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G1 magnitude" (Studio Spline)?

Genius
Genius

I can't figure out the meaning of "G1 magnitude" in the Studio Spline command, even after examining the official help.

 

Can anybody give some clues? Thanks a lot!

7 REPLIES

Re: G1 magnitude" (Studio Spline)?

Solution Partner Legend Solution Partner Legend
Solution Partner Legend

Hello,

 

The G1 magnitude makes the poles tangentional. The magnite can be choosen for the beginning and the end of the spline (also without existing curves or geometries). 

Take a look at my video. The G1 magnitude is an automatism for something you could also do by constrains

 

 

Re: G1 magnitude" (Studio Spline)?

Genius
Genius

Hi, AndreF, Thanks for the video! I know the meaning of G0, G1, G2, G3.

 

I just want to know the meaning of the number of G1 magnitude.

 

In my mind, G1 means tangent, and tangent is simply tangent. What's the role of the number "G1 Mangnitude"?

 

Thanks!

 

ScreenClip [1].pngnumber

Re: G1 magnitude" (Studio Spline)?

Gears Esteemed Contributor Gears Esteemed Contributor
Gears Esteemed Contributor

The magnitude controls how quickly the spline changes direction near the point of tangency. For a visual representation, create 2 coplanar lines then connect them with a bridge curve. Change the bridge curve's shape control to "tangent magnitude" and play with the sliders to see what effect it has on the shape of the spline.

Re: G1 magnitude" (Studio Spline)?

Genius
Genius

Thank you so much! I just followed your suggestion and tried the Bridge Curve command. Yes, it gives much better understanding about the effect of Tangent Magnitude.

 

I also find that the statement in the official help of "Bridge Curve":

 

Tangent Magnitude represents the percentage of tangency in Start and End values. These are initially set to 1.

 
The ambiguous description does drive me crazy.
 
 

 

Re: G1 magnitude" (Studio Spline)?

Pioneer
Pioneer

I wish someone from Siemens could also chime in with a specific definition of the G1 Magnitude value. 

The following sentence: "The magnitude controls how quickly the spline changes direction near the point of tangency" is too generic for my taste.

The G1 magnitude has a unit (inches) associated with it. All we want to know is: What exactly (on screen) is this measuring? 

Thanks!
Jeff

Re: G1 magnitude" (Studio Spline)?

Siemens Creator Siemens Creator
Siemens Creator

example of G1.pngexample of G2.pngexample of G3.pngexample of GO.png

Basically the quick answer is as was stated before, G1 states that the control polygon from each side curve (not shown)  is tangent making the Normal vector or curve comb inline see G1 image but not necessarily the same length that would be attained with better continuity

 

G2 would produce the unit vector to be the same length see G2

 

G3 would produce the effect of a parametric continuity in that if you were riding 2 bikes on each spline towards each other at the same speed, they would meet at the connection at the same time … I am paraphrasing big time here … there is more to this but this is for just a visual

 

More info but may be too much...

 

1) G0,G1,G2,G3 vrs C0,C1,C2,C3 Parametric vs. Geometric Continuity see google

https://www.quora.com/Whats-the-difference-between-C-and-G-continuity-for-splines

 

2) There are two ways of computing curvature deviation between curves/surfaces.

  1. Absolute curvature
  2. Relative curvature (see below )

For simplicity let us assume we are computing the curvature deviation between curves.

At the 2 end points of the curves, we can calculate the curvature values. Let us call them k1 and k2. (Note that both these are absolute values of the original curvature value.)

 

The absolute curvature deviation is the (k1 - k2). (Note this returns the absolute value).

The relative curvature deviation is calculated using different techniques and applying a ratio.

The reason we have the two ways of computing is that different software use different ways. Please correct me if I am wrong, Alias always computes absolute curvature deviation. In Imageware, we have a system preference, where we can set either absolute or relative.

 

There are advantages and disadvantages in absolute curvature deviation.

The advantage is that it gives us the exact deviation.

 

The disadvantage is that if we have a plane (curvature is 0) or a very low curvature, then the deviation value is extremely high (actually equal to the other curve), but when we use relative, it gives us an appropriate low ratio (generally to keep the value under 1).

 

Not to confuse the discussion, Imageware uses a different equation to compute the relative curvature deviation.

Relative Curvature = Absolute Curvature / Max (k1, k2). (Note all numbers are again absolute values.) This always gives us a relative curvature deviation less than 1.

 

This is right out of the UG help menu;

G2 = Curvature Deviation, measured as the difference divided by the average. 

Example:

Radius 1 = 5.0

Radius 2 = 3.0

Radius 1 - Radius 2 = 2 (Difference)

(Radius 1 + Radius 2) / 2 = 4 (Average)

Difference / Average = .5 curvature

This is how NX match edge measures curvature.

Hope this helps.

 

 

More info:

The Surface Continuity Analysis Operator (SCAO) and the Match Edge continuity checker use the same methods.

 

It is obvious how G0 and G1 are calculated. For G2, we use "Relative" values. What we mean is that the G2 value is equal to the difference in curvature for the selected edges divided by the maximum curvature value of the edges. This way, we always make sure that G2 is within 1 or 100%. G2 is essentially a percentage value.

 

G2 = mod( mod(Edge1)-mod(Edge2) ) / max( mod(Edge1),mod(Edge2) )

 

The above is used for SCAO and Match Edge Operator. I do not use the other analysis tools to check continuity and do not know what method they use!!

 

We use relative curvature since we make parts of various sizes. While working on a hood we may use larger absolute curvature values while working on an instrument panel we use smaller absolute curvature values. If the same user is designing both, how would he know which curvature is acceptable. Hence many car companies use the relative curvature like say 25%. Some European car companies use as less as 2%.

 

More info

Subject:  G2 Formula Tested and Proven Match EDGE

This one is really simple,

If you don’t use relative error then you end up with model size dependant tolerances for curvature.

Example.

User models a radio button 12mm diameter, needs curvature continuous blend on part of the feature – the actual difference in curvature might be in the order of mm, but still look bad.

Second user is working on a roof panel, part is 1500mm long , radius values are in the region of 40M (max stamping limit), hence acceptable differences would in the 100’s of mm range if not in the meters range.

If the same guy does both jobs above it gets even worse, you have no idea what numbers are good bad or otherwise.

So, we use relative difference.

Most Studios use a 1:4 ratio as the minimum acceptable difference in curvature, 25% in other words. Many (Like Jaguar,VW,Audi) use nearer 2% as the acceptable limit – everywhere.

As you can see, once you start looking at standards and the meaning of the numbers, relative error makes far more sense.

Of course for Angle (tangency) using real numbers is fine, since we are only looking at the edge condition.

Hope this helps,

 

 

Barry Waldie

Re: G1 magnitude" (Studio Spline)?

Pioneer
Pioneer

Thank you for those details, but you did not disclose or show what the G1 magnitude (with units of inches) is.