7 ms·
When splines were physical objects (2016)
- Animats 4y agoRailroad curves are usually splines. That was the original physical application. You need a curve that minimizes jerk as the radius changes.
- mech765 4y agoNow I'm wondering how the steel tracks get bent- I figure it's done on site rather than at the factory. Dunno what sort of equipment they use to bend them though. Maybe they can just use bigger "spline weights" and pin the bend points to scale from the drawing! Hmmmmmmmmm probably not but I want it to be true
- benj111 4y agoI would guess in a ring roller. Basically a roller on top pressing down and 2 rollers on the bottom and you wind the metal through tightening the top roller to increase the curve. Sorry to disappoint you. If it makes you feel better though, the whales used to set the curves on boats used to be real whales.
- jstanley 4y agoBut a ring roller produces curves of constant radius, and for the railway application it would have to be absolutely enormous. From a quick DuckDuckGo search, it looks like they basically are just laid out the same way the "splines" from the article are: the curves are gentle enough that the steel is not very hard to bend.
- Jarmsy 4y agoTalking of ducks, some think that the spline weight 'ducks' could be the origin of the expression 'have your ducks in a row'.
- twobitshifter 4y agohttps://www.arema.org/files/roadmasters/1995/1995_STRINGLINING-OF-RAILROAD-CURVES.pdf https://www.arema.org/files/roadmasters/1995/1995_STRINGLINI...
- danhor 4y agoRailroad tracks are pretty flexible, there's no need to bend them separately, you just put them in the sleepers and can fine tune them in there. You can see how much they bend in this video: https://www.youtube.com/watch?v=CpP6ar63Qxw https://www.youtube.com/watch?v=CpP6ar63Qxw (1:40). In this case they get delivered as 200m sections on normal rail cars, so they hava to withstand normal curves during transport.
- agumonkey 4y agobefore ships ?
- mbustamanter 4y agoInteresting, do you have a source where I can get deeper into the application of splines to reilroads? Specifically, how to arrive at the jerk minimization problem. All things railroads are too descriptive with little engineering/physics formulas.
- twobitshifter 4y agochapter 3.2 has a good explanation of it all. https://nap.nationalacademies.org/read/22800/chapter/3 https://nap.nationalacademies.org/read/22800/chapter/3
- s1mon 4y agoThere are tons of papers and research on this topic. Here's just one review of some of the various approaches that have been used. https://www.researchgate.net/publication/341476435_Railway_Transition_Curves_A_Review_of_the_State-of-the-Art_and_Future_Research https://www.researchgate.net/publication/341476435_Railway_T...
- joshu 4y agoi think - but am not sure - they use clothoid definitions to characterize jerk, as it is more restrictive regarding the maximum rate of turn change. you can make quite a sharp turn with a mathematical spline. but i can see how they would use the physical spline to solve this… Googling “railroad spline clothoid” got some intriguing hits — and this HN comment. https://news.ycombinator.com/item?id=10446154 https://news.ycombinator.com/item?id=10446154 semi-relatedly, this is a fun watch. https://youtu.be/aVwxzDHniEw https://youtu.be/aVwxzDHniEw even less relatedly, here is a drawing i did by torturing a clothoid optimizer https://www.instagram.com/p/CSe40DTp-WW/?igshid=YmMyMTA2M2Y= https://www.instagram.com/p/CSe40DTp-WW/?igshid=YmMyMTA2M2Y=
- samwillis 4y agoSee also French curves: https://en.m.wikipedia.org/wiki/French_curve https://en.m.wikipedia.org/wiki/French_curve And, more like that in the post, the "flexible curve ruler": https://www.ryman.co.uk/helix-flexi-curve-ruler https://www.ryman.co.uk/helix-flexi-curve-ruler I used both during my Industrial Design degree in the mid 00s, but never in practice after. I suspect some people still do though.
- chadcmulligan 4y agoMy dad used to have a set of French curves - he was a sign writer and used them for cutting the templates for silk screen printing, probably in the 60's or there abouts.
- Someone 4y agoThat “flexible curve ruler” seems to be called a Lesbian rule (after the island; https://en.wikipedia.org/wiki/Lesbian_rule https://en.wikipedia.org/wiki/Lesbian_rule), and can also be used to measure curve length (bend the rule so that is matches the curve to be measured, mark begin and end of the to-be measured length, straighten the rule, and use a straight ruler to measure the length between the marked points)
- quickthrower2 4y agoHe didn’t answer the question the first come to my mind: Is the curve from the physical spline a bezier?
- samwillis 4y agoYou should be able to describe (within any reasonable tolerance) the same curve with a bezier, however the control points will obviously be different. Any imperfections in the physical spline, say a knot if it's wooden, would translate to a slight curvature difference.
- quickthrower2 4y agoSounds like the physical curves are a subset of bezier? So there might be some bezier curves that cannot be replicated physically
- samwillis 4y agoNot really, you can just add more and more control points to a Bézier and it will be possible to describe a curve to a greater accuracy. However, in reality when using Bézier curves you want to really want to use the minimum number of control point neccesery to ensure a nice smooth curve.
- quickthrower2 4y agoI mean vice versa. Can the physical thing do any CAD Bezier?
- hamburglar 4y agoA Bézier curve can have a cusp, which you can’t do with a physical spine.
- Gordonjcp 4y ago> Not really, you can just add more and more control points to a Bézier and it will be possible to describe a curve to a greater accuracy. The more control points you add to your curve the more computationally expensive it becomes, though. This is just the law of spline demand.
- bitwize 4y agoSo if you put a few of these together in a lattice, would you be reticulating splines?
- VortexSpin 4y agoI was looking for this reference.
