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Computation of limit positions for triangle/quad by spliting and averaging (with facet traversal)

Posted by Jianbing Huang on August 24, 2005 at 10:30:20:

Hi Scott,

I've read your paper that talks about implementing subdivision step by spliting/merging and at the merging step accumulates the neighbor contribution during facet traversal. The approach seems to be attractive as it does not require explicit neighbor query.

I am wondering whether or not the limit position can be obtained in a similar manner that only requires facet traversal? For example, for the recent extension work you have done to quad/triangle subdivision scheme that improves continuity. It would be good if the same algorithm with different coefficients can be used. Otherwise the explict topological query for neighbors may be needed anyway for a subdivision system?

My second question is a more general one. While it is true that subdivision surface can be defined by an arbitrary topological mesh, this can bring some "unwelcome" or inconvenient consequences. For example, the connectivity between the vertices can severely affect the final surface shape - this is unlike traditional NURBS where its surface geometry can be defined by control point geometry only (because its mesh topology is fixed). While this topological dependence may be considered as a consequence of admitting additional flexibility, would it imply that any editor system would need to allow the user change the connectivity as well as vertex geometry? What is your opinion here?

Thanks for your attention.

Jianbing

Follow Ups:

Re: Computation of limit positions for triangle/quad by spliting and averaging (with facet traversal) Jianbing Huang 10:27:08 09/05/05 (1)
- Re: Computation of limit positions for triangle/quad by spliting and averaging (with facet traversal) Scott Schaefer 10:54:51 09/05/05 (0)
Re: Computation of limit positions for triangle/quad by spliting and averaging (with facet traversal) Scott Schaefer 10:29:06 08/25/05 (2)

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: Hi Scott, : I've read your paper that talks about implementing subdivision step by spliting/merging and at the merging step accumulates the neighbor contribution during facet traversal. The approach seems to be attractive as it does not require explicit neighbor query. : I am wondering whether or not the limit position can be obtained in a similar manner that only requires facet traversal? For example, for the recent extension work you have done to quad/triangle subdivision scheme that improves continuity. It would be good if the same algorithm with different coefficients can be used. Otherwise the explict topological query for neighbors may be needed anyway for a subdivision system? : My second question is a more general one. While it is true that subdivision surface can be defined by an arbitrary topological mesh, this can bring some "unwelcome" or inconvenient consequences. For example, the connectivity between the vertices can severely affect the final surface shape - this is unlike traditional NURBS where its surface geometry can be defined by control point geometry only (because its mesh topology is fixed). While this topological dependence may be considered as a consequence of admitting additional flexibility, would it imply that any editor system would need to allow the user change the connectivity as well as vertex geometry? What is your opinion here? : Thanks for your attention. : Jianbing

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