实现
#include
#include
#include
#include
using namespace std;
using namespace cv;
Vec4d g_line1(200, 300, 600, 300), g_line2(400, 500, 400, 100); // 垂直的两条线
// 判断两条线是否相交，若相交则求出交点和夹角
Vec4d lines_intersection(const Vec4d l1, const Vec4d l2)
{
double x1 = l1[0], y1 = l1[1], x2 = l1[2], y2 = l1[3];
double a1 = -(y2 - y1), b1 = x2 - x1, c1 = (y2 - y1) * x1 - (x2 - x1) * y1; // 一般式：a1x+b1y1+c1=0
double x3 = l2[0], y3 = l2[1], x4 = l2[2], y4 = l2[3];
double a2 = -(y4 - y3), b2 = x4 - x3, c2 = (y4 - y3) * x3 - (x4 - x3) * y3; // 一般式：a2x+b2y1+c2=0
bool r = false; // 判断结果
double x0 = 0, y0 = 0; // 交点
double angle = 0; // 夹角
// 判断相交
if (b1 == 0 && b2 != 0) // l1垂直于x轴，l2倾斜于x轴
r = true;
else if (b1 != 0 && b2 == 0) // l1倾斜于x轴，l2垂直于x轴
r = true;
else if (b1 != 0 && b2 != 0 && a1 / b1 != a2 / b2)
r = true;
if (r)
{
//计算交点
x0 = (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1);
y0 = (a1 * c2 - a2 * c1) / (a2 * b1 - a1 * b2);
// 计算夹角
double a = sqrt(pow(x4 - x2, 2) + pow(y4 - y2, 2));
double b = sqrt(pow(x4 - x0, 2) + pow(y4 - y0, 2));
double c = sqrt(pow(x2 - x0, 2) + pow(y2 - y0, 2));
angle = acos((b * b + c * c - a * a) / (2 * b * c)) * 180 / CV_PI;
}
return Vec4d(r, x0, y0, angle);
}
// 画夹角
void draw_angle(Mat img, const Point2d p0, const Point2d p1, const Point2d p2, const double radius, const Scalar color, const int thickness)
{
// 计算直线的角度
double angle1 = atan2(-(p1.y - p0.y), (p1.x - p0.x)) * 180 / CV_PI;
double angle2 = atan2(-(p2.y - p0.y), (p2.x - p0.x)) * 180 / CV_PI;
// 计算主轴的角度
double angle = angle1 <= 0 ? -angle1 : 360 - angle1;
// 计算圆弧的结束角度
double end_angle = (angle2 < angle1) ? (angle1 - angle2) : (360 - (angle2 - angle1));
if (end_angle > 180)
{
angle = angle2 <= 0 ? -angle2 : 360 - angle2;
end_angle = 360 - end_angle;
}
// 画圆弧
ellipse(img, p0, Size(radius, radius), angle, 0, end_angle, color, thickness);
}
// 画箭头
void draw_arrow(Mat img, const Point2d p1, const Point2d p2, const double angle, const double length, const Scalar color, const int thickness)
{
double l1 = length * cos(angle * CV_PI / 180), l2 = length * sin(angle * CV_PI / 180);
Point2d p3(0, 0), p4(0, 0);
int i = (p2.x > p1.x) ? 1 : -1; // i,j代表p2、p3、p4相对于p0的正负
int j = (p2.y > p1.y) ? 1 : -1;
double a1 = abs(atan((p2.y - p1.y) / (p2.x - p1.x))); // 直线p1p2相对于x轴的角度，取正值
double w1 = l1 * cos(a1), h1 = l1 * sin(a1); // 用于计算p2相对于p0的宽高
Point2d p0(p2.x - w1 * i, p2.y - h1 * j);
double a2 = 90 * CV_PI / 180 - a1; // 直线p3p4相对于x轴的角度
double w2 = l2 * cos(a2), h2 = l2 * sin(a2); // 用于计算p3和p4相对于p0的宽高
p3 = Point2d(p0.x - w2 * i, p0.y + h2 * j);
p4 = Point2d(p0.x + w2 * i, p0.y - h2 * j);
line(img, p2, p3, color, 2); //画箭头
line(img, p2, p4, color, 2);
}
// 画虚线
