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02-19-2018 11:44 PM

As well known, the success or failure in surfacing depends on the quality of starting curves.

Sometimes we need to refine a curve. A dilema in the refining process is to decide the degree and the number of segments, lower degree + more segments, or higher degree + less segments.

Hope to have your suggesions on this issue. Thanks!

Solved! Go to Solution.

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11 REPLIES

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02-20-2018 01:59 AM

Hi surfactant,

I am not an expert on this but will share my past experiences...I usually go for less number of segments and somewhat more degree for projects with less time.

It may vary from case to case. For a rough surfacing project more segments will surely be fast but for class-A or aesthetically good surfaces i always keep a tab on both of them (degrees and segment).

Usually i do not go beyond 4/5 degrees (no additional segment) and if needed then i break the surface into more primary patches (each with 3/4/5 degree) ....this however consumes a lot of time (though worthwhile).

For the primary (design intent curves) i will not recommend going more than 5/6 degrees...secondary (transition curves ) will automatically follow the route (for G2 at both ends it will be 6 degrees i guess).

one example is below...when the degree is less it is much easier to check any unwanted inflexions and most important if you keep the curve light you can get your desired comb curvature faster...below i am pulling the first node (along the tangent ) towards the end point to get a constant acceleration comb.....you will see that when you create a secondary (let us say a bridge curve) using this curve ...then you will the best bell shape comb transition.

Regards

Kapil

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02-20-2018 03:32 AM

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02-20-2018 06:03 AM

Will depend a little on the work you are doing but generally I would work with degree 5 and occasionally degree 7 and try and keep the segments to 1 and no more than 3.

Steve V

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02-20-2018 06:06 AM

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02-20-2018 08:38 AM

Most of what @StevenVickers states would be the norm/most desirable for most surfacing situations. Continuity can at times play a factor into the spline degree preference/target.

-Tim

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02-20-2018 08:45 AM

Hi @TimF Thanks for you commments!

I have totally no idea about the relationship between continuity and spline degree. If possible, hope to have more of your comments. Thank you!

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02-20-2018 12:29 PM

I would suggest switching on the pole display of a bridge curve features between two splines and seeing how it adjusts as you change constraints and shape.

Basic principles:

A single segment NURBS curve, i.e. a Bezier spline has one more pole that its degree.

So a degree 1 has two poles, one at each end, basically a straight line

degree 2 curve has 3 poles, degree 3 has 4 poles ....

If you add a segment then the the pole count increments by one per segment.

On the topic of continuity

The first pole of the spline controls its start position (well in most mathematical cases, there are exceptions but are rarely seen).

Therefor you need two poles to get G0 at both ends of the spline.

The second pole controls the tangentcy of the start of the spline. The line joining pole 1 to pole 2 is the tangency of the start at pole 1.

Therefor you need at least a mid pole to control tangentcy . A total of 3 poles (degree 2) would give you a conic blend which could be tangent at both ends to other curves but basically if you want to control the shape as well as keep tangentcy you are going to need 4 poles (degree 3). So 2 poles at each end to control tangentcy at both ends.

If you want to control starting curvature at both edge and get G2 at both edge of the spline you are going to need 3 poles at each end, that is 6 in total, i.e. a degree 5 spline.

Increasing degree above 5 gives you more control but at the same time also makes controlling the shape more difficult. Same with sections, more flexible but risk getting undulations you do not want.

Therefor if you can, usually work with single segment degree 5. But in some cases a soft starting conic blend/bridge is close enough to G2 an is more stable.

Steve V

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02-21-2018 10:31 PM

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02-22-2018 01:17 AM - edited 02-22-2018 01:19 AM

I still have another question:

To ceate a planar spline with 9 shape-controlling poles, which option would you adopt?

- 8 degree + 1 segment
- 6 degree + 3 segment
- 3 degree + 6 segment

Thanks!

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