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From: Kima
Subject: How does bezier_spline work in prism?
Date: 8 Sep 2019 18:35:01
Message: <web.5d754943280504bdecc0fada0@news.povray.org>
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.


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From: Bald Eagle
Subject: Re: How does bezier_spline work in prism?
Date: 8 Sep 2019 20:40:00
Message: <web.5d7566a1cb41806e4eec112d0@news.povray.org>
"Kima" <nomail@nomail> wrote:
> I tried to make a simple circle by bezier_spline,

IIRC, you can't do it with a single spline, but can append 2 semicircle
approximations.

See if this helps any, and see if LeForgeron's wiki page helps any.

https://news.povray.org/povray.general/thread/%3Cweb.5c47356c36095c6fbe7517870%40news.povray.org%3E/

http://wiki.povray.org/content/User:Le_Forgeron


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From: jr
Subject: Re: How does bezier_spline work in prism?
Date: 8 Sep 2019 21:30:04
Message: <web.5d757230cb41806efeeb22ff0@news.povray.org>
hi,

"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Kima" <nomail@nomail> wrote:
> > I tried to make a simple circle by bezier_spline,
>
> IIRC, you can't do it with a single spline, but can append 2 semicircle
> approximations.
> See if this helps any, and see if LeForgeron's wiki page helps any.

prisms with bezier_spline are also used in the distribution include file
'lemon.inc', under 'scenes/advanced/grenadine/'.


regards, jr.


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From: Kima
Subject: Re: How does bezier_spline work in prism?
Date: 8 Sep 2019 22:35:01
Message: <web.5d7581f3cb41806eecc0fada0@news.povray.org>
"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Kima" <nomail@nomail> wrote:
> > I tried to make a simple circle by bezier_spline,
>
> IIRC, you can't do it with a single spline, but can append 2 semicircle
> approximations.
>
> See if this helps any, and see if LeForgeron's wiki page helps any.
>
>
https://news.povray.org/povray.general/thread/%3Cweb.5c47356c36095c6fbe7517870%40news.povray.org%3E/
>
> http://wiki.povray.org/content/User:Le_Forgeron

I still don't understand why povray draws berzier curves this way.

Mathematically, the bezier curves of these points create a circle. See this
image
https://ibb.co/YykPGPM


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From: Bald Eagle
Subject: Re: How does bezier_spline work in prism?
Date: 9 Sep 2019 01:15:00
Message: <web.5d75a679cb41806e4eec112d0@news.povray.org>
"Kima" <nomail@nomail> wrote:

> I still don't understand why povray draws berzier curves this way.
>
> Mathematically, the bezier curves of these points create a circle. See this
> image
> https://ibb.co/YykPGPM

POV-Ray ought to draw Bezier curves the way all Bezier curves are drawn.
I'm not sure what your image is supposed to show, as there's no mathematical
data that relate it to Bezier curves.

Maybe try:
https://stackoverflow.com/questions/1734745/how-to-create-circle-with-b%C3%A9zier-curves

I've probably spent the last several years working on understanding Bezier
splines and patches.
Lods of mistakes and frustration and misconceptions, but eventually got it all
worked out in the end.
Tor Olav Kristensen (TOK) mentored me after I got my second wind and felt up to
attacking the topic again.



Cousin Ricky has a Bezier spline based sphere sweep in the object collection.
Jerome Grimbert (LeForgeron) likely also has some good Bezier spline/patch work
in his excellent collection of experiments.


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From: William F Pokorny
Subject: Re: How does bezier_spline work in prism?
Date: 9 Sep 2019 01:56:07
Message: <5d75b137$1@news.povray.org>
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.


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From: Kima
Subject: Re: How does bezier_spline work in prism?
Date: 9 Sep 2019 03:05:00
Message: <web.5d75c126cb41806eecc0fada0@news.povray.org>
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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From: kurtz le pirate
Subject: Re: How does bezier_spline work in prism?
Date: 14 Sep 2019 15:27:37
Message: <5d7d06e9$1@news.povray.org>
On 08/09/2019 20:32, Kima wrote:

> 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.