void draw_dotted_line(Mat img, const Point2d p1, const Point2d p2, const Scalar color, const int thickness)
{
double n = 15; // 小线段的长度
double w = p2.x - p1.x, h = p2.y - p1.y;
double l = sqrtl(w * w + h * h);
// 矫正小线段长度，使小线段个数为奇数
int m = l / n;
m = m % 2 ? m : m + 1;
n = l / m;
circle(img, p1, 1, color, thickness); // 画起点
circle(img, p2, 1, color, thickness); // 画终点
// 画中间的小线段
if (p1.y == p2.y) //水平线：y = m
{
double x1 = min(p1.x, p2.x);
double x2 = max(p1.x, p2.x);
for (double x = x1, n1 = 2 * n; x < x2; x = x + n1)
line(img, Point2d(x, p1.y), Point2d(x + n, p1.y), color, thickness);
}
else if (p1.x == p2.x) //垂直线, x = m
{
double y1 = min(p1.y, p2.y);
double y2 = max(p1.y, p2.y);
for (double y = y1, n1 = 2 * n; y < y2; y = y + n1)
line(img, Point2d(p1.x, y), Point2d(p1.x, y + n), color, thickness);
}
else
{
// 直线方程的两点式：(y-y1)/(y2-y1)=(x-x1)/(x2-x1) -> y = (y2-y1)*(x-x1)/(x2-x1)+y1
double n1 = n * abs(w) / l;
double k = h / w;
double x1 = min(p1.x, p2.x);
double x2 = max(p1.x, p2.x);
for (double x = x1, n2 = 2 * n1; x < x2; x = x + n2)
{
Point p3 = Point2d(x, k * (x - p1.x) + p1.y);
Point p4 = Point2d(x + n1, k * (x + n1 - p1.x) + p1.y);
line(img, p3, p4, color, thickness);
}
}
}
// 画延长线
void draw_extension_line(Mat img, const Vec4d l, Scalar color)
{
double x1 = l[0], y1 = l[1], x2 = l[2], y2 = l[3];
double a = -(y2 - y1), b = x2 - x1, c = (y2 - y1) * x1 - (x2 - x1) * y1;
Point2d p1(0, 0), p2(0, 0);
if (b != 0)
{
p1 = Point2d(0, -c / b);
p2 = Point2d(img.cols, ((-a * img.cols - c) / b));
}
else
{
p1 = Point2d(-c / a, 0);
p2 = Point2d(-c / a, img.rows);
}
draw_dotted_line(img, p1, p2, color, 1);
}
// 画图
void draw(Mat img, const Vec4d l1, const Vec4d l2)
{
Vec4d v = lines_intersection(l1, l2); // 判断是否相交，并计算交点和夹角
line(img, Point2d(l1[0], l1[1]), Point2d(l1[2], l1[3]), Scalar(255, 0, 0), 2); // 画蓝线
draw_arrow(img, Point2d(l1[0], l1[1]), Point2d(l1[2], l1[3]), 20, 20, Scalar(255, 0, 0), 2); // 画箭头
line(img, Point2d(l2[0], l2[1]), Point2d(l2[2], l2[3]), Scalar(0, 255, 0), 2); // 画绿线
draw_arrow(img, Point2d(l2[0], l2[1]), Point2d(l2[2], l2[3]), 20, 20, Scalar(0, 255, 0), 2); // 画箭头
draw_extension_line(img, l1, Scalar(255, 0, 0)); // 画延长线
draw_extension_line(img, l2, Scalar(0, 255, 0)); // 画延长线
draw_angle(img, Point2d(v[1], v[2]), Point2d(l1[2], l1[3]), Point2d(l2[2], l2[3]), 15, Scalar(0, 0, 255), 1); // 画夹角
if (v[0])
{
string s = "(" + to_string(v[1]) + ", " + to_string(v[2]) + ") " + to_string(v[3]);
putText(img, s, Point2d(10, 25), cv::FONT_HERSHEY_COMPLEX, 0.5, Scalar(0, 255, 0));
circle(img, Point2d(v[1], v[2]), 2, Scalar(0, 0, 255), 2); // 画交点
}
else
{
putText(img, "no", Point2d(10, 25), cv::FONT_HERSHEY_COMPLEX, 0.5, Scalar(0, 0, 255));
}
}
// 确定鼠标左键点击在两条直线的那个点上
