topic Re: spline length in AutoCAD Forum

spline length

Anonymous — Sat, 15 Sep 2018 22:37:48 GMT

How can i find the Spline length by means of its control points manually? (I do not mean AREA command, I want to calculate it by its control points manually)

In fact how AUTODESK calculate it?

Re: spline length

Kent1Cooper — Sat, 15 Sep 2018 23:21:22 GMT

The only thing you'd be able to calculate manually from control points [or fit points] would be the sum of the straight-line distances between them, which of course is not the length of the Spline. I couldn't say how AutoCAD does it, but I don't think there's anything you could use from ordinarily-available information like entity data. [May I ask why you want to do this?]

Re: spline length

Anonymous — Sun, 16 Sep 2018 11:22:25 GMT

There is a formula as follows: (https://en.wikipedia.org/wiki/B%C3%A9zier_curve)

This formula and Autocad return same value for 4 control point but for higher control point we have some mistake

Re: spline length

SEANT61 — Sun, 16 Sep 2018 13:00:00 GMT

AutoCAD uses a Degree 3 spline as default. If there are only 4 Control points then the spline is equivalent to a Bezier curve. CPs more than four either need an elevated order (Degree 4, 5, . . . ) to evaluate correctly with that formula, or you have to treat them as B-Splines and/or NURBS.

https://en.wikipedia.org/wiki/B-spline

Re: spline length

leeminardi — Sun, 16 Sep 2018 22:38:38 GMT

The default order for splines of more than 4 CVs is 3. You can modify the order and the weights at CVs of a spline with the SPLINEDIT command. You can also use SPLINEDIT to find the approximate length by converting the spline to a polyline (SPLINEDIT P ) and specify the precision. Use LIST to find the length of the resulting polyline. Experiment with the precision value to determine its sensitivity.

Re: spline length

SEANT61 — Mon, 17 Sep 2018 00:24:26 GMT

@leeminardi wrote:
The default order for splines of more than 4 CVs is 3. . . . .

$Did you actually mean "the default order for splines of 4 or more CVs is 4"? Which is to say "Degree 3", in that Degree is Order - 1.$

Re: spline length

leeminardi — Mon, 17 Sep 2018 00:36:10 GMT

Yes, I meant to say degree equals three. Thanks for noticing my misstatement.

Re: spline length

Anonymous — Mon, 17 Sep 2018 01:01:50 GMT

Thanks friends but i cant calculate it by bezier or B-Spline formula

A simple example is given control poni P0=1,1 P1=2,0 P3=3,1 P4+4,0 and P5=5,1 Can you calculate y parameter in X=2?

Re: spline length

Corsten.Au — Mon, 17 Sep 2018 04:05:43 GMT

This would be a complete different approach..

but if CAD is imported in REVIT software ( Autodesk ),

Revit gives the length of the Spline directly...

Spline Length

Re: spline length

SEANT61 — Mon, 17 Sep 2018 08:13:53 GMT

@Anonymous wrote:
Thanks friends but i cant calculate it by bezier or B-Spline formula
A simple example is given control poni P0=1,1 P1=2,0 P3=3,1 P4+4,0 and P5=5,1 Can you calculate y parameter in X=2?

This may be a misread on my part; this example isn't looking for the length of anything, just needs the y coordinate of a given X.

In the attached drawing I have a setup to find the point graphically. In the attached spreadsheet, I solve for the point parametrically - with a calculated parameter t=0.25

Re: spline length

Kent1Cooper — Mon, 17 Sep 2018 14:19:14 GMT

@Corsten.Au wrote:

.... if CAD is imported in REVIT software ( Autodesk ), Revit gives the length of the Spline directly...

If all they needed was to get the length of an already-drawn Spline, there's certainly no need to go through importing it into Revit! Either the LIST or AREA command will report it, and put the value in the PERIMETER System Variable for use in any processing or calculation desired. Or it can be extracted with AutoLisp:
(vlax-curve-getDistAtParam spl (vlax-curve-getEndParam spl))

where 'spl' is either the Spline's entity name or a VLA-object conversion of that.

But they don't want to do it that way [re-read Message 1].

Re: spline length

Kent1Cooper — Mon, 17 Sep 2018 14:27:26 GMT

@Anonymous wrote:

... A simple example is given control poni P0=1,1 P1=2,0 P3=3,1 P4+4,0 and P5=5,1 Can you calculate y parameter in X=2?

So maybe that's something of an answer to my question in Message 2 [at least it's some kind of reason for wanting to calculate something based on control points], except that it has nothing to do with the Subject line or the original question in Message 1, both being about length, which seems irrelevant to this example. Though the Bezier-curve formulas are beyond my mathematical experience, I'd still be interested in the "why" of it all....

Re: spline length

leeminardi — Mon, 17 Sep 2018 15:29:54 GMT

@SEANT61 I created a spline using the CV method with the specified control points and got the green curve as opposed to your magenta curve. The magenta curve is a 4th degree (5th order) Bezier spline whereas I believe the green curve is a 3rd degree B-Spline. Yes?

