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What is the reason behind these codes(Draw the lines of cv::HoughLines)?

On this site(tutorial), it show us how to draw the lines detected by cv::HoughLines,but I can't understand how could it find out the Point between the lines.

for( size_t i = 0; i < lines.size(); i++ )

{ float rho = lines[i][0], theta = lines[i][1]; Point pt1, pt2; double a = cos(theta), b = sin(theta); double x0 = arho, y0 = brho; pt1.x = cvRound(x0 + 1000(-b)); //?? pt1.y = cvRound(y0 + 1000(a)); //?? pt2.x = cvRound(x0 - 1000(-b)); //?? pt2.y = cvRound(y0 - 1000(a)); //?? line( cdst, pt1, pt2, Scalar(0,0,255), 3, CV_AA); }

Another codes from the openCV2 cookbook.I could understand why the codes from the cookbook work but it is more verbose.

for(auto const &data : lines){
    float const rho = data[0];
    float const theta = data[1];

    if((theta < PI/4. || theta > 3. * PI/4.)){
        cv::Point pt1(rho / std::cos(theta), 0);
        cv::Point pt2( (rho - result.rows * std::sin(theta))/std::cos(theta), result.rows);
        cv::line(result, pt1, pt2, cv::Scalar(255), 1);
    }else if{
        cv::Point pt1(0, rho / std::sin(theta));
        cv::Point pt2(result.cols, (rho - result.cols * std::cos(theta))/std::sin(theta));
        cv::line(result, pt1, pt2, cv::Scalar(255), 1);
    }
}

What is the reason behind these codes(Draw the lines of cv::HoughLines)?

On this site(tutorial), it show us how to draw the lines detected by cv::HoughLines,but I can't understand how could it find out the Point between the lines.

 for( size_t i = 0; i < lines.size(); i++ )

{ float rho = lines[i][0], theta = lines[i][1]; Point pt1, pt2; double a = cos(theta), b = sin(theta); double x0 = arho, a*rho, y0 = brho; b*rho; pt1.x = cvRound(x0 + 1000(-b)); 1000*(-b)); //?? pt1.y = cvRound(y0 + 1000(a)); 1000*(a)); //?? pt2.x = cvRound(x0 - 1000(-b)); 1000*(-b)); //?? pt2.y = cvRound(y0 - 1000(a)); 1000*(a)); //?? line( cdst, pt1, pt2, Scalar(0,0,255), 3, CV_AA); }

}

Another codes from the openCV2 cookbook.I could understand why the codes from the cookbook work but it is more verbose.

for(auto const &data : lines){
    float const rho = data[0];
    float const theta = data[1];

    if((theta < PI/4. || theta > 3. * PI/4.)){
        cv::Point pt1(rho / std::cos(theta), 0);
        cv::Point pt2( (rho - result.rows * std::sin(theta))/std::cos(theta), result.rows);
        cv::line(result, pt1, pt2, cv::Scalar(255), 1);
    }else if{
        cv::Point pt1(0, rho / std::sin(theta));
        cv::Point pt2(result.cols, (rho - result.cols * std::cos(theta))/std::sin(theta));
        cv::line(result, pt1, pt2, cv::Scalar(255), 1);
    }
}

What is the reason behind these codes(Draw Draw the lines of cv::HoughLines)?detected by cv::HoughLines

On this site(tutorial), it show us how to draw the lines detected by cv::HoughLines,but I can't understand how could it find out the Point between the lines.

    for( size_t i = 0; i < lines.size(); i++ )
  {
     float rho = lines[i][0], theta = lines[i][1];
     Point pt1, pt2;
     double a = cos(theta), b = sin(theta);
     double x0 = a*rho, y0 = b*rho;
     pt1.x = cvRound(x0 + 1000*(-b)); //??
     pt1.y = cvRound(y0 + 1000*(a)); //??
     pt2.x = cvRound(x0 - 1000*(-b)); //??
     pt2.y = cvRound(y0 - 1000*(a)); //??
     line( cdst, pt1, pt2, Scalar(0,0,255), 3, CV_AA);
  }

Another codes from the openCV2 cookbook.I could understand why the codes from the cookbook work but it is more verbose.

for(auto const &data : lines){
    float const rho = data[0];
    float const theta = data[1];

    if((theta < PI/4. || theta > 3. * PI/4.)){
        cv::Point pt1(rho / std::cos(theta), 0);
        cv::Point pt2( (rho - result.rows * std::sin(theta))/std::cos(theta), result.rows);
        cv::line(result, pt1, pt2, cv::Scalar(255), 1);
    }else if{
        cv::Point pt1(0, rho / std::sin(theta));
        cv::Point pt2(result.cols, (rho - result.cols * std::cos(theta))/std::sin(theta));
        cv::line(result, pt1, pt2, cv::Scalar(255), 1);
    }
}