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Article:
  Introduction to Cocoa Graphics, Part 2
Subject:   got a great doubt
Date:   2001-11-19 20:33:02
From:   psheldon
Response to: Question about method in NSBezierPath

I have gotten a good nights sleep, but all day rehearsed the feelings for a good observing story of being out alone in fog coming up with theories on where fog wasn't. 17 rehearsals that I had to put to bed after getting too excited about writing it up for three er two hours.
The idea of Bezier curves is to match not only endpoints but their tangents. This requires a cubic curve with its degrees of freedom afforded by coefficients of a cubic polynomial.
If someone building a framework or class of methods told Apple management that it was possible to take a circle fix its radius and two points it passes through and also make sure that there was a common tangent, it could very well be that Apple management didn't want to hear that was overdefining a problem or worse that there is no royal road to mathematics.
I myself went on a dark country road through a lot of fog, but that's another story.
Now, by sending this judgement call on Apple management, I am flaming myself, because I know the way my brain works. As soon as I write down something and try it out on someone, I worry that I am dead wrong. This is the kind of intellectual stimulation that can lose you a job but gain you enlightenment.
I am writing this flaming judgement call to intellectually stimulate myself into such embarrassment that I will figure out how Apple management was right to expect this.
How can I proceed out in such blind faith in such fog?
I believe one of my professors theorized at seeing neutrinos periodic detection matching an orbital frequency of cygnus x 1. I remarked, stupidly, to the experimentalist that he couldn't possibly have observed this because the neutrino intensity or shot rate was lower than the nyquist sampling frequency, I insulted the beloved experimentalists integrity of observation. Realizing my feu pa (I spell French and English terribly), I hurriedly set to making a fourier transform simulation to prove that the beloved experimentalist hadn't lied. I saw the period creap up out of the undersampled shot noise. I went to Ivor Page who said I had been attempting the impossible to beat the Nyquist sampling theorem and expressed my results. This immediately cleaned up his memory of what was and wasn't impossible and he showed me a paper about Poisson shot noise antaliasing from Lucasfilm.
Though shot noise, on the average may be undersampling, if you look long enough you will see high frequencies emerge.
It was the extreme embarrassment at destroying the credibility of my friend that inspired my researches and paradoxically my friendly beloved experimentalist wrote an abbreviated confident summary of my glorious victory in the terse words "We had a sufficient number of events to insure we saw this periodic motion". With that air of confidence, he was never challenged again on this point, nor did the beloved experimentalist have to cite me.
Apple may well dismiss me with an equally pithy statement such as "We knew we were right all along" but such people don't have an adventure of chasing meteors through fog with their dog utterly alone while a world sleeps, so cool. I will embarrass myself and so let the olympic flame be lit!
;-)
Boy am I gonna get inspired real fast or else.

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  1. what is this thing called triangle?
    2001-11-19 20:47:37  psheldon [View]

    • changed one line of code for info
      2001-11-19 21:36:51  psheldon [View]

      • no morning vision heuristic, ;-(
        2001-11-20 09:29:58  psheldon [View]

      • thinking in box, curve out of box ;-)
        2001-11-19 22:42:06  psheldon [View]

        • first sample code and story
          2001-11-21 09:54:45  psheldon [View]

          • tool for fluted ends of fonts, serifs (?)
            2001-11-21 12:29:22  psheldon [View]

        • happy you figured it out
          2001-11-20 22:29:03  psheldon [View]

          • The plot thickens!
            2001-11-21 06:40:57  retro [View]

            • The plot thickens! So does the fluted R.
              2001-11-21 14:20:42  psheldon [View]

          • Absolutely
            2001-11-21 05:34:53  retro [View]

            • Absolutely --- ah I see two tangential
              2001-11-21 14:52:20  psheldon [View]

        • I figured it out!
          2001-11-20 21:22:43  retro [View]

        • Thanks...
          2001-11-20 12:09:30  retro [View]

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