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tikz: subpath of Bezier curve

Dear all,

Is there a way to construct a subpath of a Bezier curve? For example,
in the following, is there a way to get the part of the curve from
(start) to
(mid)? (I couldn't find it in the manual.)

\path (0,0) coordinate (start)
        (1,0) coordinate (c1)
        (2,-1) coordinate (c2)
        (3,0) coordinate (end)
        (start) .. controls (c1) and (c2) .. (end)
        coordinate[pos=0.5] (mid);

Thanks in advance for your help.

Regards,


Marc van Dongen
0
dongen (455)
12/24/2011 1:16:52 PM
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On 2011-12-24 14:16:52 +0100, Marc van Dongen said:

> Dear all,
> 
> Is there a way to construct a subpath of a Bezier curve? For example,
> in the following, is there a way to get the part of the curve from
> (start) to
> (mid)? (I couldn't find it in the manual.)
> 
> \path (0,0) coordinate (start)
>         (1,0) coordinate (c1)
>         (2,-1) coordinate (c2)
>         (3,0) coordinate (end)
>         (start) .. controls (c1) and (c2) .. (end)
>         coordinate[pos=0.5] (mid);
> 
> Thanks in advance for your help.
> 
> Regards,
> 
> 
> Marc van Dongen

MetaPost and Asymptote do that, but Tikz… If it is not in the Manual, I 
strongly doubt it.

0
12/24/2011 7:29:45 PM
Hi,

It isn't currently available in TikZ (unless you use decorations with
the pre length and post length options - but that is not an ideal
solution). It is available in PGF using \pgfpathcurvebetweentime or
\pgfpathcurvebetweentimecontinue. The manual for the basic layer
describes these commands.

Regards

Mark

On Dec 24, 1:16=A0pm, Marc van Dongen <don...@cs.ucc.ie> wrote:
> Dear all,
>
> Is there a way to construct a subpath of a Bezier curve? For example,
> in the following, is there a way to get the part of the curve from
> (start) to
> (mid)? (I couldn't find it in the manual.)
>
> \path (0,0) coordinate (start)
> =A0 =A0 =A0 =A0 (1,0) coordinate (c1)
> =A0 =A0 =A0 =A0 (2,-1) coordinate (c2)
> =A0 =A0 =A0 =A0 (3,0) coordinate (end)
> =A0 =A0 =A0 =A0 (start) .. controls (c1) and (c2) .. (end)
> =A0 =A0 =A0 =A0 coordinate[pos=3D0.5] (mid);
>
> Thanks in advance for your help.
>
> Regards,
>
> Marc van Dongen

0
vibrovski (20)
12/27/2011 4:32:24 PM
Hi again,

Actually decorations can do this quite simply:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}


\makeatletter
\tikzset{
	start time/.initial=3D0,
	end time/.initial=3D1,
	partial curve/.style=3D{
		#1,
		decoration=3D{
			show path construction,
			curveto code=3D{
				\pgfpathcurvebetweentime{\pgfkeysvalueof{/tikz/start time}}%
				{\pgfkeysvalueof{/tikz/end time}}%
				{\pgf@decorate@inputsegment@first}%
				{\pgf@decorate@inputsegment@supporta}%
				{\pgf@decorate@inputsegment@supportb}%
				{\pgf@decorate@inputsegment@last}%
			}
		},
		decorate
	}
}
\makeatother

\begin{tikzpicture}
\draw  (0,0) coordinate (start)
        (1,0) coordinate (c1)
        (2,-1) coordinate (c2)
        (3,0) coordinate (end)
        (start) .. controls (c1) and (c2) .. (end)
        coordinate[pos=3D0.5] (mid);
\draw [red,
	opacity=3D0.5,
	ultra thick,
	partial curve=3D{start time=3D0.0, end time=3D0.5}]
	(start) .. controls (c1) and (c2) .. (end);
\end{tikzpicture}

\end{document}

although there appears to be some kind of bug where no curve is drawn
if the start time is 0.25 and the end time is 0.5.

Hope this helps

Mark
On Dec 27, 4:32=A0pm, vibrovski <vibrov...@googlemail.com> wrote:
> Hi,
>
> It isn't currently available in TikZ (unless you use decorations with
> the pre length and post length options - but that is not an ideal
> solution). It is available in PGF using \pgfpathcurvebetweentime or
> \pgfpathcurvebetweentimecontinue. The manual for the basic layer
> describes these commands.
>
> Regards
>
> Mark
>
> On Dec 24, 1:16=A0pm, Marc van Dongen <don...@cs.ucc.ie> wrote:
>
>
>
>
>
>
>
> > Dear all,
>
> > Is there a way to construct a subpath of a Bezier curve? For example,
> > in the following, is there a way to get the part of the curve from
> > (start) to
> > (mid)? (I couldn't find it in the manual.)
>
> > \path (0,0) coordinate (start)
> > =A0 =A0 =A0 =A0 (1,0) coordinate (c1)
> > =A0 =A0 =A0 =A0 (2,-1) coordinate (c2)
> > =A0 =A0 =A0 =A0 (3,0) coordinate (end)
> > =A0 =A0 =A0 =A0 (start) .. controls (c1) and (c2) .. (end)
> > =A0 =A0 =A0 =A0 coordinate[pos=3D0.5] (mid);
>
> > Thanks in advance for your help.
>
> > Regards,
>
> > Marc van Dongen

0
vibrovski (20)
12/28/2011 2:01:53 PM
Reply:

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Hi all, If I have a Bezier curve (of any order), I know how to clip at a 't' value using de Casteljau's algorithm, and I know how to compute the arc length of the curve without flattening, using the Gauss-Legendre quadrature approach for computing the curve's integral over interval t=[0,1]. So far so good - the real problem is this: how do I determine which 't' value corresponds to a certain distance along the curve? Let's say I have a curve with a computed arc length over interval [0,1] of 100 units. In order to travel across this curve at some (arbitrary) fixed-distance interval I will need to know which 't' values the distances map to, but if I need the 't' value for a distance of 71 units along the curve, 0.71 is the least likely value it will have =) Which function, or set of functions, can be used to determine the 't' value based on arc length? Regards, - Mike "Pomax" Kamermans nihongoresources.com On 23.04.2011 20:26, Pomax wrote: > the real problem is this: how do I determine which 't' value corresponds to a > certain distance along the curve? The same old way you solve any problem involving how to find the inverse of a function that doesn't allow itself to be inverted analytically: use a numerical root finder to find the place where the function takes on the given value, i.e. solve length(Curve, t) = l > Which function, or set of functions, can be used to determine the &#...

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