I've looked at the B-spline math and I find it a bit tough to follow. Since a B-spline allows local editing, can I assume only the first 4 CVs influence the shape of the spline near the beginning? At what point must the 5th CV be considered?

Re: spline length

SEANT61 — Mon, 17 Sep 2018 23:24:17 GMT

@leeminardi wrote:
@SEANT61 I created a spline using the CV method with the specified control points and got the green curve as opposed to your magenta curve. The magenta curve is a 4th degree (5th order) Bezier spline whereas I believe the green curve is a 3rd degree B-Spline. Yes?

I've looked at the B-spline math and I find it a bit tough to follow. Since a B-spline allows local editing, can I assume only the first 4 CVs influence the shape of the spline near the beginning? At what point must the 5th CV be considered?

Yes, I believe you are referring to a B-spline. Is it the same as the green spline I have in the attached? And, yes again, everything after Beziers becomes increasingly more complex. Not something I ready to set up in an XLS, anyway.

The local editing you mentioned was the motivation for B-splines, and I believe your notion of where/when CVs are evaluated is correct. There is not much visual evidence when the evaluation rules switch from one group of CVs to the next. AutoCAD will show us the point on the curve if the 3d Osnap Knot is enabled.

The process becomes even more chaotic when non uniform domains, full multiplicities, rationality are injected. Just with a slight domain modification see how the blue spline differs from the green.

Fortunately, the average programmer does not have to re-invent the 'nurbs evaluation' wheel. AutoCAD, at least, has the functionality baked into the API. If someone did want to roll their own, though, I would applaud the effort.

Re: spline length

SEANT61 — Tue, 18 Sep 2018 09:13:41 GMT

@leeminardi wrote:
. . . . At what point must the 5th CV be considered?

The way the splines are evaluated is by stepping through the parametric Range, t, a small increase at a time. The incremental t value is plugged into the equations which spit out an xyz value. Much like the spreadsheet setup I posted earlier, at any given t the influence of each of the 4 CVs (in this case) varies.

The Range, though, is split into different zones with Knots at the border. When a Knot value in reached, the influence of the earliest CV of the 4 goes to zero, and no longer play a part, and the next CV (4th from the CV just removed) in line starts to contribute to the equation. Minimally at first, but increasing as the t values progress.

See the attached drawing and chart. This 8 CV AutoCAD spline has a Knot Vector (Nurbs term) as shown in the diagram. The Points in the drawing correspond to the Knot values shown in that grouping. The term Full Multiplicity refers to when a value is repeated Degree number of times. That indicates to the algorithm to uses the corresponding CV for %100 of the influence. It is why the AutoCAD curve lands directly on the start and end CV. As t increases from 0, the next 3 CVs start contributing to the equation. Notice how the curves on the chart start rising from the initial 0 influence state.

At any point along that horizontal (X) of the Chart, a vertical line will intersect several curves, all of the Y values will total 1.0 (%100) . Notice, also, that at each knot value, one curve ends while another starts.

Re: spline length

Anonymous — Fri, 21 Sep 2018 18:43:20 GMT

in fact i need the equation of the spline, i request the y factor in x=2 to check the equation

Re: spline length

leeminardi — Fri, 21 Sep 2018 19:47:21 GMT

As noted in post #3 by @SEANT61, if you created a spline with 5 control points the AutoCAD default would be a 3rd degree (4th order) B-spline. For the points you specified in post #8 the spline should look like the green curve in the image below. The equation for a B-spline can be found in the link of post #4. Check it out if you have not yet done so. The math is more complex than a Bezier spline encouraging the use of recursion (deBoors algorithm) to calculate points on the spline.

You asked for the value of y when x = 2 (in Euclidean and not parametric space I assume). Set luprec to 8 and then add a point at the intersection of the line and the original spline using object snap int (intersection). The B-spline will be accurately evaluated. You should find that the coordinates of the point are: x = 2.00000000, y = 0.39061808.

As I noted in post #5 the splinedit command can be used to convert a spline to a polyline. This will give you a series of points along the spline.

Re: spline length

Anonymous — Tue, 25 Sep 2018 01:46:47 GMT

Thank you and other friends, all of the those formula seem true but when i want to use them the answer and Autocad are not equal.

Do you calculated y=0.39061808 by means of those formula or bring that from Autocad?

Re: spline length

SEANT61 — Wed, 26 Sep 2018 12:00:08 GMT

Here’s a crude setup to investigate the ins and outs of a uniform, degree 3 B-Splines. This spreadsheet works with the general setup shown in post# 8. It allows variable point locations (though the point count must remain at 5), as well variations in the target “X” value.

I’ve used a Lookup table to convert that target X to the appropriate parameter value; consequently, the tolerance is quite coarse.

Re: spline length

leeminardi — Thu, 27 Sep 2018 01:54:48 GMT

@sean61 congrats on getting something that works! I've been trying to write a custom VBA function for the deBoor algorithm that uses recursion to calculate the coefficients. I gave up on that and decided to limit the B-spline to degree 3 which enables a simpler computation from the appropriate 4 CVs and then successive sub control polygons. My subscripts are all screwed up so I put it aside while I tend to more pressing matters. I may give it another shot in the future.

Lee