# Gaussian curvature analysis and wall thickness analysis

#### AFROUZ.E

##### New member
Hi there

1. Could you tell me where or when this type of curvature analysis is used in designing, please?

2. The following is quoted from CATIA documentations, wall thickness analysis command. What does it mean by interpolated values? Please illustrate me how this option works.

Smooth
This option is available when On the fly is selected. It shows all values whatever your cursor position. The displayed thicknesses are interpolated values, which may lead to some inaccurate results
Thank you.

#### MrCATIA

##### Super Moderator
1. Could you tell me where or when this type of curvature analysis is used in designing, please?
Thank you.
I tried, but couldn't find the author of the following information. It was posted on another CATIA forum some time ago. I hope it answers your question. (see April 2, 2013 correction below)

"Gaussian Curvature" is more-or-less the ratios of Cmax to Cmin. (C = curvature) It is useful for judging the kind of shape the surface has. If Cmax and Cmin have the same sign (Rmax > 0 and Rmin > 0 or Rmax < 0 and Rmin < 0) the Gaussian Curvature (Cmax/Cmin) will be positive and it indicates that your surface has a bowl-like shape. If Cmax and Cmin have different signs (Rmax > 0 and Rmin < 0 or Rmax < 0 and Rmin > 0) then the Gaussian Curvature will be negative and your surface has a "saddle" shape.

(Curvature is defined as the inverse of the Radius, or C = 1/R)

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#### MrCATIA

##### Super Moderator
2. The following is quoted from CATIA documentations, wall thickness analysis command. What does it mean by interpolated values? Please illustrate me how this option works.
I think it means the thickness at the cursor position was not measured, but was calculated based on measured thicknesses in the same proximity.

(If you have ever used trig tables, you understand "interpolation" and using ratios to estimate intermediate values)

An example: If the wall thickness at Point A = 3mm, and the wall thickness at Point B (10mm from Point A) = 3.8mm, and if Point C is between Points A and Point B and 4mm from Point A, the wall thickness at Point C can be interpolated as 3.32mm

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#### AFROUZ.E

##### New member
Thanks again. Solved my problems. gaussian curvature = Cmax * Cmin.

Another question, there is another type for curvature analysis: square root gaussian curvature. What is the usefulness of this option?

#### MrCATIA

##### Super Moderator
based on Wikipedia, the previous information I posted (copied from an unknown author) may not be absolutely correct.

Wikipedia says the Gaussian Curvature is the product of the curvatures in the two principal directions of the surface. Instead of Cmax and Cmin, Cu and Cv (curvatures in u and v directions) are used to determine the surface shape.

I couldn't find anything on Square Root Gaussian Curvature, but the square root of the product would provide an average value of the two curvatures and eliminate the polarity.

My guess is this would provide another way to check the surface shape and check for variations in curvature.

Which workbench provides this option? Is there anything in the CATIA online Help?

#### AFROUZ.E

##### New member
It's possible to check the accuracy of the formula in CATIA.
1. Select a non ruled surface for gaussian curvature and at a desired location, right mouse click\keep point to create a point.
2. Once measure the minmum curvature at this point and once the maximum one. (minimum curvature and maximum curvature type)
3. You can see if gaussian curvature is Cmax * Cmin or not.

The square root gaussian curvature has a polarity yet. I've seen it in Part Design workbench of V5-6R2013 and found nothing about it in the documentation.