Re: bad bezier behavior

From: Fyodor Tkachov <"Fyodor>
Date: Thu, 06 Jan 2005 18:27:53 +0300

----boundary-LibPST-iamunique-1857719385_-_-
Content-type: text/plain

This is to replace my earlier message where I sent a graphic instead of text by mistake.
I apologize.

Someone wrote to me that this problem had indeed been seen.
The problem persists with version 1.5 BETA.
The simplest code reproducing the error is attached.

Happy New Year!
Fyodor Tkachov

PS
The Bezier curve segment b(t) is described by a 3rd order polynomial in t which is supposed to be an approximation of some curve v(t), 0<t<1 (dimensionality of b, v is irrelevant).
b(t) is fixed by four conditions:
    b(0)=v(0); b'(0)=v'(0); b(1)=v(1); b'(1)=v'(1);
For dim
this is equivalent to a Hermit's interpolating polynomial.
The four "Bezier points" are:
    b_0=v(0);
    b_1=v(0)+v'(0)/3;
    b_2=v(1)-v'(1)/3;
    b_3=v(1).
The information in the 4 points is equivalent to the four conditions required to define the curve.
The coefficient 1/3 ensures a nice visual correspondence between the points and the resulting curve.

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Received on Thu Jan 06 2005 - 16:27:53 UTC