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Show HN: A basketball hoop to maximize shots that go in [video]
- steveads 6y agoReally neat project! Loved watching the video. Do you have the code in a Github repo?
- dacohenii 6y agoI love this! I was expecting something more like Mark Rober's movign dartboard [0], which is super cool, but this is even more interesting, because of the way you used software to come up with a general solution in advance. Kudos!
- jerrre 6y agoyour [0] link is missing edit: pasted the first yt result here: https://www.youtube.com/watch?v=MHTizZ_XcUM https://www.youtube.com/watch?v=MHTizZ_XcUM
- gorgoiler 6y agoMark Rober is an interesting character. It feels like he pitches himself as a crazy inventor guy but it seems like he’s more akin to the head of a design laboratory that employs many other talented people. It’s not like he doesn’t acknowledge the other crazy-inventor people he commissions though, and I certainly don’t mean to paint him as a fraud. When he says things like, 1m45s into a video on a steerable bowling ball “in the spirit of full disclosure this is all down to [named co-collaborator]’s work” it feels like that use of full disclosure in the sense of I would rather not reveal this but I am legally obliged to. No offense to Rober or that particular collaborator. For all I know, he just didn’t want the publicity. Rober is very good and it’s almost like I feel aggrieved that if only his style was ever so slightly different he’d win my complete instead of partial admiration.
- imtringued 6y agoI don't admire him precisely because his videos are not about him. His videos are always about someone else and that's why he isn't worth admiring.
- asdf21 6y agoIsn't it a backboard, not a hoop?
- duxup 6y agoTechnically but if you google a basketball hoop or talk about one, people generally think of the backboard and hoop.
- waterside81 6y agoI'm with you. I went in thinking the rim itself would always ensure the ball goes in.
- tryamtamtam 6y agoI thought this was really cool, keep up the good work!
- r00fus 6y agoClearly the hoop that minimizes shots is what exists at funfairs all over the world. Would making the backboard convex make it near-impossible to hit? What about making the curve imperceptible so it's hard to notice it's helping/hurting?
- nbardy 6y agoThe carnival hoops I've examined all have ellipsis shaped rims. Impossible to distinguish from a circle when observed from the front, but clearly squished if you walk around and get underneath it.
- sxv 6y agoellipsis shaped rims... will leave you hanging.
- minhazm 6y agoThat's if you hit the backboard. But you don't need to hit the backboard and plenty of people can normally make the shot without it. Funfairs / carnivals probably are doing something with the hoop itself.
- DDR0 6y agoThey're also not standard basketball height, so if you're used to aiming at a standard hoop—
- JshWright 6y agoMark Rober (who is linked elsewhere in this thread for a dart board that does the same this as this backboard, but with active compensation) also did a video on how carnival games are rigged. Dart Board: https://www.youtube.com/watch?v=MHTizZ_XcUM https://www.youtube.com/watch?v=MHTizZ_XcUM Rigged Carnival Games: https://www.youtube.com/watch?v=tk_ZlWJ3qJI https://www.youtube.com/watch?v=tk_ZlWJ3qJI (Bonus, in the theme of sports equipment that wins for you) Auto bowling ball: https://www.youtube.com/watch?v=wM5NHC97JBw https://www.youtube.com/watch?v=wM5NHC97JBw
- nabla9 6y ago"Who is Monte Carlo?" Monte Carlo is for Europe what Las Vegas is for the US. The first name that comes to mind when you think gambling. Monte Carlo method is repeated random sampling to obtain numerical results. Monte Carlo algorithms are heuristic algorithms that solve problems with random process that can give wrong answers. Las Vegas algorithms are algorithms that solve problems with randomness but get always correct result or knows that it failed. Runtime is finite. Atlantic City algorithm is a probabilistic polynomial time algorithm that gives correct answer > 50% of the time (or 75% of the time by some definition).
- jhncls 6y agoWell, his question was "Who is Monte Carlo?", a witty reference to the fact that Monte Carlo is named after a real prince [0]. [0] https://en.wikipedia.org/wiki/Charles_III,_Prince_of_Monaco https://en.wikipedia.org/wiki/Charles_III,_Prince_of_Monaco
- milesvp 6y agoI laughed out loud when he said this. I take for granted how much gambling knowledge I have (especially since I generally think gambling is stupid), but I thought everyone knew about Monte Carlo. I'm going to have to look up Las Vegas algorithms though, this is the first I've heard of them. Course, it's been a while since I've broadly looked at the current state of probabilistic algorithms. Makes me think it might be time to step back and look at some more general theory, especially since some recent DSP work led me to look into particle filters in an attempt to estimate a pair of rotating phasors.
