Skip to main content
J
john_clark5-Regular Member
5-Regular Member
September 20, 2024
Question

Curvature of a surface MCAD 15 M050

  • September 20, 2024
  • 4 replies
  • 2559 views

This sheet first plots a series of x,y,z data points for a floor elevation survey. surface is plotted as raw data

 

Then it does a surface regression analysis and generates a polynomial the poly surface is plotted.

 

I need to determine the curvature and then radius of curvature for any and all points.  I will use an overlay of distress to determine the radius of curvature that causes distress, I currently have a slice method of raw date and of the surface  but this is cumbersome. 

 

A math prof colleague provided a solution  that runs OK on his old version  of Maple.

I'm attempting to get this solution using MCAD 15 but getting errors.  I think it may be  a simple deal but don't know. 

 

Can anyone help?

 

I've placed a number of markers in this sheet in Bold large font red text.. 

 

Solution  starts on page 9.  There's  hand written solution  at top right of page 1 and repeated lower.

 

BTW this is a problem I've been work on for a number of years trying various strategies.  I think this is the best one.

 

Thanks in advance of any help or suggestions

 

jmc

 

 

 

 

 

 

 

 

4 replies

S
StuartBruff23-Emerald V
23-Emerald V
September 20, 2024

Hi, John.

 

I've just had a quick skim through your worksheet.  Wow, that's a lot of work, and it would take me a long time to get to grips with it.

 

However, I think I might have spotted the cause of your unexpected nested vector of 49x1 vectors:

 

2024 09 20 D.png

 

Vectorization only applies to the vectors it sees in the variables/explicity defined matrices.  It does not apply to the results of an expression that uses those vectorized variables.  Hence, the behaviour you see in the clip above.

 

Stuart

 

PS.  Edited to add that I used Mathcad Prime 10 to view your M15 worksheet.

 

J
john_clark5-Regular MemberAuthor
5-Regular Member
September 22, 2024
Here’s a prime 11 copy that works. I tried to recreate it to of no avail.

The key is correctly calculating the unit vector. n

Can you help with this?

My math prof colleague provided hand written text which I attempted but there’s still something correct

On Sep 22, 2024, at 9:09 AM, John Clark <jc@clark-engineers.com> wrote:

Thanks for your response.

I found some errors since posting. But it’s still not working.

See pdf below.

I’ll also send mcad ts response with comments.

W
Werner_E25-Diamond I
25-Diamond I
September 20, 2024

Are you sure that L.xx(1,2) should be a vector but g.xy(1,2) is just  a scalar?

I guess L.xx(1,2) should be a scalar, too. Otherwise it would be wrong to call an expression which contains L.xx using vectorization.

Werner_E_0-1726860181887.png

Its a good idea to test functions which expect scalar arguments if the result is as expected before you call them vectorized with vector arguments.

 

According the cross product I am a little bit confused what it should denote. As far as I know a cross product of two vectors is only defined for 3 and for 7 dimensions!

 

J
john_clark5-Regular MemberAuthor
5-Regular Member
September 22, 2024

Thanks for all the help

 

I found some errors and I responded to emails and am replying here.

 

My latest edits are in the attached file along with my questions. 

 

The issue is computing the unit vector n correctly.

I've included a section  of the  derivation from my math colleague. 

 

I made an attempt but its still incorrect.

 

Thanks in advance for any help

 

jmc

 

 

 

 

 

 

 

W
Werner_E25-Diamond I
25-Diamond I
September 22, 2024

Can't comment on the vector n

You promised a working Prime 11 worksheet which you did not attach - guess you meant Mathcad 11 as Prime 11 does not yet exist in public use 😉

And if its a Mathcad 11 sheet, you should be able to open it in Mathcad 15 (or 14) and use it !?

 

Just a comment on the polynomial fit of your data. I don't understand why the data is rounded down to 0 decimals before doing the polynomial fit.

Furthermore the coefficients for the polynomial fit could also be calculated by using polyfitc, the function defined via polyfit.

There seems to be no need for the spline interpolation.

But then, I have not looked in full detail in your sheet, so I may be wrong, indeed.

Werner_E_0-1727021708477.png

 

J
john_clark5-Regular MemberAuthor
5-Regular Member
September 22, 2024
Apologies for the confusion

Mcad ts supplier an off done in 11. I was I was surprised as well.

I’ll post the pdf.

Still looking for resolution of unit vector n


jmc
A
anursinghCommunity Manager
Community Moderator
October 7, 2024

Hi @john_clark,

 

I wanted to see if you got the help you needed.

If so, please mark the appropriate reply as the Accepted Solution. It will help other members who may have the same question.
Please note that industry experts also review the replies and may eventually accept one of them as solution on your behalf.
Of course, if you have more to share on your issue, please pursue the conversation. 

 

Thanks,
Anurag 

J
john_clark5-Regular MemberAuthor
5-Regular Member
October 7, 2024
Thank you

I have a solution but it appears to be an order of magnitude off on results.

Working on checks by other methods.
Terms & ConditionsAccessibility statement