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Le 29/07/2009 11:27, Thomas de Groot nous fit lire :
> Hi all,
>
> I need a CSG object that basically has the shape of a cone, but with the
> apex as a straight edge parallel to the base, with a length equal to the
> diameter of the base. I tried all kinds of combinations but am unable to get
> this right.
>
> Any help will be much appreciated. Thanks a lot.
>
Can you check "apex as a straight edge *parallel* to the base."
apex is a point.
On standard "right circular" cone, the apex is projected on the center of the base
circle.
Your description seems to describe an oblique circular cone, whose apex is projected
on a
point of the base circle. Distance between projection plane and apex being diameter of
the
circle.
You need a quadratic equation. Either as isosurface or quadric.
Isosurface has been provided, but a quadric might provide a different rendering time,
bounded by a unit box.
A x2 + B y2 + C z2 + D xy + E xz + F yz + G x + H y + I z + J = 0
A centered circle on <0,0,0>, radius 1: A=B=1, J=-1; D=0; G=0; H=0;
symetry implies E=0;
Remains C,F,I
with apex on <0,1,2>:
0+1+4C +2F+2I-1=0
4C+2F+2I=0
Also <0,1,1> on surface.
0+1+C+F+I-1=0
C+F+I=0
therefore C=0;
and F=-I
<0,0,1> also on surface
I-1=0 so I=1
intersection {
box{ <-1,-1,0>,<1,1,2> }
quadric { <1,1,0>,<0,0,-1>,<0,0,1>,-1}
}
have a nice day.
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Darren New <dne### [at] san rrcom> wrote:
> I was thinking more scale it from x=1.0 y=1.0 to x=1.0 y=0.0 as you move
> from z=0 to z=1, if that makes sense. Not an intersection, but a non-linear
> scaling.
Here's the catch: You can't do non-linear scaling in POV-Ray (unless you use
parametrics, isosurfaces or some such).
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Further thinking about your description, if apex really a segment parallel to base:
check volume 3 of news://news.povray.org:119/496f790c@news.povray.org
(title: "6 volumes" OP: Le_Forgeron, Date 15 january 2009)
It's a conocuneus, a quartic.
Toothpath tube classical end.
intersection {
box {<0,-1,-1><2,1,1>}
quartic {
<0,0,0,0,0, 0,0,1,0,-1,
0,0,0,0,0, 0,0,0,0,0,
0,0,0,0,0, 4,0,0,0,0,
0,0,0,0,0> }
}
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"Darren New" <dne### [at] sanrrcom> wrote in message
news:4a7078d0$1@news.povray.org...
> clipka wrote:
>> Darren New <dne### [at] sanrrcom> wrote:
>>> Could one start with a cylinder instead? Since the top is as wide as the
>>> bottom in at least one direction?
>>
>> Hm, yes, I guess a cylinder intersected with a wedge would fit Thomas'
>> bill, too
>> (at least nominally, though it may not be what he looked for, due to the
>> hard
>> edges this would produce)
>
> I was thinking more scale it from x=1.0 y=1.0 to x=1.0 y=0.0 as you move
> from z=0 to z=1, if that makes sense. Not an intersection, but a
> non-linear scaling.
>
That's what two of the three examples I posted this morning do, one using an
Isosurface, the other using slices of a sphere, (but a cylinder would work
the same). The third example I posted used the method Clipka outlined, which
generates a slightly different shaped surface.
I think there is at least one more way without using shear, which is to
scale a cone non uniformly, rotate and slice it, such that the horizontal
section becomes circular while the edge is vertical, then fill out the
middle as before.
Regards,
Chris B.
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"Chris B" <nom### [at] nomailcom> wrote in message
news:4a70803b@news.povray.org...
>
> I think there is at least one more way without using shear, which is to
> scale a cone non uniformly, rotate and slice it, such that the horizontal
> section becomes circular while the edge is vertical, then fill out the
> middle as before.
>
In fact I've tried it and I don't think my fourth way works because you
always end up with a parabolic conic section.