- deleted 6y ago[deleted]
- irrational 6y agoIs Monte Carlo (I need to look up where that actually is) as gaudy (I might have said trashy) as the Las Vegas strip?
- 6y ago
- numuliank 6y agoNope, expected something interesting, but this is based on a boring brute-force simulation. He did hint at using a parabolic shape, like in satellite dishes. Why not use some actual calculus and differential equations to figure out the optimal parabolic-like shape here?
- dang 6y agoIt's great that you know more, but can you share what you know without putting others or their work down? Doing the latter really poisons the well here. A much better pattern than "Nope, expected something interesting" is to first affirm something that the author got right or did well, and then build on that with suggestions for refinement, further development, learning. There's plenty of opportunity to show how much you know that way, plus you won't also come across as an internet jerk. Keep in mind that project creators and authors are often reading these threads, and one nasty comment makes more of an impression than the rest of a thread put together. A single bee sting is more memorable than a field of butterflies. It's too bad that it doesn't work the other way around, but the pattern is super clear. Even the thread the other day with the C Committee guys, which was one of the best technical threads HN has ever hosted, made this impression on them: "Wow, I had no idea people were so mad about locales" (not a direct quote). I hadn't noticed, and when I found the comments they didn't even seem that mad.
- 2bitencryption 6y ago"brute-force" is what you call monte carlo if you don't know what monte carlo is
- v37p 6y agoHow is it different from a Newton-Raphson approach, which requires you to make an initial guess as it iterates through several derivatives to get to the root?
- OscarCunningham 6y agoThere won't be a closed form answer because the optimal solution depends on the distribution of the angles and velocities of the shots coming toward the backboard, which will be a complicated real-life distribution.
- mNovak 6y agoDoes it bug anyone else not to have the analytic solution?
- milesvp 6y agoFun story. I was in college taking differential equations. And I was faithfully attempting to apply what I'd learned in class, and having a somewhat hard time at it (this was before I realized how useful matlab was). When I was doing some research on the side, and I learned that the vast majority of differential equations are unsolvable, you can only approximate an answer. After that, I was thouroughly annoyed at wasting time in a class doing all this math by hand, and having to assume the answer was of a form that was solvable (and, yes, many useful engineering diff eq are of a solvable form). So, now to answer your question. I thought this backboard seemed like a problem that dish makers should be able to trivially solve, but getting to know the math, and modifying it enough to solve this particular problem can take more time than setting up a simple probabilistic simulation. And after my experience with diffeq, I'm happy with a quick and dirty approximate solution, and then moving on with your life. Then maybe you run into someone who knows the math and is motivated enough to apply it, and maybe you update your project then.
- mywittyname 6y agoThis should be solvable without differential equations, since it is basically a parabolic antenna with an off-axis feed.
- milesvp 6y agoSorry, I didn't mean to imply it required diff eq to solve these parabolic equations. I merely meant to give an anecdote about one of the first times I felt truly betrayed by mathematics. A subject I'd previously held in the highest regard.
- aj7 6y agoNo it’s not. Parabolic antennas work well for a single particular parallel input beam. That’s why they’re on gimbals, and directed at the anticipated direction, or scanned back and forth. Here, he is attempting to image many different parabolic paths onto a small circle in the plane of the rim.
- avilay 6y agoThat was a pretty cool video! I loved how he used 3D Monte-Carlo and side-stepped all the complicated math. I wonder if he was using a Physics engine like Bullet or ODE to calculate the simulated trajectories. Also, a good intermediate step might've been to build the backboard in something like Unity and shoot some hoops to catch the radius error before actually machining it out.
- remcob 6y ago> Physics engine like Bullet or ODE to calculate the simulated trajectories Probably not, the trajectories are simple parabolic and you can assume perfect elastic collision. Easy enough to implement, compared to interfacing with a physics engine. In fact, it sounded like he approximated the ball by a point and ignored the radius.
- Gravyness 6y agoWhile interfacing a physics engine is hard, I feel like it would be hard to forget to add the radius in a physics simulation, making mistakes like this rather difficult. So yeah, you can reinvent the wheel but using specialized tools gets the job done too, usually with less painful mistakes, but that's the price to pay for the lack of learning you get with the tool.
