static bool insideTriangle(int x, int y, const Vector3f* _v)

{
    // TODO : Implement this function to check if the point (x, y) is inside the triangle represented by _v[0], _v[1], _v[2]
    Vector2f vertex2p[3], vertex2vertex[3];
    int i;
    //储存顶点到测试点的向量
    for (i = 0;i < 3;i++) {
        vertex2p[i] << x - _v[i].x(), y - _v[i].y();
    }
    //储存顶点到顶点之间的向量
    for (i = 0;i < 3;i++) {
        vertex2vertex[i] << _v[(i + 1) % 3].x() - _v[i].x(), _v[(i + 1) % 3].y() - _v[i].y();
    }
    //计算叉乘法.
    int result[3];
    for (i = 0;i < 3;i++) {
        result[i] = vertex2vertex[i].x()*vertex2p[i].y()
                            -vertex2vertex[i].y()*vertex2p[i].x();
    }
    if(result[0]>0 && result[1]>0 && result[2]>0){
        return true;
    }
    else if(result[0]<0 && result[1]<0 && result[2]<0){
        return true;
    }
    else{
        return false;
    }

}

void rst::rasterizer::rasterize_triangle(const Triangle& t) {
    auto v = t.toVector4();

    // TODO : Find out the bounding box of current triangle.
    // iterate through the pixel and find if the current pixel is inside the triangle
    float xmin,ymin,xmax,ymax;
    xmin=std::min(std::min(v[0].x(),v[1].x()),v[2].x());
    ymin=std::min(std::min(v[0].y(),v[1].y()),v[2].y());
    xmax=std::max(std::max(v[0].x(),v[1].x()),v[2].x());
    ymax=std::max(std::max(v[0].y(),v[1].y()),v[2].y());
    xmin=std::floor(xmin);
    xmax=std::ceil(xmax);
    ymin=std::floor(ymin);
    ymax=std::ceil(ymax);
    
    for(int x=xmin;x<=xmax;x++){
        for(int y=ymin;y<=ymax;y++){
            if(insideTriangle(x+0.5,y+0.5,t.v)){
                // If so, use the following code to get the interpolated z value.
                auto[alpha, beta, gamma] = computeBarycentric2D(x, y, t.v);
                float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
                float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
                z_interpolated *= w_reciprocal;
                    // TODO : set the current pixel (use the set_pixel function) to the color of the triangle (use getColor function) if it should be painted.
                if (z_interpolated<depth_buf[get_index(x,y)]){
                    set_pixel(Vector3f(x,y,z_interpolated),t.getColor());
                    depth_buf[get_index(x,y)]=z_interpolated;
                }
            }
        }
    }