On Wed, 22 Mar 2017 22:54:12 -0700, William Elliot wrote:
>On Wed, 22 Mar 2017, James Waldby wrote: > >> On Wed, 22 Mar 2017 09:55:22 +0000, Popping mad wrote: >> >> > A = x cos? + y sin? >> > >> > Has anyone seen the proof for this >> > for a line. I ran across it in the Hough Transform as a parameterized >> > version for the definition of a line >> >> I don't know just what you mean by the "for a line" phrase, > >Yes, fadish speedthink is incoherent. > >The equation of a line in the xy plane is > ax + by = c. > >Dividing through by sqr(a^2 + b^2) gives the form > x.sin t + y.cos t = d.
Which can be written as:
y = d / cos(t) - x * tan(t)
Why does parameterizing help?
>> but if, for example, your rho is the length of the hypotenuse >> of a right triangle with horizontal side length x and vertical >> side length y, then x = rho cos theta, y = rho sin theta, >> whence x cos theta + y sin theta = rho cos^2 theta + rho sin^2 theta >> which equals rho because cos^2 theta + sin^2 theta = 1. > >There was no rho in his equation. >News groups are plain text only. >Control characters don't show correctly to everybody.