if a piece of flat card say 2" x 12" is placed on edge on a flat surface and curved so it's extreme limits touch two points say 11" apart, then tilt the card a few degrees, either the ends lift from the base or, the center lifts from the base. To shape a piece of card so it sits flat along the base yet is tilted inwards or outwards a given number of degrees requires a rectangle having three straight edges and the other edge curved. Can anyone show me a mathematical method of developing such a shape? One use of such a formulae is to construct the sides of a small boat which has an eliptical plan top and bottom, a flat bottom and sheered sides. (Although the sheered sides would need a shape having top and bottom edges curved) Help will be much appreciated.

the method you request involves the use of very complex 3d geometry. Basically you need the equation of the curved surface (an elliptic cyilinder) tilted by some degree and then intersect it with the formula of a plane (let's suppose a cartesian plane with coordinates x and y, in which case the equation of the plane in 3d coordinates is z=0) and with another plane parallel to the previous (let's say 2" above, in which case the equation of the plane is z=2). Putting the equation in a system you can solve it by finding the trace of the cylinder on the plane, or vice versa, find the trace of the plane on the surface. At this point there is the further difficulty to trnsform this equation in another equation relative to a flat surface. Written in this way may seem easy, but it's not as this method requires medium-high to high knowledge of mathematics. Why not using a 3D software to draw your shape? It's faster, more accurate and gives less headache.:grin:

WOW! Now that was an answer! I didn't understand any of it, so I'll just wait for the model to come out and leave the math to you experts. :-D

Card Shapes thanks to "hpept; Kevin G & wunwinglow for your replies. To hpept I would comment: like KG, the complexities of your solution baffle me. However, I must argue that a simpler solution is probably available. I already have a means of developing a card shape which when complete, produces the shape of an inward leaning ship's bulwark, which is similar to that of a outward leaning side. It is quite simple to do needing triangulation and a compass point.My problem is I am unable to adapt the method to a ship's side and I think one or two extra moves are missing from my repertoire! To "wunwinglow I can only say I can not afford to buy software for this purpose. I shall keep trying!

If you want a practical solution, make a set of frames and glue them together to give you some reference points, the tack-glue an oversize piece of paper in place. Carefully mark the frame ends on the paper, peel it off and 'join the dots' using a pencil and some 'French Curve' drawing guides. You can get those flexible ruling tools as well, although mine always ended up with little kinks in it. Flatten the paper and scan the result into your drawing/painting software, clean up the line, reprint and test assemble. You might need to go round this loop a couple more times to refine the shape, but you will be pretty close! Tim P

wjt (or whatever) Fear not. hepatitis doesn't seem to fully understand the explanation either and dumbcluck ... err .... wunwinglow has his rhino provided free by his employer and probably wouldn't be allowed to afford his own copy ....:grin: Whilst you may not yet have mastered the full range of development drawing techniques they really aren't too many or too complex, just tedious. See the following link for suggestions on how to improve your mastery. http://www.cardmodels.net/forum/showthread.php?p=25386#post25386 Meanwhile for no cost and short learning curve you may find it useful to follow this link http://www.cardmodels.net/forum/showthread.php?t=2596&highlight=hulls They sort of deal in the sort of ideas you've sort of been thinking about and are sort of really easy to use. BTW welcome. Cheers Maurice

Actually, Roberto HAS a good handle on the math involved--it's just not something that can be tossed out in a paragraph or two. I wa a math major until I discovered molecular biology, and the math to calculate such a curve is daunting. Then there's the problem of transfering the calculated curve into a drawing program. Use the method model ship builders use to shape the planks for their models. It involves measuring--tranfering the measurements and a bit of trial and error. There's no "EASY BUTTON" in the real world.

Rob Perhaps I was a bit unfair there but spouting off about the convolutions needed in algebraic geometry wasn't really the way to go with greeting a newbie and the explanation was hardly well presented even given the space limitations. Whilst algebraic geometry has little practical application the graphical methods of technical drawing, including development drawing, are a vital use of mathematics in the real world and with knowledgeable application can eliminate the need for both calculation and trial and error. As I've said before I wouldn't want any potential designer to think otherwise. And no it's not an easy button so I would prefer if you did not attempt to imply that I was presenting it as such. (BTW In your time as a math major did anyone suggest you learn technical drawing? (No need for an answer I know what it is :grin) (BTBTW I studied maths to the point where the text book suggested that anyone who could not wonder at the marvels of an abelian group should reconsider their relationship wiith maths ... I did.:twisted Cheers Maurice Edit Or was that marvel at the wonders ... ? I've never quite been able to remember which.

First of all thank you Rob for defending me. Second, i would like to excuse with wjt: really i didn't want to discourage or confuse your mind with abstruse explanations. Third, Maurice... i don't know which problem you have. What is hepatitis? if you are referring to my nick, it's hpept, and i'm sure you don't even know what it means. It's an acronym for High Power Electric Propulsion System, a project on which i worked for five years, so please don't freely interpretate. About your complaints on the explanation i gave, the only thing i can agree with you is that it was not completely clear because i wrote it in a hurry, but I just wanted to stress that, as wjt requested "a mathematical method", this is was not really the way to go to obtain the desired shape. An analytical development is far too complex and graphical or trial and error methods work best.

Boy I tell you what........... I guess somebody (Maurice) has not had a good new years. Critisism is welcome so long as it is contructive.......not destructive. Name calling and a general superior attitude is un-necessary. Maurice, re-read your post and see if you would like what was said and imagine how you would feel if it was pointed at you. I haven't contributed to this thread, and at risk of being mauled I could not set back and just watch. This is a friendly site and people should feel comfortable contributing without un-necassarly cruel barbs being tossed about. Maurice I hope you have a better new year. And thanks for the threads I liked the Hull software and the pictures of the boats people have built. john

John And in turn I suggest that if you re-read wjt's first and second posts you will see that the initial responses in no way met his needs. The superscilious aspects of those responses simply *issed me off because like you I prefer this to be a helpful place. The first paragraph of my post was totally unnecessary and I apologise for over reacting. Maurice Edit Obviously I need to restrict that apology to only one of the offended parties. The other would apparently prefer to feel free to carry on about it in perpetuity across the entire forum.

hull sides metsequoia is a free download try that, there is a lot of info on using it on this site. Do it quick though there are rumours the guy who wrote is about to downgrade the freebie.

www.wings3d.com Dumbcluck (just remembered this; amazing, for someone so stupid, a memory that occasionally works....)

http://www.milkshape3d.com/ I've been Milkshaping for 6 years with no regrets. (Excellent texture mapper included!)