Nevertheless, Le Forgeron looks as though he's still churning out more
alternatives :-)
Geometry questions seem popular. Any more ;)
Regards,
Chris B.
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Toothpaste tube end indeed covers the bill :-)
Thomas
"Le_Forgeron" <jgr### [at] freefr> schreef in bericht
news:4a707f48$1@news.povray.org...
> Further thinking about your description, if apex really a segment parallel
> to base:
>
> check volume 3 of news://news.povray.org:119/496f790c@news.povray.org
> (title: "6 volumes" OP: Le_Forgeron, Date 15 january 2009)
>
> It's a conocuneus, a quartic.
> Toothpath tube classical end.
>
> intersection {
> box {<0,-1,-1><2,1,1>}
> quartic {
> <0,0,0,0,0, 0,0,1,0,-1,
> 0,0,0,0,0, 0,0,0,0,0,
> 0,0,0,0,0, 4,0,0,0,0,
> 0,0,0,0,0> }
> }
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"Le_Forgeron" <jgr### [at] freefr> schreef in bericht
news:4a707f48$1@news.povray.org...
> It's a conocuneus, a quartic.
> Toothpath tube classical end.
>
> intersection {
> box {<0,-1,-1><2,1,1>}
> quartic {
> <0,0,0,0,0, 0,0,1,0,-1,
> 0,0,0,0,0, 0,0,0,0,0,
> 0,0,0,0,0, 4,0,0,0,0,
> 0,0,0,0,0> }
> }
This is now the most elegant solution. Thanks a lot!
Thomas
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"Le_Forgeron" <jgr### [at] freefr> schreef in bericht
news:4a707f48$1@news.povray.org...
> Further thinking about your description, if apex really a segment parallel
> to base:
>
> check volume 3 of news://news.povray.org:119/496f790c@news.povray.org
> (title: "6 volumes" OP: Le_Forgeron, Date 15 january 2009)
>
Maybe me, but this reference is not pointing to anything on news.povray.org
....
Thomas
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"Thomas de Groot" <tDOTdegroot@interDOTnlANOTHERDOTnet> schreef in bericht
news:4a7d349d$1@news.povray.org...
>
> "Le_Forgeron" <jgr### [at] freefr> schreef in bericht
> news:4a707f48$1@news.povray.org...
>> check volume 3 of news://news.povray.org:119/496f790c@news.povray.org
>> (title: "6 volumes" OP: Le_Forgeron, Date 15 january 2009)
>
Seriously, I cannot find any message related to this on the server in any
n.g. (I used Search). Neither title nor date refer to a message. Any help?
Thomas
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"Thomas de Groot" <tDOTdegroot@interDOTnlANOTHERDOTnet> wrote in message
news:4a7fcc36$1@news.povray.org...
>
> "Thomas de Groot" <tDOTdegroot@interDOTnlANOTHERDOTnet> schreef in bericht
> news:4a7d349d$1@news.povray.org...
>>
>> "Le_Forgeron" <jgr### [at] freefr> schreef in bericht
>> news:4a707f48$1@news.povray.org...
>>> check volume 3 of news://news.povray.org:119/496f790c@news.povray.org
>>> (title: "6 volumes" OP: Le_Forgeron, Date 15 january 2009)
>>
>
> Seriously, I cannot find any message related to this on the server in any
> n.g. (I used Search). Neither title nor date refer to a message. Any help?
>
> Thomas
>
Hi Thomas.
See:
From: "Le_Forgeron" <jgr### [at] freefr>
Newsgroups: povray.binaries.images
Sent: Thursday, January 15, 2009 6:57 PM
Subject: 6 volumes
The URL above incorporated the port number (119) in a way that screwed up
the link on my newsreader (and I imagine on yours too). It's the default
port anyway, so when I removed that it popped up ok in the Windows Mail
client on Vista. ie news://news.povray.org/496f790c@news.povray.org
It's also available through the browser interface at:
http://news.povray.org/povray.binaries.images/thread/%3C496f790c%40news.povray.org%3E/?ttop=318396&toff=250
It seems that Le Forgeron foresaw your very question at the start of the
year. Next Psychic challenger please :-)
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