- wtallis 6y agoWould a physics engine actually make it any easier to solve this inverse problem? Simulating where the ball ends up relative to the hoop after bouncing off the board is the kind of forward problem that I tend to think of physics engines as designed for, but the problem here is to (repeatedly) determine what angle of board would yield the desired post-bounce trajectory. Does something like Bullet have a flexible enough inverse kinematics solver to handle this kind of problem?
- thebean11 6y agoI'm guessing a brute force approach wouldn't take that long for this problem
- yissp 6y agoAny physics experts know what the actual optimal shape is? I imagine it would be a pretty gnarly problem to work out.
- gshdg 6y agoWell, IIRC, theatrical lights use parabolic reflectors to focus a non-point source into a point on a lens, so that might be a good place to start.
- lonelappde 6y agoLight and sound gets to ignore gravity.
- justinator 6y agoHaha well light can, if far enough away from a black hole!
- deleted 6y ago[deleted]
- baddox 6y agoI was wondering how you could get an analytical solution, but I think you’d have to define the problem much more rigorously to do so. As he mentions in the video, different basketball paths can contact the same point on the backboard from any number of angles, so it seems fairly clear that there is no perfect solution.
- contravariant 6y agoIf you fix the position of the 'thrower' and just throw them at ridiculous speeds so gravity doesn't matter you'd end up with a hyperbolic backboard. So annoyingly for an 'optimal' solution you'd need to specify where people can throw from and how fast. Frankly you might as well just use a hyperbola with one foci on the hoop and the other on the middle of the court, or maybe a point slightly higher than the court itself as the balls will be coming in at a lower angle (or maybe even a downwards angle?).
- gordon_freeman 6y agoThis is pretty cool! I wonder if he could also figure out, which attempted balls would naturally go in vs through the help from the backboard!
- buzzdenver 6y agoNext level: a camera and a couple of motors to see the speed/location of the ball and adjust the backboard accordingly.
- nmca 6y agoLike this perhaps? https://m.youtube.com/watch?v=MHTizZ_XcUM https://m.youtube.com/watch?v=MHTizZ_XcUM
- linsomniac 6y agoReally liked his static approach vs. Mark Rober's robotic dartboard.
- jhncls 6y agoDid other people also wonder what a French cleat might be? It is a molding with a 30–45 degree slope used to hang cabinets or other objects. [0] https://en.wikipedia.org/wiki/French_cleat https://en.wikipedia.org/wiki/French_cleat
- dsaavy 6y agoI put up a giant wall of these in my home and they're incredibly useful. You can build any type of contraption and throw a cleat on the back of it and boom, just put it on the big wall. Reconfigure it every month, build new things to mount up there, it truly is simple and versatile. French cleats truly are terrific.
- williamdclt 6y agoI like the idea. It's a bit invasive, but if you don't mind would you share a photo of what this wall looks like?
- IanCal 6y agoSomeone else below has shared a video on the same kind of thing you might be interested in: https://www.youtube.com/watch?v=65n9h3tFpVg https://www.youtube.com/watch?v=65n9h3tFpVg
- justinator 6y agoWe used them a lot when hanging up art work.
- Cogito 6y agoYeah it sounds a lot like a picture rail[0], the main difference is that the picture rail runs around the whole wall while this is more specific. [0] https://en.wikipedia.org/wiki/Molding_(decorative)#Picture_rail https://en.wikipedia.org/wiki/Molding_(decorative)#Picture_r...
- zimpenfish 6y ago
- anjc 6y agoCan someone briefly eli5 how the Monte Carlo simulations feed into learning the optimal surface?
- jrockway 6y agoYou pick a random position and a random shot (angle, speed), see where it hits the backboard, and then change the angle of the backboard there to direct the ball through the rim after the bounce. Do this enough times, and you have a surface. (I don't know how the number work out, so there are probably points that have multiple values and surfaces with discontinuities. I guess you average the values at a given point and then smooth the surface, and call that "as good as possible".)
- lonelappde 6y agoSimulate random throw angle/power and random angle at point of impact; remember which angles lead to basket.
- anjc 6y agoThanks
- soheil 6y agoIs this not something that just an optics equation in Physics would give you? Specially if not taking the radius of the ball into effect.
- hencq 6y agoMaybe, but as he explains a normal parabola (like a satellite dish) wouldn't work, since the shots themselves are arced because of pesky gravity. I thought using a Monte Carlo analysis and finding a fixed point was actually a very clever way to solve it.
