[games101] operation 4 B é zier curve

One . Job description

Two . Homework analysis

1. recursive Bezier Implementation code

Analyzed the meaning of the next document , It is probably achieved by recursion De Casteljau Algorithm . It's easy to implement , The recursive exit of recursive function is control_points The number of points in is 1 when , Return to the calculated point , The recursive code is as follows .

void bezier(const std::vector<cv::Point2f> &control_points, cv::Mat &window) 
{
    
    // TODO: Iterate through all t = 0 to t = 1 with small steps, and call de Casteljau's 
    // recursive Bezier algorithm.


    for (double t = 0.0; t <= 1.0; t += 0.001) 
    {
       
        auto point= recursive_bezier(control_points,t);
        std::cout <<  point.x << ", "<< point.y << ")" << '\n';
        window.at<cv::Vec3b>(point.y, point.x)[1] = 255;
    }

}

cv::Point2f recursive_bezier(const std::vector<cv::Point2f> &control_points, float t) 
{
    
    // TODO: Implement de Casteljau's algorithm
    if(control_points.size()==1){
    return control_points[0];} 
    std::vector<cv::Point2f> v;
    for(int i=0;i<control_points.size()-1;i++)
    {
    
        cv::Point2f p=t*control_points[i]+(1-t)*control_points[i+1];
        v.push_back(p);
    }    
    return recursive_bezier(v,t);

}

Directly call the native_bezier.

The effect of calling the two functions together is as follows .

2.Bezier Curve anti aliasing

Directly draw divided Bezier The curve has the problem of aliasing .

The idea of anti aliasing is to calculate the adjacent to the current point in the Jiugong lattice 8 Distance between pixel coordinates and current point coordinates , And set the color linear gradient according to the distance （ Train of thought reference Homework 4（ Improve ） contain Bazier Anti aliasing of curve ） The edge effect drawn according to this idea is stronger than other methods .

void bezier(const std::vector<cv::Point2f> &control_points, cv::Mat &window) 
{
    
    // TODO: Iterate through all t = 0 to t = 1 with small steps, and call de Casteljau's 
    // recursive Bezier algorithm.


    for (double t = 0.0; t <= 1.0; t += 0.001) 
    {
       
        auto point= recursive_bezier(control_points,t);
        std::cout <<  point.x << ", "<< point.y << ")" << '\n';
        for(int i=-1;i<=1;i++){
    
            for(int j=-1;j<=1;j++){
    
                cv::Point2f t;
                t.x=point.x+i;
                t.y=point.y+j;
                float d=sqrt(pow(t.x-((int)t.x+i)-0.5,2)+pow(t.y-((int)t.y+j)-0.5,2));
                float ratio=1.0-sqrt(2)/3.0*d;
                window.at<cv::Vec3b>(t.y, t.x)[1] = std::fmax(255*ratio,window.at<cv::Vec3b>(t.y, t.x)[1]);
            }
        }
        // window.at<cv::Vec3b>(point.y, point.x)[1] = 255;
    }

}

The anti aliasing effect is as follows , The effect is much smoother than before .