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"a sphere has 4 edges" Is this right?

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"a sphere has 4 edges" Is this right?

Posted by santi at February 23. 2012

http://docs.salome-platform.org/salome_6_4_0/gui/SMESH/constructing_meshes_page.html

 

"Now you can define 1d Algorithm and 1d Hypotheses, which will be applied to the edges of your object. (Note that any object has edges, even if their existence is not apparent, for example, a sphere has 4 edges). Click the "Add Hypothesis" button to add a hypothesis."

 

Does anybody know where are the edges of a sphere?.

 

I can't believe this.

Re: "a sphere has 4 edges" Is this right?

Posted by Saint Michael at February 24. 2012

This is so because in the parametric space of surface the sphere is a rectangle -> 4 edges.

Two degenerated edges (3D length==0) are at poles and two edges (coincident in 3D space) connect poles.

St.Michael

Re: "a sphere has 4 edges" Is this right?

Posted by santi at February 25. 2012

I see, well in analytical geometry  you can define a sphere as the points with the same distance to an origin:

 

(x-x0)2 + (y-y0)2 + (z-z0)2= r2

 

So you don't need a rectangle to define a sphere.

 

I understand from your post that salome uses another parametric definition in wich you transform a rectangle into  a sphere. I don't know why it is  made in that way, or what benefit you have from it. Am I wrong?

 

 

 

 

Re: "a sphere has 4 edges" Is this right?

Posted by Saint Michael at February 27. 2012

SALOME uses Boundary Representation model of geometry.

Consider a way to address a point on the sphere. In SALOME two angles are used for this: inclination angle [-PI, PI] and azimuth angle [0, 2*PI]. In 2D space of those angles the sphere is a rectangle.

Re: "a sphere has 4 edges" Is this right?

Posted by santi at February 27. 2012

I understand, I have been searching this morning to learn about this deeply, I have found this book:

 

http://www.amazon.com/Boundary-Representation-Modelling-Techniques-Stroud/dp/1846283124/ref=sr_1_1?ie=UTF8&qid=1330351495&sr=8-1

 

If you enter in amazon , there is a "look inside" the book, and you can see the table of contents, it would be great if there are a chapter explaining exactly the method that uses salome to make the mesh.

 

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