- Kwantuum 4y agoWebsite is completely broken in firefox when javascript is enabled.
- alacritas0 4y agono it isn't. Running 107.0 here and it looks fine
- xg15 4y agoBroken in Firefox for Android 107.1 as well.
- fhd2 4y agoDoes seem a bit odd at second glance, seems like hitting the back button undos scrolling instead of navigating back to HN, depending on how much I scrolled. Maybe it's a feature though. Firefox for Android 107.1.0 with uBO.
- pimlottc 4y agoFine here. Firefox 107.0 w/ uBlock Origin
- crossingTime 4y agoIn Brave I see "Enter a caption (optional)" on every picture. <span class="caption public_hide" contenteditable="false" id="78a560_1776">Enter a caption (optional)</span>.
- jeffrallen 4y agoThey still are in wooden boat building. See Sampson Boat Company on YouTube from a few years ago.
- jabl 4y agoCame here to say exactly that. In particular, the episodes that deal with lofting (24 & 25): https://www.youtube.com/watch?v=oKJagvumvCI&list=PLB00JHoTw1TeX82Qw8hoFLRJI89Us_jMw&index=25 https://www.youtube.com/watch?v=oKJagvumvCI&list=PLB00JHoTw1...
- pimlottc 4y agoIntriguing videos! There's a good section of him laying down splines at 10:58 in episode 25: https://youtu.be/gfuPTLSBQfY?t=658 https://youtu.be/gfuPTLSBQfY?t=658
- selimthegrim 4y agoIs this where they would be used with mitres?
- deleted 4y ago[deleted]
- blacklion 4y agoNow bronze spline weights go $66, not $50. +8% in 6 years.
- AnOnymouse2200 4y agoIt's +32%
- blacklion 4y agoOoops, divide instead of multiply :-(
- sitkack 4y agoAside, there is no reason for them to be bronze, they look nice, but you could 3d print them and fill them, cast out of ceramic in plaster mold, make them from plaster, etc. If I were going to do a one-off set, I'd 3d print them and fill with sand.
- ChrisMarshallNY 4y agoMy father used to have these curves that were segmented rulers. You could bend them, and they would retain the shape. They were made from rubber, with metal, inside. The segments forced the curves to be smooth (you couldn’t kink the rulers). He also had a couple of slide rules.
- nonrandomstring 4y agoI have a certain nerdy penchant for the "stationary" objects we used to pack in our school bags; slide rules, protractors, set squares, compasses, stencils sets for things like chemistry and flow charts, hard pencils and sharpeners. They still feel like instruments of ritual and magic.
- lonk 4y agoIs it possible to reticulate physical splines?
- drewolbrich 4y agoYes, but this requires specialized equipment and a licensed technician.
- nraynaud 4y agoMy uncle used to work at a tool maker shop for the stamping industry in the 70’s. For the round molds for the wheel wells, they did grind the piece of steel by hand, and the curves were checked by a soft bending ruler.
- crazygringo 4y agoI'm so curious but the article doesn't mention: how were these splines "defined"? In other words, if you have to reproduce your work for a new draft, how do you make sure you draw the exact same curve? (Without tracing the prior draft.) Are there "control points" like Bézier curves have? Do those have anything to do with the placement of the whales? Or was this all just done "by eye" so that these splines assisted in drawing a perfectly smooth curve, but the result was just trial-and-error to find a curve that looks good?
- Jarmsy 4y agoAn interesting question, since you could record the positions of the whales, but that alone doesn't fully determine the curve. I guess you'd have to also record the distances along the spline between those pinned points.
- Someone 4y agoI think the pins aren’t ‘pinning’ specific points on the wood strips to specific locations, but just prevent the strip of wood from becoming a straight-lined strip of wood. The tendency of the strip of wood to straighten itself would provide enough force to make the wood slide along the pins to find the minimum energy solution. (Edit: https://en.wikipedia.org/wiki/Flat_spline https://en.wikipedia.org/wiki/Flat_spline seems to confirm that)
- Jarmsy 4y agoBoth types are used - pinning and sliding. See figure 3.19 in https://www.levien.com/phd/thesis.pdf https://www.levien.com/phd/thesis.pdf
- bee_rider 4y agoIs it a requirement, to be able to copy a design without tracing? Blueprints seem to have been the main way of storing designs for quite a while. Maybe the drawings are just as good as it gets until you have computers that really want numbers. Think about buying a ship for example — I guess the person buying it would just specify a type of hull (or for high end stuff, go to a shipwright they specializes in a type of hull), and a couple dimensions. As to actually doing the design, must be their experience plus conventions built on outcomes from the field — this part of the hull has to be convex, etc etc. So, trial an error, but built up over generations.
- twobitshifter 4y agoIt seems that the software interaction is not as nice as in the real world. I often end up fussing with the spline tools in programs to get what I want but this looks much more straigtforward.
- gregschlom 4y agoI loved playing with those weights as a kid. Their funny shape and hefty weight made them into interesting characters. The spline themselves were definitely off limits to my little hands, though. One thing the article doesn't mention is that splines were also made out of clear plastic, not just wood. This made them more bendable and durable, I believe, and it was nice to be able to see through them when positionning them.
- raphlinus 4y agoI have some stuff on real splines (their similarity and difference from the mathematical idealization) in section 3.12 of my thesis (page 39 of https://www.levien.com/phd/thesis.pdf https://www.levien.com/phd/thesis.pdf). There's also a bunch of stuff in there about Euler spirals (aka clothoids), including application to railways - see section 6.6, page 106. Fun fact, I'm going to get my first tattoo soon, and it will be an Euler spiral.