Re: C-Programming

From	Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups	comp.lang.c
Subject	Re: C-Programming
Date	2014-12-18 17:06 +0000
Organization	A noiseless patient Spider
Message-ID	<87vbl8yjip.fsf@bsb.me.uk> (permalink)
References	(5 earlier) <m6rl24$jsq$1@reader1.panix.com> <_ngkw.80215$P42.58745@fx24.am4> <kfnppbi6vyy.fsf@x-alumni2.alumni.caltech.edu> <i8jkw.255968$MH.237866@fx12.am4> <a97288fe-4f46-4f91-b09a-83bd780d7c6b@googlegroups.com>

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Malcolm McLean <malcolm.mclean5@btinternet.com> writes:

> On Wednesday, December 17, 2014 5:34:16 PM UTC, Richard Heathfield wrote:
>> 
>> Thank you. I wasn't aware of that. My Bezier-drawing function uses only 
>> two control points (I /was/ aware that you can use more, but two seemed
>> to me to be a sufficiency for the time being), 
>>
>> It has, of course, become the tradition, when I post ancient code, for 
>> people to find a good half-dozen bugs in it. No doubt the same will happen 
>> here. But this code does draw splines, really it does. :-)
>> 
> It's a reasonable approach, but not very fast or high quality.
> You won't get every pixel for extreme curves, and you're calling
> a lot of multiplications.
> You can draw a Bezier a lot faster by forwards differencing.
>
> First express as two cubics in x and y, with t being the time variable.
>
>       a3 = -x0 + 3 * cpax + -3 * cpbx + x3;
> 	a2 = 3 * x0 + -6 * cpax + 3 * cpbx;
> 	a1 = -3 * x0 + 3 * cpax;
> 	a0 = x0
>
> Now we can draw a cubic at 100 points by calculating 
>
> f(t) = a0 + a1*t + a2*t^2 + a3*t^3
>
> d  = 0.01
>
> the forward difference algorithm becomes
> t[0] = 0;
> f(0) = a0;
> delta1 = a1 *d + a2 *d^2 + a3*d^3
> delta2 = 2*a2*d^2 + 6*a3*d^3
> delta3 = 6 *a3 *d^3
> for i = 1 to k do
>    t[i] = t[i-1] + d
>    f(t[i]) = f(t[i-1]) + delta1
>   delta1 = delta1 + delta2
>   delta2 = delta2 + delta3
> endfor
>
> You do that for x and y.

Being for a fixed number of steps, this has the same problem of missed
pixels and/or not producing tight curves very well.  But...

> If either delta1_x or delta1_y goes over
> 0.5, halve all the delta values. If it goes  below 0.125, double
> them. Then you're sampling at sub-Nyquist frequency, with is 0.5
> of the grid and guaranteed a pixel-perfect curve.

I don't follow this.  My (no doubt naive) attempt to code your halving
and doubling does not produce the right curve.  Can you give the pseudo
code for this pixel-correct version?

-- 
Ben.

