# use-livecode Digest, Vol 123, Issue 56

James Hurley jhurley0305 at sbcglobal.net
Tue Dec 31 10:51:24 EST 2013

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> Message: 12
> Date: Mon, 30 Dec 2013 19:04:04 -0700
> From: Roger Guay <irog at mac.com>
> To: How to use LiveCode <use-livecode at lists.runrev.com>
> Subject: Re: Flow/wrap text into an irregular shape
> Message-ID: <EF2CF37D-27DD-47AA-9F23-C3C5920943CB at mac.com>
> Content-Type: text/plain; charset=windows-1252
>
> Jim,
>
> Could you please briefly explain this distinction between Euclidian and Cartesian geometry as it applies to Turtle Graphics?
>
> Thanks,
>
> Roger
>
>
> On Dec 30, 2013, at 10:08 AM, James Hurley <jhurley0305 at sbcglobal.net> wrote:
>
>> The basic advantage of TG is that it speaks a language closer to Euclidian than Cartesian geometry.
>

Hi Roger,

Good question. Best answered with an example. Euclidean geometry is concerned with shapes (lines and angle), while Cartesian geometry is concerned with points in a Cartesian coordinate system.

A script for a Cartesian polygon might look like this:

on mouseUP
drawPolygon 6,100
end mouseUP

on drawPolygon N, L
--draw an N side polgon with sides of length L
set the points of grc "poly" to ""
put trunc( the width of this card/2) into x0
put trunc( the height of this card/2) into y0
put x0 into xOld
put y0 into yOld
put 0 into tAng
repeat N+1
—Draw each side relative to its predecessor
put xOld + L* sin(tAng*pi/180) into xNew
put yOld + L * cos(tAng*pi/180) into yNew
put xNew,yNew & cr after tPoints
put xNew into xOld
put yNew into yOld
add 360/N to tAng
—set the points of grc “poly” to tPoints; Use this if you want to see the polygon evolve
end repeat
set the points of grc "Poly" to tPoints
end drawPolygon

That script is full of Cartesian coordinates and trig.

The same polygon may her accomplished in TG with something like this:

on drawPolygon N, L
startTurtle --
repeat N
forward L
left 360/N
end repeat
end drawPolygon

The script if nothing but lengths and angles.
One might a easily construct a handler to draw an N sided polygon whose circumference is C:

on drawPolygonGivenCircumference N, C
st
repeat N
fd C/N
left 360/N
end repeat
end drawPolygonGivenCircumference

Of course RunRev recognized the complexity of analytic, cartesian geometry in such cases and introduced several drawing tools: Rectangle, Line, Oval, Freehand curve, Polygon, Regular polygon, to deal with these special cases.

But I have also built into TG the ability to handle Cartesian geometry as well, with such functions as xCor(), yCor(), xyCor(), direction(), etc. for there are times when that is the best route to take. How else would one draw a parabola. (y = x^2)

Jim

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