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Has anyone written a function for a caternaroid(?) that works just like
Paraboloid_Z in shapes_old.inc?
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Le 11/02/2015 04:13, Mike Horvath a écrit :
> Has anyone written a function for a caternaroid(?) that works just like
> Paraboloid_Z in shapes_old.inc?
I'm afraid not: Paraboloid_Z is a quadric, but a caternaroid (do you
mean something like a Pringles) would need something like cosh in the
equation.
http://bennbatt.tumblr.com/
z = A.cosh(x) - B.cosh(y)
Now, I might just be wrong, because the displayed equation
z = x²/a² -y²/b² with x²/a²+y²/b² < 1 would be something easy on a
quartic, with intersection of a cylinder along z for the <1 part.
// create a quadratic (2nd order) infinite polynomial surface
quadric {
<1, -1, 0> // A x^2 + B y^2 + C z^2 +
<0, 0, 0> // D xy + E xz + F yz +
<0, 0, -1> // G x + H y + I z +
0 // J
}
--
Just because nobody complains does not mean all parachutes are perfect.
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On 2/11/2015 3:04 AM, Le_Forgeron wrote:
> Le 11/02/2015 04:13, Mike Horvath a écrit :
>> Has anyone written a function for a caternaroid(?) that works just like
>> Paraboloid_Z in shapes_old.inc?
>
> I'm afraid not: Paraboloid_Z is a quadric, but a caternaroid (do you
> mean something like a Pringles) would need something like cosh in the
> equation.
>
> http://bennbatt.tumblr.com/
>
> z = A.cosh(x) - B.cosh(y)
>
> Now, I might just be wrong, because the displayed equation
>
> z = x²/a² -y²/b² with x²/a²+y²/b² < 1 would be something easy on a
> quartic, with intersection of a cylinder along z for the <1 part.
>
> // create a quadratic (2nd order) infinite polynomial surface
> quadric {
> <1, -1, 0> // A x^2 + B y^2 + C z^2 +
> <0, 0, 0> // D xy + E xz + F yz +
> <0, 0, -1> // G x + H y + I z +
> 0 // J
> }
>
>
Sorry. I meant a caternary surface of revolution. Looks almost like
Paraboloid_Z, but a little bit different. Thanks.
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Le 15-02-11 19:48, Mike Horvath a écrit :
> On 2/11/2015 3:04 AM, Le_Forgeron wrote:
>> Le 11/02/2015 04:13, Mike Horvath a écrit :
>>> Has anyone written a function for a caternaroid(?) that works just like
>>> Paraboloid_Z in shapes_old.inc?
>>
>> I'm afraid not: Paraboloid_Z is a quadric, but a caternaroid (do you
>> mean something like a Pringles) would need something like cosh in the
>> equation.
>>
>> http://bennbatt.tumblr.com/
>>
>> z = A.cosh(x) - B.cosh(y)
>>
>> Now, I might just be wrong, because the displayed equation
>>
>> z = x²/a² -y²/b² with x²/a²+y²/b² < 1 would be something easy on a
>> quartic, with intersection of a cylinder along z for the <1 part.
>>
>> // create a quadratic (2nd order) infinite polynomial surface
>> quadric {
>> <1, -1, 0> // A x^2 + B y^2 + C z^2 +
>> <0, 0, 0> // D xy + E xz + F yz +
>> <0, 0, -1> // G x + H y + I z +
>> 0 // J
>> }
>>
>>
>
>
> Sorry. I meant a caternary surface of revolution. Looks almost like
> Paraboloid_Z, but a little bit different. Thanks.
It's probably closer to an hyperboloid.
Alain
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On 2/12/2015 3:57 PM, Alain wrote:
>> Sorry. I meant a caternary surface of revolution. Looks almost like
>> Paraboloid_Z, but a little bit different. Thanks.
>
> It's probably closer to an hyperboloid.
>
>
> Alain
Well, I want the one closer to a paraboloid.
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On 2/10/2015 10:13 PM, Mike Horvath wrote:
> Has anyone written a function for a caternaroid(?) that works just like
> Paraboloid_Z in shapes_old.inc?
Sorry, "caternaroid" is not the name of the shape I'm looking for. Does
anyone know how to create a formula for a shape similar to a paraboloid
but with a catenary cross-section? Thanks.
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On 15.02.2015 4:11, Mike Horvath wrote:
> Sorry, "caternaroid" is not the name of the shape I'm looking for. Does
> anyone know how to create a formula for a shape similar to a paraboloid
> but with a catenary cross-section? Thanks.
If you're ok to approximate with a spline you could create
an "sor" object from a catenary.
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On 2/15/2015 12:26 PM, Christian Froeschlin wrote:
> On 15.02.2015 4:11, Mike Horvath wrote:
>
>> Sorry, "caternaroid" is not the name of the shape I'm looking for. Does
>> anyone know how to create a formula for a shape similar to a paraboloid
>> but with a catenary cross-section? Thanks.
>
> If you're ok to approximate with a spline you could create
> an "sor" object from a catenary.
>
I'd rather not. The shape is going to be large, prominent and reflective
in my scene, so I want it to look right.
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Le 16/02/2015 06:27, Mike Horvath a écrit :
> On 2/15/2015 12:26 PM, Christian Froeschlin wrote:
>> On 15.02.2015 4:11, Mike Horvath wrote:
>>
>>> Sorry, "caternaroid" is not the name of the shape I'm looking for. Does
>>> anyone know how to create a formula for a shape similar to a paraboloid
>>> but with a catenary cross-section? Thanks.
>>
>> If you're ok to approximate with a spline you could create
>> an "sor" object from a catenary.
>>
>
> I'd rather not. The shape is going to be large, prominent and reflective
> in my scene, so I want it to look right.
and why does it have to be a revolving-catenary ?
Cannot it be approximated by a paraboloid ?
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On 2/16/2015 4:45 PM, Le_Forgeron wrote:
> Le 16/02/2015 06:27, Mike Horvath a écrit :
>> On 2/15/2015 12:26 PM, Christian Froeschlin wrote:
>>> On 15.02.2015 4:11, Mike Horvath wrote:
>>>
>>>> Sorry, "caternaroid" is not the name of the shape I'm looking for. Does
>>>> anyone know how to create a formula for a shape similar to a paraboloid
>>>> but with a catenary cross-section? Thanks.
>>>
>>> If you're ok to approximate with a spline you could create
>>> an "sor" object from a catenary.
>>>
>>
>> I'd rather not. The shape is going to be large, prominent and reflective
>> in my scene, so I want it to look right.
>
> and why does it have to be a revolving-catenary ?
> Cannot it be approximated by a paraboloid ?
>
It's intended for the nose cone of my spaceship. All the pressure is
supported at the "base" of the cone, so the caternary is the correct
shape. On the other hand, Wikipedia says the caternary requires calculus
to model. I'd rather not mess with any of that.
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