topic Re: combine three matrixes to make 3d spline in Mathcad

combine three matrixes to make 3d spline

SK_13639906 — Mon, 06 Oct 2025 06:30:49 GMT

Hello, I'm trying to draw 3D spline go through 5 points defined by matrix "a" .

After defining matrix of x range, y and z, these three matrixes are not able to be combined by "augment" function.

Are there any way to combine these three xyz matrixes? or any other way to plot xyz?

Re: combine three matrixes to make 3d spline

terryhendicott — Mon, 06 Oct 2025 07:35:39 GMT

It is the age old problem of turning a range to a vector that Prime 11 uses the vec() function.

As this is a Prime 10 worksheet I have used a Range2Vec() function from an @StuartBruff worksheet. Thanks Stuart.

Cheers Terry

Re: combine three matrixes to make 3d spline

terryhendicott — Mon, 06 Oct 2025 09:42:08 GMT

As this forum is a learning opportunity have for Prime 10 or lower the following sheet that explains ranges and vectors:

Re: combine three matrixes to make 3d spline

Werner_E — Mon, 06 Oct 2025 09:56:21 GMT

What you did would have worked OK up to Prime 9 because an inline evaluation (the = right after the definition of the range) converted a range into a vector. As an evaluation should not change the data type, PTC decided to get rid of this undocumented trick of turning a range into a vector in Prime 10. It was not until Prime 11 that PTC provided a convenient alternative by implementing the new "vec" function.

So in Prime 10 you have to use a user-function to convert a range into a vector, as Terry had shown, or you could have created x1 as a vector right ahead.
BTW, in Terry's sheet its not necessary to use "Range2Vec" when you define y1 and z2. It does no harm but "interp" creates vectors right ahead anyway if the last argument (x1) is a vector, so its not necessary to turn the vector into a vector using "Range2Vec" 😉 .

Personally I would have chosen a different approach without defining a vector for the x-values.

You may define a function f(x) which returns a 3x1 vector with the coordinates of the corresponding interpolated point.

Now you have two option for plotting the curve.

1) define a range for x (! similar to what you did) and plot f(x)

or as I would prefer

2) use Prime's "CreateSpace" function to do the job

P.S.: I would suggest that for future questions you say which version of Prime you are using - especially if you are not using the latest. This prevents that the answers you get are with worksheets you can't open.

Prime 10 sheet attached

Re: combine three matrixes to make 3d spline

Werner_E — Mon, 06 Oct 2025 11:06:05 GMT

One additional remark: The method for a 3D interpolation of a couple of point you had chosen is limited. It only works if the x-coordinates of the points are strictly in ascending order.

A more universal approach would be to make x, y and z dependent on an (ascending) parameter t.

The choice of this parameter naturally also shapes the outcome! So you have to chose it depending on your needs.

In the pictures below you can compare the outcome if you chose the parameter as

1) the x-coordinate of the point (F, blue). this was your approach

2) a simple sequential numbering of the points (G, green)

3) the distance of the points (G2, orange); a quite common choice for the parameter

Prime 10 sheet attached

Re: combine three matrixes to make 3d spline

SK_13639906 — Tue, 07 Oct 2025 03:11:45 GMT

Thank you so much for your help!

Re: combine three matrixes to make 3d spline

SK_13639906 — Tue, 07 Oct 2025 03:14:22 GMT

I'm using Prime10. so I can open your sheet. Thank you so much!

Re: combine three matrixes to make 3d spline

Werner_E — Tue, 07 Oct 2025 09:08:07 GMT

@SK_13639906 wrote:

I'm using Prime10. so I can open your sheet. Thank you so much!

Yes, I noticed that the sheet you posted was in the format of the older Prime 10 which is the reason I posted the answers with Prime 10 sheets rather than the current Prime 11. But for future questions you are on the save side if you mention yourself which version of Prime you are using.

Re: combine three matrixes to make 3d spline

SK_13639906 — Wed, 08 Oct 2025 02:28:14 GMT

understand. I'll keep it in mind