Developable surface - exact ruling lines from edge curves

[sadovshikov (Vitaly Sadovshchikov)]

@davidcockey

Create a line between the pulled curve and the start point of the ruling line… One way to do this is to the Line command with the Tangent option and selecting the pulled curve as the start of the curve and the ruling line end point as the end point. Another way is to use Line with the ruling line start point as the start location and then use the Tan Osnap to find the tangent point on the pulled curve. In some situations it may not be possible to create the tangent line. Those situations will be discussed in a future post.

If there are more than one tangent line should we choose the shortest?

[davidcockey]

@sadovshikov

In some cases, the pulled curve with a cusp does have the tangent point with the start point. However, employing the tangent point evidently gives us the wrong ruling line. Should we always use the cusp tip if it is there on the pulled curve?

@sadovshikov

If there more than one tangent line should we choose the shortest?

Either choice satisfies the criteria for an individual ruling line. A reasonable choice would be the shortest line.

[sadovshikov (Vitaly Sadovshchikov)]

@davidcockey

Either choice satisfies the criteria for an individual ruling line

Hmm, but the usage of the cusp tip point looks much better

Cusp&Tangent.3dm (3.9 MB)

[sadovshikov (Vitaly Sadovshchikov)]

Hi @davidcockey! Could you provide me with some recommendations?

1. What is the best way to build a developable surface through a bunch of found exact ruling lines? Is it Sweep2, DevLoft, or perhaps something else?
2. Is the UnrollSrf tool a reliable method to unroll a developable surface without deformation, in the case when we handle a truly Developable surface?
3. The more ruling lines we utilize the closer to a real Developable our surface will be - is the assumption correct?

[davidcockey]

@sadovshikov

What is the best way to build a developable surface through a bunch of found exact ruling lines? Is it Sweep2, DevLoft, or perhaps something else?

My usual method for a developed surface from two edge curves:
Usually there will not be exact ruling lines between the ends of the curves. I look at the curves, and decide which ends need to be extended so that exact ruling lines between the curves are possible.
Start at the end of one curve and find the exact ruling line to the other curve.
If no ruling line exists to the end other curve, then either extend the other curve or start at the end of that curve.
Repeat at the other ends of the curves.
Trim the edge curves with the end ruling lines.
DevLoft for a developable surface between the extended/trimmed edge curves.
Check the surface using Curvature (not CurvatureAnalysis) to see if the curve is close enough to developable. Curvature shows the principal curvatures as circles at a point on the circle. If the surface id developable at that point one of the principal curvatures is zero and curvature circle will be a straight line. I check at multiple locations on the surface.
If the surface is not close enough to developable determine additional exact ruling lines between the curves. Use the -DevLoft version of DevLoft with the AddRuling option to add the exact ruling lines.

@sadovshikov

• Is the UnrollSrf tool a reliable method to unroll a developable surface without deformation, in the case when we handle a truly Developable surface?

I believe so but have not extensively tested.

@sadovshikov

The more ruling lines we utilize the closer to a real Developable our surface will be - is the assumption correct?

This depends on how the developable surface is created. At some point adding exact ruling lines stops improving the accuracy.

[sadovshikov (Vitaly Sadovshchikov)]

@davidcockey

I encountered a case where a ruling line obtained from a tangent point was not suitable to generate a developable surface. At first glance, the second pulled curve appears to have a cusp, but upon zooming in, it turned out that there was no authentic cusp, only a sharp bend. I would appreciate your advice how to handle the ruling line in the case.

Ruling.3dm (2.4 MB)

[davidcockey]

Snap to the cusp using the Tan Osnap. Let me know if you you still have a question.
Ruling DC.3dm (1.6 MB)

[sadovshikov (Vitaly Sadovshchikov)]

Oh, there is also a tangent point on the bend/cusp. Much obliged David!