[x3d-public] Tessellation…convert to IFS?

[Joseph D Williams]

Also note thee are several ways to represent a shape in x3d. If the name includes Indexed then the user code includes the coordinates for the points and the sets of coordindex numbers that tell the browser how to make the triangles. 
Some styles of shapes do not require the user to supply coordIndex, then the points are default auto-indexed into triangles by a standardized  formula depending on name and included user code for points. 

So, when you say shape Sphere then the browser encodes that depending on its internal spec sphere. 
You can see the result in a browser that can just show the points or triangles of the shape sphere otherwise it will appear as a solid but the details of the actual coordinates of points and tessellation (indexing) of those points will not appear in the user code because what does the user care about what the browser uses to create your Sphere? . 
 
So, for the default shape Box, probably uses two triangles per side. 
I think there is x3d Shape user code to present a box in both indexed and auto-indexed form. 
 
Here is classic-style user code with lots of defaults for one side of a box. 

 DEF boxfront Shape {
  appearance Appearance {
    material Material { }
    texture ImageTexture {
      url [ "textures/boxfront.jpg" ]
    }
  }
  geometry IndexedFaceSet {
    coordIndex [ 0 1 2 3 -1 ]
    coord Coordinate {
      point [ -1 -1 1, 1 -1 1, 1 1 1, -1 1 1 ]
    }
    texCoordIndex [ 0 1 2 3 -1 ]
    texCoord TextureCoordinate {
      point [ 0 0 1 0 1 1 0 1 ]
    }
  }
}

Joe


From: GPU Group
Sent: Saturday, April 22, 2023 2:33 PM
To: John Carlson
Cc: X3D Graphics public mailing list
Subject: Re: [x3d-public] Tessellation…convert to IFS?

Depends what you're doing. Assuming you're starting with a point cloud, if you're tessellating something almost flat, and with irregular points, then you can use something like Delaunay algorithm to optimize the edges between points to give triangles that are more equi-angular.
If you are on a 3D dimensional surface, but know its close to being convex -- like a sphere or cube -- then you can move the planar math around a spherical center, and crop points in the distance / on the other side of center when triangulating. 
Or you can remove and add points from a pre-triangulated sphere (I just made this up). Looking orthogonally at an existing triangle on your sphere, add a point from your point cloud, to the appropriate triangle, based on its yaw and pitch, or latitude, longitude, while ignoring its radius/height. When you have all your points added, then start removing the sphere's points. After each step of adding (or removing sphere points at the end), do Delaunay recursive triangle swaps on the local plane. 
Or ask ChatGPT - it might know.
-Doug

On Sat, Apr 22, 2023 at 3:05 PM John Carlson <yottzumm at gmail.com> wrote:
When one is tessellating a shape, like Box, is it typical to convert to IFS?

Thanks!

John
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