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Re: Trimmed NURBS and subdivision

Posted by Scott Schaefer on January 25, 2005 at 13:15:29:

In Reply to: Re: Trimmed NURBS and subdivision posted by Jianbing Huang on January 20, 2005 at 23:16:29:

: Yes, I understand that subdivision is easier to deal with for modeling purpose - due to the generalization of subdivision rules to extraordinary vertices. While smoothness is very important when modeling organic shapes which are the subject of some industries, to properly model crease shape is equally important in other industries, for example CAD. This is where I am not so confident/comfortable about subdivision surface - but it could just be my lack of understanding and practice. From the several papers about this subject, current available methods seem to use ad-hoc rules to generate crease edges. There are also some papers that deal with this subject more systematically, such as NURSS. In your opinion, what are the pros and cons of two competing methods (modified rule for crease vertices and weight-based NURSS) to model crease edges?

You're correct in saying that there has not been a lot of trimming work done for subdivision surfaces.

In terms of your question comparing NURSS and crease edges... NURSS's are interesting, but complicated. I'm not necessarily convinced that the proof in that paper of smoothness is exactly correct either (analyzing non-uniform subdivision schemes is very difficult and many stationary techniques do not apply). However, maybe NURSS's are really no more compilicated than NURBS.

I like crease rules because they are simple modifications to the subdivision rules (usually stationary) that generate the desired feature. I don't believe that all of these rules are ad-hoc and they are usually built to form uniform cubic B-splines on crease edges with certain tangent plane continuity. There are even schemes that allow you to control the normals at specific places of the surface and can allow you to piece together different surfaces with C^1 continuity.

: I guess I was trying to understand the question "can subdivision readily model trimmed NURBS" and "if it can what benefit can we gain"? While trimming can be useful/convenient in the modelling process, it does pose some challenges. For example, tessellation of trimmed NURBS is significantly more costly. More importantly, trimming curves increase the size of model and the model size can become crucial in many occasions. So one thing I am trying to understand is "can equivalent subdivision representation be much smaller than trimmed NURBS" and if it can "what techniques do we have to convert trimmed NURBS to subdivision". Its seemingly size advantage, together with its graphically friendly characteristics (easy refinement), subdivision seems to be a good/compact candidate for data representation. I guess I am trying to look for an answer, and if there is not an answer trying to decide if this could be the right area to spend more time on.

To answer this question, I'd have to say that I'm not sure. It may be possible to use NURSS's to generate trimmed NURBS surfaces. Tom Sederburg has recently been publishing new work on what he calls T-splines as well. These surfaces are like NURBS except that you don't need the tensor product structures that you do for NURBS. I think that Tom has also generalized them to arbitrary valences as well so you might take a look at that. I think he's had a paper in SIGGRAPH 2003 and 2004 about this topic.

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: : Yes, I understand that subdivision is easier to deal with for modeling purpose - due to the generalization of subdivision rules to extraordinary vertices. While smoothness is very important when modeling organic shapes which are the subject of some industries, to properly model crease shape is equally important in other industries, for example CAD. This is where I am not so confident/comfortable about subdivision surface - but it could just be my lack of understanding and practice. From the several papers about this subject, current available methods seem to use ad-hoc rules to generate crease edges. There are also some papers that deal with this subject more systematically, such as NURSS. In your opinion, what are the pros and cons of two competing methods (modified rule for crease vertices and weight-based NURSS) to model crease edges? : : You're correct in saying that there has not been a lot of trimming work done for subdivision surfaces. : In terms of your question comparing NURSS and crease edges... NURSS's are interesting, but complicated. I'm not necessarily convinced that the proof in that paper of smoothness is exactly correct either (analyzing non-uniform subdivision schemes is very difficult and many stationary techniques do not apply). However, maybe NURSS's are really no more compilicated than NURBS. : I like crease rules because they are simple modifications to the subdivision rules (usually stationary) that generate the desired feature. I don't believe that all of these rules are ad-hoc and they are usually built to form uniform cubic B-splines on crease edges with certain tangent plane continuity. There are even schemes that allow you to control the normals at specific places of the surface and can allow you to piece together different surfaces with C^1 continuity. : : I guess I was trying to understand the question "can subdivision readily model trimmed NURBS" and "if it can what benefit can we gain"? While trimming can be useful/convenient in the modelling process, it does pose some challenges. For example, tessellation of trimmed NURBS is significantly more costly. More importantly, trimming curves increase the size of model and the model size can become crucial in many occasions. So one thing I am trying to understand is "can equivalent subdivision representation be much smaller than trimmed NURBS" and if it can "what techniques do we have to convert trimmed NURBS to subdivision". Its seemingly size advantage, together with its graphically friendly characteristics (easy refinement), subdivision seems to be a good/compact candidate for data representation. I guess I am trying to look for an answer, and if there is not an answer trying to decide if this could be the right area to spend more time on. : To answer this question, I'd have to say that I'm not sure. It may be possible to use NURSS's to generate trimmed NURBS surfaces. Tom Sederburg has recently been publishing new work on what he calls T-splines as well. These surfaces are like NURBS except that you don't need the tensor product structures that you do for NURBS. I think that Tom has also generalized them to arbitrary valences as well so you might take a look at that. I think he's had a paper in SIGGRAPH 2003 and 2004 about this topic.

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