A little reading there :
<https://stackoverflow.com/questions/1734745/how-to-create-circle-with-b%C3%A9zier-curves>



-- 
Kurtz le pirate
Compagnie de la Banquise


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From: Leroy
Subject: Re: How does bezier_spline work in prism?
Date: 18 Sep 2019 16:50:01
Message: <web.5d825f0dcb41806e610414250@news.povray.org>
This may be a little late to help you much.
So here it goes. A long ago I fell in love with Prisms and Polygons, or I should
say it was the shapes they created. I think one of my first POV files was a
snowflake maker using Polygons, then prisms. There are an infinite number of
shape s you can come up with. To keep up with all those shapes I came up with,
and make new ones I wrote a windows program.
You can find it at  http://leroyw.byethost15.com/

 But you where asking about a circle(really a cylinder) using Prism and
bezier_spline. We should be able to let POV make one of any size for us.

You know the basics data
point1, control1, control2, point2
point2, control1, control2, point3
 :          :         :        :
pointN, controlNa, control1a, point1

if the prism is center is <0,0> and the number of points is N
 all the points are just point1 rotated around the center evenly
 the control points are a little more complicated
 if you use the formula with K=N
  control1(K)=(Pnt(N)+Pnt(N+1))*.333 and control2(K)=(Pnt(N)+Pnt(N+1))*.6666
  you will a n sided polygonal shape
 but if you adjust the control points out using
  L=vlength(Pnt(0))
  control1(K)=vnormalize(control1(K))*L
  control2(K)=vnormalize(control1(K))*L
 you should get a nice circle

This is just an over view. The code will have to be different. Prism doesn't
like 3d vectors and vnormalize outputs a 3d vector
I may be wrong, I haven't tried it.

Have Fun!


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From: Alain Martel
Subject: Re: How does bezier_spline work in prism?
Date: 18 Sep 2019 22:59:16
Message: <5d82b6c4$1@news.povray.org>
Le 2019-09-18 à 12:45, Leroy a écrit :
> 
>   This may be a little late to help you much.
> So here it goes. A long ago I fell in love with Prisms and Polygons, or I should
> say it was the shapes they created. I think one of my first POV files was a
> snowflake maker using Polygons, then prisms. There are an infinite number of
> shape s you can come up with. To keep up with all those shapes I came up with,
> and make new ones I wrote a windows program.
> You can find it at  http://leroyw.byethost15.com/
> 
>   But you where asking about a circle(really a cylinder) using Prism and
> bezier_spline. We should be able to let POV make one of any size for us.
> 
> You know the basics data
> point1, control1, control2, point2
> point2, control1, control2, point3
>   :          :         :        :
> pointN, controlNa, control1a, point1
> 
> if the prism is center is <0,0> and the number of points is N
>   all the points are just point1 rotated around the center evenly
>   the control points are a little more complicated
>   if you use the formula with K=N
>    control1(K)=(Pnt(N)+Pnt(N+1))*.333 and control2(K)=(Pnt(N)+Pnt(N+1))*.6666
>    you will a n sided polygonal shape
>   but if you adjust the control points out using
>    L=vlength(Pnt(0))
>    control1(K)=vnormalize(control1(K))*L
>    control2(K)=vnormalize(control1(K))*L
>   you should get a nice circle
> 
> This is just an over view. The code will have to be different. Prism doesn't
> like 3d vectors and vnormalize outputs a 3d vector
> I may be wrong, I haven't tried it.
> 
> Have Fun!
> 
> 
> 
> 
If all your points share the same Y coordinate, there is no problem. 
Same if they share the same X or Z.
You can multiply every point by <1,0,1> to ensure that you are on the 
X-Z plane.


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