# [cairo] Fwd: Bezier curve

Dov Grobgeld dov.grobgeld at gmail.com
Tue Nov 15 02:10:08 PST 2011

```If you really want to get into the mathematics of how to choose the control
point in order to get an optimal approximation of a quarter of a circle,
then you should have a look at the MetaFont source code by Donal Knuth.
See: http://www.tex.ac.uk/ctan/systems/knuth/dist/mf/mf.web .

But if you want simply want to do calculations like this it might be easier
to use Asymptote http://asymptote.sourceforge.net/ , which is an evolution
of MetaFont (via MetaPost). With Asymptote you can create paths by
specifying with directions and tension, and it will calculate the control
points for you.

Hope this helps.

Regards,
Dov

On Tue, Nov 15, 2011 at 11:43, Andrea Canciani <ranma42 at gmail.com> wrote:

> (I forgot to write to the list... sorry for the double mail)
>
>
> ---------- Forwarded message ----------
> From: Andrea Canciani <ranma42 at gmail.com>
> Date: Tue, Nov 15, 2011 at 10:42 AM
> Subject: Re: [cairo] Bezier curve
> To: Inderjit Singh <inderjit.singh at spaceapplications.com>
>
>
> On Mon, Nov 7, 2011 at 3:42 PM, Inderjit Singh
> <inderjit.singh at spaceapplications.com> wrote:
> > Hi,
> >
> > I'm new to cairo and I'm trying to draw a smooth curve between using an
> > array of points.
> >
> > Say I have an array with (x,y) coordinates as: POS_T pos = {{0.0, 0.0},
> > {1.0,1.0}, {1.5, 2.0}, {0.5, 3.0}, {0.0, 4.0}};
> >
> > So basically, a half round 'circle'. I've been looking in cairo docs but
> the
> > closest thing I get to is the cairo_curve_to but for that it requires
> > control points. How is it determined? I want a simple smooth line but
> using
> > Bezier algorithm requires additional data to make it happen. Is that
> > correct?
>
> Yes, the additional data determines how the smoothing between the
> points is performed.
> You can choose the control points and get different smoothing types
> You might want to read something about splines (cairo supports cubic
> Bezier curves, which in turn can represent any parametric cubic
> curve).
> You can find an algorithm for cubic spline interpolation here
> http://en.wikipedia.org/wiki/Spline_interpolation
> (I didn't test it).
>
>
> >
> > Or can I simply use curve_line_to and then interpolate this? currently
> the
> > code looks like this for line:
>
> cairo_line_to() would connect the points with straight line segments.
>
> >
> > ...
> >     for(uint32_t i = 0; i < boundary; i=i++)
> >     {
> >         cairo_move_to(cr, station->coverage[i].x,
> station->coverage[i].y);
> >
> > //        cairo_line_to(cr,
> > //                      station->coverage[(i+1) % boundary].x,
> > //                      station->coverage[(i+1) % boundary].y);
> >
> >         cairo_curve_to(cr,
> >                      station->coverage[i].x,
> >                      station->coverage[(i].y,
> >                      station->coverage[i+1].x,
> >                      station->coverage[i+1].y,
> >                      station->coverage[i+2].x,
> >                      station->coverage[i+2].y);
> >     }
> >
> >     cairo_set_line_width (cr, 1.5);
> >     cairo_stroke(cr);
> >
> >     cairo_destroy(cr);
> >
> >
> > Any help would be appreciated. Thanks.
> > Indy
>
> If you need further information, just write ;)
>
> Andrea
>
> >
> >
> > --
> > cairo mailing list
> > cairo at cairographics.org
> > http://lists.cairographics.org/mailman/listinfo/cairo
> >
> --
> cairo mailing list
> cairo at cairographics.org
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>
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