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control point conditions for curvature continuity

This is getting down deep into the math. I know that you can make a spline (or surface) tangent to another by making the first control points line up. At SEU2014 we used this trick to make a spline that would be mirrored vertically tangent by constraining the first control point horizontal. What would you do with the control points if you wanted to make the curves curvature continuous (or better)?

 

I've looked on the web but I can't find a reference that describes continuity in terms of control points.

Using the simple example of the spline to be mirrored where do the second and third control points need to be constrained.

6 REPLIES

Re: control point conditions for curvature continuity

if this is a mirrored spline, you should NOT try to make it curvature continuous as it will be curvature continuous by definition (the curvatures are by definition the same at points just to the left and right of the connect point, because it is a mirror).
Dan Staples
Director, Solid Edge Product Development

Re: control point conditions for curvature continuity

So those conditions would give you a mirrored spline that was C2 continuous. Does that mean that if the curve is above 4th order it will also be C3 continuous?

 

 

Re: control point conditions for curvature continuity

it doesn't matter what order it is. It will be C3 continuous by definition. The curve on the left and right are identical, so the rate of curvature change on each is identical.

Dan Staples
Director, Solid Edge Product Development

Re: control point conditions for curvature continuity

If I make the example more complicated and instead of a mirror it is a different spline could brute force constrain the control points so that there was C2 or C3 continuity?

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Accepted by topic author HS
‎08-26-2015 04:32 AM

Re: control point conditions for curvature continuity

You can get C2 without mucking with control points. If its 2 3D curves, just click on the little handle that pops up for end conditions of the curve and set it to Curvature Continuous (C2). If its in 2D sketch, a similar thing, but use the Tangent Constraint and then choose the curvature continuous option on its drop down in command bar. 

 

It would be highly unusual to require C3. What application are you working that could possibly require this?

Dan Staples
Director, Solid Edge Product Development

Re: control point conditions for curvature continuity

I got curious if it was possible after learning you could constrain control points. C3 is one of the things that Alias uses to show that thet are better and I wondered how close we could get with Solid Edge. I have done some chrome auto accessories that could have benifited from it.

 

Thank you Dan