Cubic splines lack of accuracy.

[kiwi]

From Mathwold "A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points."

Draw a 3 sided polygon, duplicate and you'll see that if you change the second vertex to a cubic vertex (or smooth cubic) the graphical representation doesn't mach the mathematical description... the curve doesn't pass trough the cubic bezier (zoom in).

Now draw the line between the first and the third vertex, and another one from the middle of this last one to the second vertex. On the IP multiply the last line length by two and place a locus at the new end point. Now draw a polyline using our locus as bezier point and the precedent start and end points... on this case the cubic representation is close correct.

I say "close to correct" because on a earlier post (on the vectorscript forum) I notice that in VW the bezier splines representation doesn't follow perfectly the De Casteljau's algorithm (only for parameters 2^x).

I may add that the split tool doesn't show regular result's when working on polylines. You can find points where the tool doesn't work properly, and the results vary with the selected mode.

I found this one splitting a couple of hundreds of plolylines... he seem that time to time I hit on the wrong spot forcing me to complex maneuvers to get the job done.

So far, even if annoying, this facts where not a real problem. But the cubic representation lack of accuracy is not acceptable... is way of range, and it becomes difficult to mach objects form a graphical point of view.

[Andrew Bell@NV]

I believe you're misreading Mathworld.

By the Mathworld definition, it's the polynomials that pass through the control points, not the spline itself. Otherwise, it would be "which passes" (singular), not "which pass." (plural)

[kiwi]

English is not my native language, and I hardly manage to badly express myself... I can only accept your explanation, and agree about the polynomials passing though the control points.

But this means that the spline doesn't follow the polynomials? this only confuses me, since the polynomials are the spline definition... a bit like if an arc is defined by a center and radius, but the arc drawing end up with a different curvature. As a graphical definition, any cubic spline point should respect the polynomial definitions, and if the control point respect the definitions it should be part of the spline.

I do agree there will always be some delta factor, but on this case he seem disproportionate, and he raises the uncertainty when verifying the accuracy of some algorithms I'm developing in VS aiming to emulate cubic splines.

I'll run cubic splines on Mathlab and other CAD software to see how they behave... It may should have been the first step on my understanding, but again I'm just learning and seeking answers on my dealing with polylines.

[MullinRJ]

Hi Kiwi,

I have done a lot with modeling Polylines using the parameters available in VS to recreate the curves. My downfall has been VW implementation of the cubic spline. Beziers and Arc control points are no problem, and CubicSpline control points surrounded by CornerPoints are also managable. However, I have trouble when there are a string of CubicSpline points in a row. I have requested technotes on the implementation of the various control points for Polylines from NNA in the appropriate techboard section, but never heard anything from them.

I would be happy to compare notes with you. If you'd like to contact me, I can be reached at mullinrj at aol.com

What you have pointed out is very interesting and

I would also like to compare it to a math model in another environment.

All the best,

Raymond

[michaelcobb]

I have had trouble when there are numerous CubicSpline points in a row too. If there is another point following these points that is not very "colinear" witht the others the cubic spline curve inevitably produces an anomalous bump at this transition. Its too bad. If there were control points like in illustrator this could be a useful tool but every time I have tried to produce a "prettier" curve with this polyline with anything more than a two or three point curve it it has summarily not done the job. Its a pity because this is the only curve that has the potential to produce a good looking site section line that ALSO has the accuracy for passing exactly through the control points pulled from the topo lines. If memory serves illustrator basically has two tangent vectors off of a control point (or is it called and anchor point). The magnitude and direction of these vectors is how one controls the shape of the curve. Any possiblity of there being something like this. For those of us still drawing our elevations and section this could be a VERY useful time-honored (dare I say this term in the brave new world of software developement?) tool. Any chance of seeing this in the future?

[dunsterville]

This is a very interesting discussion. As a pretty new user, I'm very open for trying to come up with a variety of approaches to get what I want to see regardless of what is optimal. 'anchor points' would be a simple standard to adjust what in other programs is known as 'tensions'.

The biggest trouble for me is when I make an 'offset' that has to be altered with all those extra points ? offsetting a cubic spline especially so.

[michaelcobb]

Yes! Tensions! That would be a great feature on the cubic spline tool. Is this possible or does this somehow violate the definition of a cubic spline. The bottom line is this: Is there a polyline curve that could have anchor points that the curve passes through AND at the same time have adjustable tensions on that curve.

BTW, I am STOKED you guys now have arrowheads on your polylines. NICE WORK!!!!!!!

[dunsterville]

Yep, its those little things that make it a pleasure use VW!

The sort of functions you look for are known as 'bezier' in other programmes: Illustrator, Eovia Amapi, and Maxon Cinema use beziers in the way you'd like ? but these work very differently in VW, not sure why.

[axhake]

Not sure if this will be of any use to anyone but I have been drawing up a viaduct structure where a control line was provided from another design team using Microstation. The control line is from a railway lower rail level so any calculations, setting out etc need to be accurate. The design string is made up of vertical and horizontal curves with two transitions. After spending several days trying to create the viaduct which the building surrounds to form a station building I found several problems with the way Vectorworks manages polylines/qubic spline curves.

To demonstrate the problem a simple model was created in Vectorworks and as a comparison to see how other CAD software manages spline curves I also created the same model in (Microstation, ProgeCAD, ArchiCAD) to compare the results which can be seen in the attached PDF in the native application and also when exchanged/referenced into the other CAD software.

All but Vectorworks managed to create  spline curves that pass through the control points, Vectorworks came close but not through the points which explains the problems I was having.

making collaboration with others a problem.

Vectorworks_Notes.pdf

Edited June 23, 2017 by axhake

[Kevin McAllister]

4 hours ago, axhake said:

Not sure if this will be of any use to anyone but I have been drawing up a viaduct structure where a control line was provided from another design team using Microstation. The control line is from a railway lower rail level so any calculations, setting out etc need to be accurate. The design string is made up of vertical and horizontal curves with two transitions. After spending several days trying to create the viaduct which the building surrounds to form a station building I found several problems with the way Vectorworks manages polylines/qubic spline curves.

To demonstrate the problem a simple model was created in Vectorworks and as a comparison to see how other CAD software manages spline curves I also created the same model in (Microstation, ProgeCAD, ArchiCAD) to compare the results which can be seen in the attached PDF in the native application and also when exchanged/referenced into the other CAD software.

All but Vectorworks managed to create  spline curves that pass through the control points, Vectorworks came close but not through the points which explains the problems I was having.

making collaboration with others a problem.

Vectorworks_Notes.pdf

That's a great comparison. Personally I would file this as a bug.

Kevin

[axhake]

It's been with UK Vectorworks support for a couple of weeks now, I'm awaiting a reply, will update this post when I receive a reply.

Alan

 

[axhake]

Still no reply from VW UK, I have just submitted this as a BUG.