3 Replies Latest reply on Apr 5, 2010 6:52 AM by Kieran Choy

# View -> Display -> Curvature

I was wondering what the curvature mode shows you precisely, in the help file it is somewhat explained:

"You can display a part or assembly with the surfaces rendered in different  colors according to the local radius of curvature. Curvature is defined as the  reciprocal of the radius (1/radius), in current model units. By default, the  greatest curvature value displayed is 1.0000, and the smallest value is  0.0010."

Some other programs use different terms, and have a few different modes of showing curvature with colours.

"Alias help file:

• Mean –  Average the two principal curvatures at each point  on the surface.
• Gaussian –  Multiply the two principal curvatures at each point  on the surface.
• Principal Min/Principal Max –  Use the minimum or  maximum curvature values (that is, the curvature of the steepest or flattest curves that pass through each point).

Mean or Gaussian curvature is most useful for detecting surface  irregularities.

Principal Min or Max curvature is most useful for detecting inflection points."

Now...which of all these terms relates closest to what Solidworks is using?

and what do these all even really mean?

• ###### Re: View -> Display -> Curvature

I am impressed the Help file said that much.

I have asked questions before about exactly how accurate SW curvature combs are and how it relates to the real world - ie how much to worry about the apparent waviness and the scaling...of course you never get an answer to things like this...but you can ponder it again as you read about it in some other application Help and it sets you wondering about the bits that are carefully guarded secrets in SW rather than open user knowledge...

At one time - now years ago- we were relatively happy IDers naively making simple wishes for finer control over splines and even daring to propose auto smoothing routines for combs etc etc. If I remember Think3 picked up on that idea...

Then there was a divine moment in the UI redesign department when the CAD world changed as they decided everyone should forget about technical ambitions and that curvature would be henceforth displayed by the relative curliness of hairy caterpillars. Apparently the existing curvature outline had suddenly become too inaccurate and boring to use.

I cant remember what the details of the last forum discussion about curvature display were about now... perhaps it was relative curvature where 2 surfaces meet..I seem to remember doing an illustration for an idea for it or something.

Anyway it turned out to be another one of those contributions we make in good faith only to be beaten down in the marketing priorities by the shininess of mouse gestures...

It would be nice to think that SW might eventually tackle such things as this and offer more display options but I fear they are about number 4832 on the list of enhancements. ie 19 releases away and all the original proposers will have long turned to dust....

• ###### Re: View -> Display -> Curvature

Really nice question, Kevin. Maybe we can get someone from SW to answer it. Patrick Rainsberry, Southwest Technical Manager, gave a presentation at SWW2010 on the math behind parametric geometry. I downloaded the presentation and he has one slide about Surface Curvature, but he didn't go into any detail at all, presumably because "the mathematics are quite complex and require significant derivation".

It seems like it would be relatively easy to make an ellipsoid and check to see how the given radius of curvature compares to what geometry tells us, but I don't seem to be able to get the ROC to show up when I try it.

Jerry Steiger

• ###### Re: View -> Display -> Curvature

My understanding of the Display Curvature tool is that it shows the radius of curvature at a given point, in a similar way that Spline Tools >> Show Min Curvature displays the minimum radius of curvature for 2D splines.

Radius of Curvature is the largest circle you can draw at a given point that is tangent to that point and meets it most smoothly (ie "kisses" it best). See http://en.wikipedia.org/wiki/Osculating_circle

In the above image, I created a cigar shape by revolving a semi-ellipse 50mm x 200mm. Curvature at the point is 0.0489614. The Radius of Curvature is 20.4243mm

1/20.4243 is 0.0489614 and vice versa. Curvature here is an indication of how tight a surface is - so if the Radius of Curvature is large, Rate of Curvature is low, until you get a straight line with an infinitely large radius of curvature and 0 rate of curvaturel. Likewise as Radius of Curvature becomes tighter, Rate of Curvature increases until the Radius reaches (very close to) 0, and Rate = 1.

Interestingly, it seems that Display Curvature shows the minimum curvature at a given point, or maybe just the minium of either the U or V direcion at a given point (needs further investigation). If I hover my mouse close to the center of the cigar, the Radius of Curvature approaches 25mm (the minor axis is 50mm).

The cool thing is that Display Curvature will actually display the curvature of the sketch segment if I hover over it. At the middle of the ellipse Radius approaches 400mm, at the end it is 6.25mm, which agrees with Spline Tools Minimum Rad of Curvature. So if you are looking to work out the Radius of Curvature in an arbitrart given direction, try either using Face Curves, Spline on Surface or an Intersection Curve.

What Display Curvature does give you is a way to locate areas that may be causing problems Shelling or Offsetting. For complex surfaces it is best to only try Offsetting (slightly less than) the distance of the minimum radius of a surface. Here it would make sense if the colour scale was not absolute (0 to1) but relative to the max and min of the surfaces shown. Alternatively a tool that simply highlights areas that are below or above a certain Radius of Curvature would be useful, since you could then just enter the distance you wish to Offset a surface and see if there are any problem areas.

Kevin, in regards to Mean, Gaussian and Min/Max Principal, my guess would be that currently SolidWorks is only showing Minimum Principal. I assume Principal here refers to the U and V directions. Perhaps a macro that uses Face Curves could give you Mean and Gaussian values?

Neil, you are referring to Deviation Analysis, which identifies the amount of angular deviation from tangency at a given edge between two surfaces.