Answer to a question no one asked
James Hurley
jhurley at infostations.com
Fri Jan 7 10:36:58 EST 2005
>
>Message: 1
>Date: Thu, 6 Jan 2005 16:20:44 -0500
>From: James Steiner <gregortroll at gmail.com>
>Subject: Re: Answer to a question no one asked
>To: How to use Revolution <use-revolution at lists.runrev.com>
>Message-ID: <5ec6743205010613203b1ad415 at mail.gmail.com>
>Content-Type: text/plain; charset=US-ASCII
>
>On Thu, 6 Jan 2005 07:40:10 -0800, James Hurley
><jhurley at infostations.com> wrote:
>> What is the perpendicular distance between a point and a line?
>>
>> Application for which there is no redeeming social value:
>> if x3-x2 is 0 then
>> return (x1-x2)
>> else
>> put (y3-y2)/(x3-x2) into m -- The slope
>> return (m*(x1-x2)-(y1-Y2))/sqrt(1+m*m)
>> end if
>
>Oddly, this is the answer to a question I asked on another users list
>for another programming environment, months ago -- netlogo-users.
>
>For a drawing utility, I needed to create a query that returns the set
>of "patches" (grid cells) with a perpendicular distance of N from the
>line between two arbitrary cells.
>
>Using your formula, I can now use this (netlogo) code:
>
>set line-patches ( patches with [ ( perpdist myself start-point
>end-point ) < n ]
>
>The prior solution was extremely verbose, convoluted, and slow. This
>seems like it will be faster.
>
>Thanks!
>
>~~James
James,
Glad it was useful. It has a number of applications to problems in geometry.
(To derive this result it is best to use the "Normal" form for the
straight line. Instead of the standard form, y = m x + b, the line
is defined by a perpendicular line from the origin to the straight
line. The distance from the origin to the line is p and the angle
this construct makes with the x-axis is phi. Then the line is defined
by the equation: x cos(phi) + y sin(phi) = p.)
Interesting that you came to RR from LOGO. So did I--or rather from
LOGO to HC to RR.
Some time ago I wrote a little book, illustrating the use of LOGO to
solve physics problems--"LOGO Physics", Holt, Rinehart and Winston.
But I soon learned that students had a much easier time with
HyperTalk than LOGO, and so I wrote a Turtle Graphics interpreter for
HT. You can find in on the RR web site:
http://downloads.runrev.com/stacks_apps/ or for download:
http://downloads.runrev.com/stacks_apps/turtlegraphics.php
Jim
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