Thread

C-Programming arvindgupta01031988@gmail.com - 2014-12-06 11:09 -0800
  Re: C-Programming "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2014-12-06 11:16 -0800
  Re: C-Programming James Kuyper <jameskuyper@verizon.net> - 2014-12-06 14:46 -0500
    Re: C-Programming Kleuske <kleuske@nowhere.net> - 2014-12-07 10:48 +0000
      Re: C-Programming Keith Thompson <kst-u@mib.org> - 2014-12-07 07:43 -0800
  Re: C-Programming Siri Crews <chine.bleu@yahoo.com> - 2014-12-06 12:22 -0800
    Re: C-Programming gordonb.ukogy@burditt.org (Gordon Burditt) - 2014-12-19 03:29 -0600
      Re: C-Programming Siri Crews <chine.bleu@yahoo.com> - 2014-12-19 01:34 -0800
        Re: C-Programming Richard Heathfield <invalid@see.sig.invalid> - 2014-12-19 10:18 +0000
          Re: C-Programming jacob navia <jacob@spamsink.net> - 2014-12-19 17:42 +0100
            Re: C-Programming rouben@shadow.(none) (Rouben Rostamian) - 2014-12-19 19:00 +0000
              Re: C-Programming jacob navia <jacob@spamsink.net> - 2014-12-19 20:31 +0100
                Re: C-Programming jacob navia <jacob@spamsink.net> - 2014-12-19 20:42 +0100
              Re: C-Programming Keith Thompson <kst-u@mib.org> - 2014-12-19 11:54 -0800
        Re: C-Programming raltbos@xs4all.nl (Richard Bos) - 2014-12-19 11:29 +0000
          Re: C-Programming Noob <root@127.0.0.1> - 2014-12-20 10:22 +0100
            Re: C-Programming Keith Thompson <kst-u@mib.org> - 2014-12-20 11:48 -0800
        Re: C-Programming Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-19 03:33 -0800
          Re: C-Programming Siri Crews <chine.bleu@yahoo.com> - 2014-12-19 04:02 -0800
      Re: C-Programming glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-19 17:28 +0000
  Re: C-Programming jacob navia <jacob@spamsink.net> - 2014-12-06 21:27 +0100
  Re: C-Programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-07 13:07 +0000
  Re: C-Programming David Brown <david.brown@hesbynett.no> - 2014-12-08 01:24 +0100
    Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-16 04:44 -0800
      Re: C-Programming David Brown <david.brown@hesbynett.no> - 2014-12-16 15:02 +0100
        Re: C-Programming BartC <bc@freeuk.com> - 2014-12-16 18:27 +0000
          Re: C-Programming David Brown <david.brown@hesbynett.no> - 2014-12-17 01:01 +0100
            Re: C-Programming BartC <bc@freeuk.com> - 2014-12-17 00:23 +0000
        Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-16 16:30 -0800
          Re: C-Programming David Brown <david.brown@hesbynett.no> - 2014-12-17 02:18 +0100
            Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-16 18:23 -0800
              Re: C-Programming David Brown <david.brown@hesbynett.no> - 2014-12-17 09:59 +0100
                Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-17 08:52 -0800
                Re: C-Programming David Brown <david.brown@hesbynett.no> - 2014-12-18 11:11 +0100
                Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-18 09:49 -0800
          Re: C-Programming JohnF <john@please.see.sig.for.email.com> - 2014-12-17 10:14 +0000
            Re: C-Programming Richard Heathfield <invalid@see.sig.invalid> - 2014-12-17 14:26 +0000
              Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-17 09:13 -0800
                Re: C-Programming Richard Heathfield <invalid@see.sig.invalid> - 2014-12-17 17:34 +0000
                Re: C-Programming Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-17 23:26 -0800
                Re: C-Programming Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-18 00:21 -0800
                Re: C-Programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-18 17:06 +0000
                Re: C-Programming Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-18 09:29 -0800
                Re: C-Programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-19 02:36 +0000
                Re: C-Programming Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-19 03:41 -0800
                Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-18 08:52 -0800
              Re: C-Programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-17 23:23 +0000
                Re: C-Programming BartC <bc@freeuk.com> - 2014-12-18 00:02 +0000
                Re: C-Programming Richard Heathfield <invalid@see.sig.invalid> - 2014-12-18 00:15 +0000
                Re: C-Programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-18 16:37 +0000
                Re: C-Programming Richard Heathfield <invalid@see.sig.invalid> - 2014-12-18 18:08 +0000
                Re: C-Programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-19 02:40 +0000
                Re: C-Programming Richard Heathfield <invalid@see.sig.invalid> - 2014-12-19 07:51 +0000
            Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-17 09:07 -0800
              Re: C-Programming JohnF <john@please.see.sig.for.email.com> - 2014-12-19 04:22 +0000
                Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-19 09:22 -0800
                Re: C-Programming Greg Martin <greg.at.softsprocket@dot.com> - 2014-12-20 02:39 +0000
                Re: C-Programming JohnF <john@please.see.sig.for.email.com> - 2014-12-20 06:57 +0000
  Re: C-Programming Tim Rentsch <txr@alumni.caltech.edu> - 2014-12-15 23:53 -0800

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