Mathematically correct Quad Sphere ?


#1

I am using LW 7.5c.Don’t reckon there’s a plug to make mathematically correct Quad Sphere ?

As you can see the lines change in there location.
Have my doubts either quad sphere is correct.

I am assuming mathematicians would know but I am not even close to a mathematician.
So anybody know the Math formula to tell you the corect location of every point ?

Thanks
RorrKonn
http://www.Atomic-3D.com


#2

Well a sphere is the locus of points equidistant from a point(the center of the sphere) so for a point to be correct sqrt[ (sqrt[(X^2) + (Y^2)]) + (Z^2)] would have to equal the radius of the circle. However its not like you can really check each point and make sure it works and even if you do the problem bascally boils down to that you’re trying to express a perfectly round object with alot of flat objects. The best way to get a perfect sphere is to just add a null to a scene and apply hypervoxels to it. Hope some of this helps cuz i’m not entirely sure what you are trying to do.


#3

Thanks Padmus.I am not entirely sure how to explain what I am looking for.
Take a Cube.make the cube Segments x,y,z 4.then spherize.
Makes a quad sphere.

But depending on where the dots start with in the cube.
Is where the dots will be for the sphere.

So if I make two deferent cubes with the dots in deferent places.
The sphere dots our in deferent places.

So I have 2 deferent answers for one question.
So there for one has to be wrong.

So I am looking for the correct answer of where does the dots go in the sphere.

RorrKonn
http://www.Atomic-3D.com


#4

I think that both are wrong. They are both just estimations of a sphere shape using flat quads, each being slightly different from each other. The “Ball” primitive is also an estimation of a sphere using a combination of quads and tris.

Out of curiosity, why do you need a perfect sphere?


#5

It’s impossible to represent a perfectly smooth sphere with a polygon-based object. Subdividing it will get you closer, but no matter how much you do, it’s never going to be perfectly round. Where precision like that is mission-critical, NURBS are your best option.


#6

Apparently I have not explained my self very well,
Hopefully this will explain what I am trying to do.

Tibes,They probably our both wrong but if we had a mathematical equation.
we could check to see if there both wrong and know how to make the correct one.

Triple G,Reckon ya calling Splines, Nurbs cause there the same thing more or less.
but for what I am trying to do. don’t think there be much help.

I don’t need a perfect sphere.
I need a balanced quad sphere mesh that looks like “B”,“C” part of the .jpg.
This one just don’t look right to me cause it’s not very balanced.

A_ The highlighted Sphere dots our Equal distance apart,so I think that’s right.
The quad sphere dots our not equal distance apart, so I think there wrong.

B,C_I Think the cube is correct ,cause all the dots our Equal distance apart.
The Quad sphere Dots our not they bunch up at the sides so I think that’s wrong.

I know for the Quad Sphere all the dots our not going to be equal distance apart cause the curve of the sphere will distort them some.

But I do think they should be more balanced then what they currently our.

Thanks for your all’s help.

RorrKonn
http://www.Atomic-3D.com


#7

Actually, I know what I wrote, and that’s what I meant. NURBS are a type of spline, and are not supported in Lightwave. They are mathematically precise because they don’t need to rely on polygons to define their surface…so they are capable of being infinitely smooth regardless of how you look at them.

But you say that you don’t need a perfectly smooth sphere? Sorry man, I just don’t see what the problem is. You say that one picture is right and another one is wrong? Wrong how? They are both spheres…if you look at them in orthographic views, are they not the same size? Of course their topology is going to be slightly different…they were created in totally different ways, but they’re still both spheres. :shrug:


#8

The perfect roundness of the sphere is not important here.
ah how did you know I had Nurbs ?

not 100% sure I know the definition of topology.
but if topology is where the wire frame and dots go.
then that’s what I am trying to get right.

want the dots in the right place.

RorrKonn
http://www.Atomic-3D.com


#9

Rorr,
I guess youre looking for a sphere that is tesselated but with quads. If I understand correctly you want each quad to be the same size? Try metaforming a cube (shift D) and see if that works.


#10

Don’t know if this is what you are after, but C4D make some nice HyperNurbed quad-spheres from cubes (see attachment). Perhaps a C4D owner can export you a sphere? (the demo is save disabled)


#11

Correct. each quad needs to be as close as posable to the same size.
of corse cause of the Shape of the Sphere thay will not be exsact same shape,size.
just would like to get as close as posable.

Metaformed a cube twice + Spherize.
placed a 16 sided cylinder on it’s edge to compare.

A_ is a cube Metaformed twice.

B_ is the cube Metaformed twice + Spherize.

C_is a close up as to how close it got.

D_is a wireframe shade view.

This is close enuff.I like this Quad Sphere.

Posted it on Atomic-3D.com at
http://www.atomic-3d.com/RK_Materials_DarkTree/00_Materials_MainFrame.htm

Thanks alot for everyones help
RorrKonn
http://www.Atomic-3D.com


#12

Petterms.
Originally got BodyPaint for LW7,and TS.
BodyPaint 2 is killer Get’s 5 Stars from me.

Anyways I happen to have C4D8 also. hyperNurbs will be about the same as .jpg A.
Haven’t found C4D’s Spherize yet but they probably have one to.

I use multiple App’s, Love them All.
Would never pick one over the other.

RorrKonn
http://www.Atomic-3D.com


#13

I am just wondering of what use this would be to anyone?

jud


#14

Jud,

1_Thought about making a Organic and a Mechanical Character.Named him Chrome.
http://forum.caligari.com/discus/messages/1583/16116.html?1092026361
Mechanical Character will have Quad Spheres at some of his joints.

2_Not all App’s have SubPatch that Subdivide Tri’s,
There Sub Division system works like LW’s Subdivide.Will turn Tri’s to Quads.

3_If ya get a regular LW Ball with the Tri’s at top bottom. and a QuadSphere.
I like the way the QuadSphere Sub Divides better.

4_I’ve always been told,best to use Quads,not Tri’s.

RorrKonn
http://www.Atomic-3D.com


#15

Ahh right’o

jud


#16

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