- carlob 6y agoYeah but the acceleration from gravity is constant so maybe there is just a (possibly non linear) change of coordinates that can be applied to the regular paraboloid. Also a paraboloid would work only for rays that are parallel to one another.
- mannykannot 6y agoAnother difference from optics is that the vlocity is not fixed, and that affects the extent to which gravity modifies the trajectory.
- Misdicorl 6y agoDepends on the importance of a couple effects that light is immune to (at least for an optics equation) 1) gravity post impact with backboard 2) impact angle for a given (start, backboard) tuple depend on velocity and launch angle for a basketball, but are always the same for light. Also the impact angle for the basketball and light are very different
- mywittyname 6y agoI think it's safe to ignore both of these factors at this scale. 1) The effects of gravity is bounded and negligible on the surface of the Earth. 2) (I suspect) the wideness of the launch angle and hoop size are probably directly proportional, so you could shape the back board based on a direct impact to get a point to center the hoop on. The hoop can only get so big and still be considered reasonable.
- nogabebop23 6y agoWho uses the back board? This doesn't help at all with "nothin' but net"
- philwelch 6y agoNo respect for Tim Duncan.
- quickthrower2 6y agohttps://www.coachup.com/nation/articles/bank-shots-in-basketball https://www.coachup.com/nation/articles/bank-shots-in-basket...
- jrockway 6y agoThis appears to be a massively underrated YouTube channel. I love it when I find one of these. I've also never seen someone cut wood on their Tormach CNC. Seems to work well!
- Animats 6y agoThe first 10 seconds pretty much covers the subject. It's not the hoop, it's the shape of the backboard, which is a reflector formed to focus the ball on the target. Now, the really cool thing would to build a flat backboard with controlled bounce properties. Interesting 3D printing problem. That would look like an ordinary backboard but still focus bounces.
- jansan 6y agoAnother idea would be a hoop controlled by servos that always moves the hoop where the ball is going.
- elliottkember 6y agoThe solution is explained pretty quickly. But the implementation in the rest of the video is still worth watching!
- ForrestN 6y agoDid anyone else imagine just a very large hoop?
- jtbayly 6y agoI imagined a large funnel.
- hliyan 6y agoReally impressed with the use of Monte Carlo method. A while back I ran into some resistance trying to advocate simpler statistical methods to solve a problem domain similar to this, while the team in question repeatedly wanted to reach for a machine learning solution. I'd love to know if I was wrong here. In my mind, when an algorithmic or heuristic path to a solution is available, we should attempt it first before reaching for ML.
- deleted 6y ago[deleted]
- Taek 6y agoA common trap in tech is to reach for the fanciest tool instead of the simplest. The best engineering often comes from mastery of the simple tools, and the most beautiful engineering is the one that makes you say 'that's so obvious, why didn't anyone ever come up with that before?'
- IgorPartola 6y agoOne of my favorite software solutions that I came up with was “human learning” powered. A few years ago I was working as the engineering manager at a small company. I had 8 other people who I was in charge of and we had moved to a new office in the middle of this. Our team took up two rooms in the office and I had to figure out who would be sitting where. I had some preconceived notions of who would be productive together, who would annoy each other, etc., but there were enough possible combinations to make this a large enough search space. So I wrote a very simple python script that would randomly generate layouts of who would sit in each room and next to whom. Every time it gave me a result I scanned it for conditions that would make it not work and add a rule to skip such configurations. After about six such edits I got a layout I thought was acceptable. The team as far as I know was happy and nobody questioned it for the entire time we were there. This saved me time because I didn’t have to pre-program all the conditions, only add ones I had already seen not work. Saved both CPU and brain cycles, so to speak.
- npunt 6y ago
- prodigyboi 6y agoTo say I’m impressed by the video and more specifically the algorithm would be the understatement of the century. This is amazing. Please let me buy one :)
- tiffanyh 6y agoDoes this only work if you’re exactly aligned in front of the hoop? (eg Free-Throw Line)
- andbberger 6y agoNo it's optimized to work from anywhere in the court, although he didn't say what distribution he used.
- justinator 6y agoActually from the video, he miscalculated so it's optimized only when the basket is farther away then usual from the backboard. I would theorize that this may have made the solution work better, albeit unintentionally.
- hammerton 6y agoThat was really cool, thank you!
- ericvolp12 6y agoThis was really well explained and interesting. Funnily enough I'm pretty sure this is a really similar method to urinal design, so if this whole basketball thing doesn't work out for ya, you could always work for American Standard...
