William F Pokorny <ano### [at] anonymousorg> wrote:
> On 9/8/19 2:32 PM, Kima wrote:
> > I tried to make a simple circle by bezier_spline,
> >
> >      prism {
> >        bezier_spline
> >       0,-.3,32,
> > <0.154,0.605>,<0.128,0.605>,<0.128,0.605>,<0.1105,0.6225>
> > <0.1105,0.6225>,<0.093,0.64>,<0.093,0.64>,<0.093,0.666>
> > <0.093,0.666>,<0.093,0.691>,<0.093,0.691>,<0.1105,0.709>
> > <0.1105,0.709>,<0.128,0.727>,<0.128,0.727>,<0.154,0.727>
> > <0.154,0.727>,<0.18,0.727>,<0.18,0.727>,<0.1975,0.709>
> > <0.1975,0.709>,<0.215,0.691>,<0.215,0.691>,<0.215,0.666>
> > <0.215,0.666>,<0.215,0.64>,<0.215,0.64>,<0.1975,0.6225>
> > <0.1975,0.6225>,<0.18,0.605>,<0.18,0.605>,<0.154,0.605>
> >
> >        pigment { color rgb<1,0,0>}
> >
> > }
> >
> > but instead of a circle, it gave me an octagon as it seems the control points
> > are connected instead of start and end points.
> >
> > What is wrong with my setting <start,control1,control2,end>?
> >
> > Note that I want to understand bezier_spline rather than finding an alternative
> > for creating a specific shape.
> >
> Your control points in each segment are identical.
>
> The usual way to do circles with Bezier curves is with 4 segments using
> the method from: Michael Goldapp, "Approximation of circular arcs by
> cubic polynomials" Computer Aided Geometric Design (#8 1991 pp.227-238).
>
> I'm lazy and keep a point list created by this method for a circle at a
> radius of 1.0 at the origin laying around - which I can scale, move etc.
> So a circle within a circle to create a prism ring of sorts becomes:
>
> #declare Cheese = srgb <1,0.65098,0>;
> #declare Prism00 = prism {
>      bezier_spline
>      linear_sweep
>      -0.2, 0.2, 32,
>      <1,0>,<1,0.552285>,<0.552285,1>,<0,1>
>      <0,1>,<-0.552285,1>,<-1,0.552285>,<-1,0>
>      <-1,0>,<-1,-0.552285>,<-0.552285,-1>,<0,-1>
>      <0,-1>,<0.552285,-1>,<1,-0.552285>,<1,0>
>      <0.5,0>,<0.5,0.276143>,<0.276143,0.5>,<0,0.5>
>      <0,0.5>,<-0.276143,0.5>,<-0.5,0.276143>,<-0.5,0>
>      <-0.5,0>,<-0.5,-0.276143>,<-0.276143,-0.5>,<0,-0.5>
>      <0,-0.5>,<0.276143,-0.5>,<0.5,-0.276143>,<0.5,0>
>      pigment { color Cheese }
> }
>
> Bill P.

Thanks, Bill. I got it that the problem is my points, but your answer came
before I correct myself. Like your set, the controls should have identical x OR
y, but mine has both together, and that was the problem.

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