> From: Kenneth Sloan <
[hidden email]>
> Date: October 17, 2013 at 5:05:51 CDT
> To: Michael Schmid <
[hidden email]>
> Cc: Michael Schmid <
[hidden email]>
> Subject: Re: Strange results after "Fit Spline"
>
> Well, perhaps it's just old, like me. I don't have my references at hand, but the name Lee comes to mind. I have been teaching this trick for about 25 years. My standard example is a sequence of points in the shape of a 'J', with one point at the top of the vertical stroke, one point at the start if the circular hook, one at the very bottom, and finally one at the end of the hook.
>
> Fit a Bézier curve using three methods of assigning parameter (think of t = time) values to the 4 points. First, use uniform t values. Then try using the distance between points, and finally use SQRT(distance). One curve will overshoot, one will take a very wide turn, and one will follow the 'J'.
>
> In general, use D raised to some power p, for p in 0..1.0 (or beyond). You get a family of curves. p=0.5 looks best to my eye. Your mileage may vary.
>
> -Kenneth Sloan
> (von meinem iPhone4S gesendet)
>
>> On Oct 17, 2013, at 4:23, "Michael Schmid" <
[hidden email]> wrote:
>>
>> Hi Kenneth,
>>
>> yes I agree!
>> (BTW, using the sqrt of the point distance also came into my mind last night - but I was not aware that is is an old and well-known result).
>>
>> I'll submit the new version to Wayne.
>>
>> Michael
>> ________________________________________________________________
>> Michael Schmid email:
[hidden email]
>> Institut für Angewandte Physik, Technische Universität Wien
>> Wiedner Hauptstr. 8-10/E134, A 1040 Wien, Austria
>> Tel. +43 1 58801-13452 or -13453, Fax +43 1 58801 13499
>> ________________________________________________________________
>>
>>> On Oct 16, 2013, at 22:25, Kenneth Sloan wrote:
>>>
>>> A superior scheme is to have t depend on the sqrt of the distance between the points. This is an old and well known result.
>>>
>>> --
>>> Kenneth Sloan
>>>
[hidden email]
>>>
>>>
>>>>> On Oct 16, 2013, at 11:55 , Michael Schmid <
[hidden email]> wrote:
>>>>>
>>>>> I think that the solution could be the following: The independent coordinate of the x- and y-spline should depend on the (Euclidian) distance between the points (currently, the point number is used). This would reduce overshoot if there are short and long segments. I am not sure, however, whether it would completely eliminate the overshoot at the end in all cases.
>>>
>>> --
>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>
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