Vec6d define_area(const Vec4d l1, const Vec4d l2, const Point2d p)
{
Vec6d v(-1, 0, 0, 0, 0, 0);
double w = 20, h = 20;
double x1 = l1[0], y1 = l1[1], x2 = l1[2], y2 = l1[3];
double x3 = l2[0], y3 = l2[1], x4 = l2[2], y4 = l2[3];
Rect r0(x1 - w, y1 - h, 2 * w, 2 * h); // l1的起点
Point2d p1((x2 + x1) / 2, (y1 + y2) / 2); // l1的中间点
Rect r1(p1.x - w, p1.y - h, 2 * w, 2 * h);
Rect r2(x2 - w, y2 - h, 2 * w, 2 * h); // l1的终点
Rect r3(x3 - w, y3 - h, 2 * w, 2 * h); // l2的起点
Point2d p2((x3 + x4) / 2, (y3 + y4) / 2); // l2的中间点
Rect r4(p2.x - w, p2.y - h, 2 * w, 2 * h);
Rect r5(x4 - w, y4 - h, 2 * w, 2 * h); // l2的终点
if (r0.contains(p)) // 判断点是否在矩形中
{
v = Vec6d(0, x1, y1, 0, 0, 0);
}
else if (r1.contains(p))
{
v = Vec6d(1, x1, y1, x2, y2, 0);
}
else if (r2.contains(p))
{
v = Vec6d(2, x2, y2, 0, 0, 0);
}
else if (r3.contains(p))
{
v = Vec6d(3, x3, y3, 0, 0, 0);
}
else if (r4.contains(p))
{
v = Vec6d(4, x3, y3, x4, y4, 0);
}
else if (r5.contains(p))
{
v = Vec6d(5, x4, y4, 0, 0, 0);
}
return v;
}
// 根据鼠标移动相应的修改直线的起点和终点
void modify_line(Vec4d &l1, Vec4d &l2, const Vec6d area, const double w, const double h)
{
if (area[0] == 0)
{
l1[0] = area[1] + w;
l1[1] = area[2] + h;
}
else if (area[0] == 1)
{
l1[0] = area[1] + w;
l1[1] = area[2] + h;
l1[2] = area[3] + w;
l1[3] = area[4] + h;
}
else if (area[0] == 2)
{
l1[2] = area[1] + w;
l1[3] = area[2] + h;
}
else if (area[0] == 3)
{
l2[0] = area[1] + w;
l2[1] = area[2] + h;
}
else if (area[0] == 4)
{
l2[0] = area[1] + w;
l2[1] = area[2] + h;
l2[2] = area[3] + w;
l2[3] = area[4] + h;
}
else if (area[0] == 5)
{
l2[2] = area[1] + w;
l2[3] = area[2] + h;
}
}
// 鼠标回调函数
void mouse_callback(int event, int x, int y, int flags, void *param)
{
static Point2d p1(0, 0), p2(0, 0);
static Vec6d area(-1, 0, 0, 0, 0, 0);
switch (event)
{
case cv::EVENT_LBUTTONDOWN: // 鼠标左键点击
p1 = Point2d(x, y);
area = define_area(g_line1, g_line2, p1); // 确定鼠标所要移动的区域
break;
case cv::EVENT_MOUSEMOVE: // 鼠标移动
if (area[0] > -1) // 移动直线
{
p2 = Point2d(x, y);
double w = p2.x - p1.x, h = p2.y - p1.y;
modify_line(g_line1, g_line2, area, w, h); // 根据鼠标移动相应的修改直线的起点和终点
}
break;
case cv::EVENT_LBUTTONUP: // 鼠标左键释放
p1 = Point2d(0, 0);
p2 = Point2d(0, 0);
area = Vec6d(-1, 0, 0, 0, 0, 0);
break;
default:
break;
}
}
// 主函数
int main()
{
string window_name = "image";
namedWindow(window_name, WINDOW_AUTOSIZE);
int w = 800, h = 600;
Mat image_original = Mat(h, w, CV_8UC3, Scalar(255, 255, 255));
cv::setMouseCallback(window_name, mouse_callback); // 调用鼠标回调函数
while (true)
{
Mat img = image_original.clone(); // 拷贝空白图片，方便重复画图
draw(img, g_line1, g_line2); // 画图
imshow(window_name, img);
if (waitKey(3) > 0) // 退出循环
break;
}
return 0;
}
操作方法：
鼠标点击直线起点或终点并按住移动，可改变直线。鼠标点击直线的中间点并按住移动，可平移直线。在键盘按任意的键可退出程序。
运行结果：