How can I draw gradient like this?

I want to draw gradient of circle.
First idea, I could create a white line and empty image I. Then to go through loop with angle from 0 to 89, in every iteration do I++; and angle++; rotate this line with fixed origin at x=radius, y=0; This would create one image of gradient. Then I need to copy the image 3 times in a loop rotating it +90° in every iteration.
Now **I ask what functions to use to copy the pixels from the original line to the image using rotation** and how to do the same with an image. It's basically the same difference is only in image dimensions. That line is radius,0 and image dimensions are radius*2,radius,2
What I tried after Lorena pointed me to try linearPolar:
int radius = 4;
int side = 2*radius;
int size = 1 + 2*side;
Mat I = Mat::zeros(size, size, CV_8UC1);
Point center;
center.x = 2*radius+1 -1; center.y = 2*radius+1 -1;
int sigma = radius%2==0 ? radius+1 : radius;
cv::Size kernelSize = CvSize(sigma, sigma);
Mat L = Mat::zeros(1, center.x, CV_8UC1);
I = Mat::zeros(size, size, CV_8UC1);
Point a,b;
L = Mat::zeros(center.x, 1, CV_8UC1);
a.x=0; a.y = 0; b.x=0; b.y = radius-1;
line( L, a, b, cv::Scalar( 255, 255, 255 ), 1, 8 );
cv::GaussianBlur( L, L, kernelSize, sigma );
imshow("blured line",L);
waitKey(0);
cv::Size dsize= cv::Size(radius*10, radius*10);
resize(L, I, dsize );
Point2f fcenter;
fcenter.x = (float) radius/16 ;
fcenter.y = (float) radius/16 ;
cv::linearPolar(I, I, fcenter, radius, INTER_LINEAR );
imshow("linearPolar",I);
waitKey(0);
The resulting image contains some gradient which is horizontal instead circular.
Edit: New code (radius 25) - same problem:
// Mat::zeros( 5, 5, CV_8UC3 );
int radius = 25;
int side = 2*radius;
int size = 1 + 2*side;
Mat I = Mat::zeros(size, size, CV_8UC1);
Point center;
center.x = 2*radius+1 -1; center.y = 2*radius+1 -1;
/*
circle( I,
center,
radius,
cv::Scalar( 255, 255, 255 ),
-1, // when thickness is negative, filled circle is drawn
8 );
imshow("circle",I);
waitKey(0);*/
int sigma = radius%2==0 ? radius+1 : radius;
cv::Size kernelSize = CvSize(sigma, sigma);
/*
cv::GaussianBlur( I, I, kernelSize, sigma );
imshow("blured circle",I);
waitKey(0);*/
/** ANGLE GRADIENT **/
Mat L = Mat::zeros(1, center.x, CV_8UC1);
I = Mat::zeros(size, size, CV_8UC1);
Point a,b;
/*
a.x=0; a.y = 0; b.x=radius; b.y = 0;
int c = 255;
line( I, a, b, cv::Scalar( c ), 1, 8 );
*/
/** ANGLE GRADIENT **/
L = Mat::zeros(center.x, 1, CV_8UC1);
a.x=0; a.y = 0; b.x=0; b.y = radius-1;
line( L, a, b, cv::Scalar( 255, 255, 255 ), 1, 8 );
cv::GaussianBlur( L, L, kernelSize, sigma );
imshow("blured line",L);
waitKey(0);
cv::Size dsize= cv::Size(size, size);
resize(L, I, dsize );
Point2f fcenter;
fcenter.x = (float) radius ;
fcenter.y = (float) radius ;
cv::linearPolar(I, I, fcenter, size, INTER_LINEAR );
imshow("linearPolar",I);
waitKey(0);
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