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mitooquerer | 4 Apr 12:00
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Re: TikZ for geometric drawings?


I know it is not TikZ, but haven´t you tried Mathspic?
http://www.ctan.org/tex-archive/graphics/mathspic/dos/mpicm21.pdf (old
manual, see page 14, 25)

Downloads: http://dante.ctan.org/indexes/graphics/mathspic/

I used the DOS version, I assume the Perl version works better. I think it
should solve some of your problems... like perpendiculars, middle point,
etc..

Mitoo

Alain Matthes-2 wrote:
> 
> 
> Le 11 févr. 07 à 22:13, rouben.rostamian <at> comcast.net a écrit :
> 
>> Daniel Flipo <daniel.flipo <at> univ-lille1.fr> wrote:
>>
>>> I am starting to learn TikZ and I wonder whether I could use TikZ for
>>> geometric constructions like, say, the "nine points circle" of a
>>> triangle (EPS appended: mp-exemple.1).
>>
>> I too wish that TikZ had greater capability for doing
>> standard geometric constructions. As far as I can tell,
>> basic functionality, such as querying the coordinates
>> of an intersection is not available (yet). In November I
>> wrote to this mailing list asking: "Given points P and Q,
>> is there a way to draw a circle centered at P that goes
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rouben.rostamian | 14 Feb 03:05
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Re: TikZ for geometric drawings?

"Mark Wibrow" <M.Wibrow <at> uea.ac.uk> wrote:

> rouben.rostamian <at> comcast.net wrote:
>
> > Till, if you are reading this, I have something to
> > offer. In an attempt to do geometry in TikZ, I have derived
> > accurate polynomial approximations (using Chebyshev
> > interpolation points) to the functions sine, cosine,
> > and sqrt. Therefore these can be computed when needed
> > (with the help of the calc package) without the need for
> > a table lookup.  If such functionality can be of help in
> > adding geometry constructions to TikZ, I will be glad to
> > send them to you.
>
> I'd be interested to know if Chebyshev interpolation in TeX is more
> accurate/efficient than a Newton-Raphson approximation (with 10
> iterations):
>
> [Nice TeX program for finding square roots
>  via Newton's iteration deleted]

Newton's method is an iterative algorithm.  Accuracy is
controlled by the number of iterations.  Polynomial
approximation is non-iterative.  Accuracy is controlled
by the degree of approximating polynomial.

I either method, we need to decide what accuracy we need,
then apply the proper control to achieve that accuracy.
In either method, a higher accuracy requires more
computation.
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Mark Wibrow | 14 Feb 16:55
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Re: TikZ for geometric drawings?

Hi,

This is great! Polynomial approximation *is* much more efficient. I've
just dashed off a test version in TeX, and even with the necessary
truncating/rounding of the coefficients to 5 decimal places, accuracy is
good.

The only "fly in the ointment" is that the accuracy is spoiled by the
calculation of a/b. I can do this with (barely) tolerable accuracy, but as
a/b needs to be squared for this approximation, the errors get compounded

Current accuracy, using the polynomial approximation is typically within
+/- 0.5pt for small to mid-range values, but for large values eg a=900pt
b=1000pt I get errors of around 5.0pt.

I'll take proper look at it later (undergraduates do occasionally have to
do some work...)

Mark

rouben.rostamian <at> comcast.net wrote:
> "Mark Wibrow" <M.Wibrow <at> uea.ac.uk> wrote:
>
>> rouben.rostamian <at> comcast.net wrote:
>>
>> > Till, if you are reading this, I have something to
>> > offer. In an attempt to do geometry in TikZ, I have derived
>> > accurate polynomial approximations (using Chebyshev
>> > interpolation points) to the functions sine, cosine,
>> > and sqrt. Therefore these can be computed when needed
(Continue reading)

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Gmane