How to extend hough lines over the image space

I need to extend lines over the image space. I used Hough transform to finde vanishing lines, but i need to get lines longer and see where is vanishing points. How can i do it? Please help. This is my code:

clear; clc;

%rotI = imrotate(I,33,'crop');
bw_I = rgb2gray(I);
BW = edge(bw_I,'canny');

figure, imshow(BW); %pause;

BW=edge(BW,'canny',(graythresh(I)*(0.3)),'horizontal');

figure, imshow(BW); %pause;

[H,T,R] = hough(BW);
imshow(H,[],'XData',T,'YData',R,'InitialMagnification','fit');
xlabel('\theta'), ylabel('\rho');
axis on, axis normal, hold on;
P  = houghpeaks(H,15,'threshold',ceil(0.3*max(H(:))));
x = T(P(:,2)); y = R(P(:,1));
plot(x,y,'s','color','white');
% Find lines and plot them
lines = houghlines(BW,T,R,P,'FillGap',200,'MinLength',200);
figure, imshow(I), hold on

for k = 1:length(lines)
xy = [lines(k).point1; lines(k).point2];
plot( xy(:,1) ,  xy(:,2),  'LineWidth',2,'Color','green');

% Plot beginnings and ends of lines
plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow');
plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red');
end


Fit a line through the end points using standard line model $ax+by+c=0$. Then draw them on the image from -10000, 10000. The points remaining on the image will give you what you are asking for.

A very simple numerical approach:

• Pad your image with zeros up to the size that you want the final image/lines to be

• Run your Hough transformation code

• Draw the lines in the padded image

The zeros don't give you additional signal in the Hough transformation, hence the resulting lines will be the same. By padding the image, you enlarge the area to paint the lines onto.