About Hough transform and its plot(with 3 points to plot)

Question

I have a 3 points:

(1,3) (2,4) (3,5)

which equation is :

y = x + 2

and its

slope = 1
intercept = 2

After Hough Transform and plot,

# Hough Transformin in my code
r_axis[i] = x_point * math.cos(th) + y_point * math.sin(th)

I got:

This plot tell me:

r = 1
theta = 135 deg (???)

But my equation y = x + 1 tell me

theta = 
arctan(slope) ( -pi < tan < +pi ) = 
45 deg

The answer should be 45 deg, not 135 deg.

I'm confused

following is my source code:

code

Answer 1

Ok, after I think hardly.

The intersection of plot is theta = 135 deg, r=1.414 not theta = 135 deg, r=1

We modify y = x + 2 to y - x = 2

the answer:

r = 1.414
theta = 135 deg

We substitute to

1.414 = y*sin (135 deg) - x*cos(135 deg)
=> 2 = y - x
=> y = x + 2

So, code and plot both not problem