Developable surface


hi, i’m working on this boat that will be made out of aluminum. i’ve tried loft / developable and i’ve tried the dev-srf plug-in and neither of these commands will make a very good surface for the top or bottom surfaces of this boat. so, i set my own ruling lines and used sweep 2 rail for both surfaces. they both unroll just fine. just wondering what anyone thinks about this ?

thanks, w

marisa, nu.3dm (87.4 KB)

(David Cockey) #2

The bottom is twisted. The side has some twist, but not as much. If it works okay when built then the twist is not too much. If the twist it to much there will be some distortion when built. You might try building a simple scale model to test.

Use the Curvature command to see the principal curves at various points on each surface. A true developable surface will have one principle curve as a straight line everywhere on the surface.

What was not good?


loft / developable on the bottom surface puts ruling lines from the bow all the way to the back corner and if you pick up an intersection curve with a cutting plane going square to the world across the surface in the bow area, the convex curve to the outside has most of the bend at the end of the curve toward the keel. it seams that this shape or curve should be more symmetrical. the surface that i made with sweep 2 rails and ruling lines has a nice intersection curve in the bow.

(Pascal Golay) #4

Hello - V6’s DevLoft seems to make a decent surface from these curves -I added a ruling line, maybe not the right one, in -DevLoft - dunno if that is at all what you’re after.

marisa, nu_Maybe.3dm (99.3 KB)



ok, i tried loft / developable on the bottom surface again, it really depends where you pick the rails with this surface. picking a certain way at the bow end of the rails, i got a better surface with a good shape across the surface, better ruling lines. i think i’ll go with this. thanks for your help again.



this is my suggestion. delete all section curves and sweep2 with simple sweep. chine and side board surfaces are good with just sweep2 but the bottom is tricky. dont expect the surface will be good as a result of just using a command. use commands as a tool that gives you a referance surface that you can work on them by moving the control points.

search for fairing, curvature graph, degree and point count of a curve and surface.

marisa, nu.3dm (1.6 MB)


From my experience the sections need to have some curvature, if the plates shall be developable. Don´t believe that this is buildable. In your file they are almost straight. Gaussian also indicates that there are some problems. I tried to make a surface with more evenly spread rulings. Still needs some refinements in the bow and midships. Blastered solution looks strange to me and does´nt unroll.


They look like reasonable rulings for a developable surface to me.


thanks nick.


If Ncik says it is good, it should be!

(David Cockey) #11

My solution: marisaDC01.3dm (159.6 KB)
Several of the curves needed adjustment near the ends due to twist/reverse curvature. Without the adjustment a true developable surface would be difficult or impossible.

I extended the curves as needed to enable true developable surfaces.
Calculated “exact” ruling lines based on the extended curves.
Used -DevLoft in V6 with Density=20 and used the Untwist option to adjust the surface to match the previously calculated ruling curves.


with some more tweaking I can get it completely green…

(David Cockey) #13

Your color scale is -10.12 to 10.12. The illustrations I posted above have a scale of -1.9e-06 to 1.9e06,which is less than 1 / 5 million of your scale. “Green” by itself is meaningless. Any Guassian curvature plot can be all green with a large enough scale. How large Guassian curvature is acceptable?

I prefer to use the Curvature command and scan the surface to check that one of the principal curvature “circles” is close to a straight line everywhere.


David, you are right, green is just a color and no proof of developability. That’s why I checked to see, how the Gaussuan Color looks like, when I take the rhino “auto” values, after tweaking your file. The file looks the same with the values you have. I’m mainly trying to make the rulings to fan out nicely- distance between them and angle. I still don’t like what happens close to the transom, I’ll try to get better solution, just had 10min to work on that file.
Your curvature based developability check sounds interesting, can you explain that in more detail? The question is a bit, why does Rhino calculate these values, and what are the correct values depending to units and size?


(David Cockey) #15

The direction of the rulings of a true developable surface are determined the the edge curves only, The user can decide what spacing to use, etc when displaying ruling lines but not the direction.

What don’t you like? Given the edge curves rulings will cross the transom. If the edge of the transom needs to be a straight ruling then the edge curves need to be altered.

I assume you are aware that while all developable surfaces are ruled surfaces, not all ruled surfaces are developable surfaces.

A developable surface has one principal curvature which is zero everywhere. The Curvature command calculates the magnitude and direction of the principal curvatures at a point on the surface, and displays a pair of circles which illustrate the principal curvatures. If a principal curvature is zero then the corresponding circle is a straight line.

Guassian curvature is the most common measure of how close a surface is to developable. That is probably because it is a scalar and easy to display. If one principal curvature is zero then the Guassian Curvature is zero and vice-versa. I prefer looking a principal curvature because I can see how close the surface is to having zero principal curvature in one direction.


marisa-joerg1.3dm (8.7 MB)

Have a look…
I still don´t like the side panel…

(David Cockey) #17

Looks reasonable to me. What don’t you like about the side panel?


Some areas with dense rulings…



Is it possible for me to message you off the forum ? e-mail ?


(David Cockey) #20

Use Rebuild to globally reduce number of control points, and use RemoveKnot to locally reduce number of control points. (Don’t use RemoveControlPoint because it usually changes the surface more than RemoveKnot.) Make sure to save the original surface, and compare the surfaces to see how large any changes in shape are.