# Which surface is better?

Hi dears
I have two question:

## First question

If i want to create single-span surfaces for a car hood witch way is Better?

1. First way(as you see in the picture below)

1.create surface from four single-span curves(1,2,3,4,) with EdgeSrf command
2.Mirror surface
3.Match surfaces with G2 continuity (average surface)
4 . Split surfaces with curve number 5

In this way we have good reflection of surface but top edge have many control points so top edge is not a single-span

1. Second way(as you see in the picture below)

1.create surface from four single-span curves(1,2,3,4,) with EdgeSrf command
2.Mirror surface
3.Match surfaces with G2 continuity (average surface)

In this way we donâ€™t have good reflection but top edge is a single-span

## Second question

In first question ( first way) :top edge wasnâ€™t a single-span,is it causing that our surface doesnâ€™t a single-span surface?

Thanks

your curves have to be single span to get a surface that is single span- for g2 you need to be degree 5 with 6 cv- Each curve should match this requirement, and the resulting surface will be then single span-

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Hi Shayan - Iâ€™d go with the trimmed version - avoid pinched corners on the underlying surface where possible and keep the structure nice and rectangular.

-Pascal

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Only my personal (untrained) opinion: The goal of the modeling process should always be to describe a form within known tolerances ,with minimal math and maximum fairness. All three things are important. Your tolerances,I do not mean the units settings maybe â€śmethod of productionâ€ť is better - will greatly impact the final look. Things milled in wood, possible with some secondary surface treatment (sanding,lacquer) will hide local continuity problems but a lumpy surface, which can be perfectly g2/g3 continuous is, in this case, a bigger problem.(Local continuity vs. Fairness)
Minimal Math means the simples Surface which is true to the design intend should be used. Usually we strive for pulled, smooth surfaces. Single span just has the benefit that it is always curvature continuous. ( If your cv count is one higher than our degree and all point weights are 1, your crv is singlespan If you canâ€™t achieve a specific form in single span donâ€™t shy away from multispan.(but use at least degree 5, as any lower can lead to kinks in your multispan-crv) For blends your first cv controls G0 continuity, your second cv G1 continuity and so forth. For mirrored srf G1 is sufficient as they are automatically G2 continous (maybe this is wrong )but most of the time your better of building a â€śbridgingâ€ť srf over the centeraxis, as this is requires the least amount of cv and you dont have to match your half surface in the middle.
Maximum Fairness is arguably the most subjective of the three. 1. fundamental question: Maybe not every crv should have maximum fairness? 2. How do we define and perceive fairness? But usually this means a the change of curvature of curve should be monotone( or continous) over small and large distances. The simple way to put it how â€śniceâ€ť the curve is. To evaluate this it helps to look at curvature graphs and reflections. The reflections will move over the surface â€śtwice as fastâ€ť revealing small â€śdefectsâ€ť like breaks, dipping, â€¦

I hope this is of any value for you ( or others), again this isnâ€™t anything that was thought to me so take it with a grain of salt, also some parts are probably lost in translation from german.

I also would like to hear how the rest of the community judges a â€śgoodâ€ť model .

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They are automatically G2, but not G3, i.e. there can be a kink in the curvature graphs where they meet at the centerline - this can be adjusted out, often, if needed, but something to look for, if you want to take it that farâ€¦

-Pascal

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yeah that what I thought

@eleven10: Thank you so much for sharing your opinion! I, as a rhino amateur, found it really interesting and appreciate the effort you made!

youâ€™re welcome

I donâ€™t understand your mean in this two case :

Local continuity vs. Fairness:
take these two crv. notice the bad cv placement in the left one.

it causes the blend crv to dip and will result in a dent in the surface.

â€“The resulting crv has perfect local continuity but poor fairness.

matching only to g1 tangency aviods this and depending on the specific geometry can give good results. Also â€śyour method of productionâ€ť can hide the small tangency break. I would argue this resulting crv has better fairness at the cost of continuity.

the proper solution is to trim the crv back and blend over a larger distance.

"bridging" crv over the centeraxis:

the top curves describing both sides with one singlespan crv , in contrast to the ones below which take two. the top one has the benefit of being always smooth over the center while the other one needs to be matched. notice the â€śg3 breakâ€ť after transforming in the lower one.

sadly I donâ€™t know of any native tool in Rhino to enforce symmetry over a axis - so this tends to be manual labor

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Hi dear pascal

In modeling car chassis , but not all surfaces are single-span?

the goal of using single span is to have a internally smooth surface and nice reflections. when you donâ€™t achieve that there is no point in using single span.