- remarkEon 6y agoUpvoted this because I'm tired of peeing on urinals in bars and restaurants that have flat walls, and every time I do I think "gosh don't these guys have any engineers on their payroll?".
- TeMPOraL 6y agoIt's the same thinking as with software UI/UX. Doing things right is so last century, you have to stand out somehow.
- rurban 6y agoSimilar methods exists for all kinds of engineering problems, like architecture (form follows function), roofs, bridges, city planning, or just the economy. The optimal form is always an optimization problem. Just define the constraints. Maybe the most famous example is Gaudi calculating the form of the roofs of the Sagrada Familia, and then Frei Otto for the Munich Olympics. City planning is easier as their is no gravity, just more constraints. Think of SimCity run in a simulation with feedback loops. The best planning approach is always prolog-like. Define the facts and rules, and the forms will fall out eventually by itself. Then optimize the solutions iteratively according to cost functions. It's called OR, operations research. I did a lot of that with free-forms, also even simply office layouts, when I worked as architect. We even sold CAD programs to special manifacturers to design a good roof or other free-form shapes. Like for Disney.
- deleted 6y ago[deleted]
- dhosek 6y agoSpeaking of Disney and architecture and parabolic shapes, apparently when the Disney concert hall was first built, the curved shapes of the building acted as parabolic reflectors which focused on nearby apartment buildings. They had to sand the panels to reduce the reflectivity because they were heating the apartments to as much as 140°F.
- ptrenko 6y agoconvexity!
- curiousgal 6y agoI mean, is it really Monte Carlo? He's iteratively trying to optimize a function which makes this more like SGD, no?
- jasonheh 6y agoIt definitely felt that way to me. When he was finding the optimal angle for a single sampled shot, that's the partial derivative of his probability of making the basket for that shot wrt the surface normal at the backboard hit position (or something like that). If you average all of those you get a gradient descent update.
- jefftk 6y agoNow I want to make a backboard that always misses unless you know the right amount of spin to put on the ball.
- eagsalazar2 6y agoI want before/after shot %. Also someone should totally sell these. We already have short hero hoops, with this hoop we could all be Kobe every day, circus shots in the general direction, 55% fg%, legendary!
- yalogin 6y agoSo do you use only one spot to shoot from for the data collection or do you shoot from all over the floor?
- aj7 6y agoRed Auerbach knew something in real life. If you bend the whole rim downward, even a little bit, it becomes a “sewer,” pro just-miss shots start going in. He would check the baskets, before each game, to make sure this wasn’t being used against the Celtics.
- fchu 6y agoThis is very cool. If you can mass produce such boards (plastic molds maybe?), It could be a fun novelty gadget/gift
- remarkEon 6y agoAside from the Apollo 13 in Real Time website, this is the coolest thing I've seen on the internet in the last 3 months. Sent this to my brother, which of course precipitated a huge sibling argument about which player would've benefited more from this assuming we're talking about players that tend to shoot jump shots. I'll let you guys know who wins. Edit: We mostly disagree on the type of shot that certain players make and which would be more advantageous here. And credit to the creator, he alludes to this early in the video where he talks about "line drive" vs "arc" shots.
- cmonnow 6y agoOMG just found out about this - https://apolloinrealtime.org/ https://apolloinrealtime.org/
- imvetri 6y agoGood work. thanks for sharing
- kidintech 6y agoVery out of left field, but how does one start doing these kind of things? My background is in CS and math, and I could have come up with and built everything up to exporting the mesh into triangles, but would have needed months of google searching and trial and error to do the actual "machining" part of things. And then even if I went through the painful process of learning it on the job for this task, the learned skills would probably not transfer very well into the next adventure. Additionally, I imagine the machine used in the video is fairly expensive and not worth purchasing for one experiment. I'm asking this because I find these kind of builds fascinating, but I'm always humbled about my skills when I think about the transition from digital to material.
- chrisco255 6y agoYouTube videos are one of the best ways to learn mechanical/material skills. Just start. You'll suck at first. Keep at it and eventually you'll suck a little less. One day you'll be mediocre. And if you keep at it you'll be skilled.
- gnramires 6y agoCan confirm. For general knowledge I recommend two fantastic channels: (1) Click Spring (2) Matthias Wandel. They're always doing interesting things and usually some technique comes up in the videos that I didn't know of. There are probably countless others. Youtube really shines in this because there is much to see happening. Much of the information is visual and mechanical on how to do things well (or at all). You generally need lots of tools to build stuff though (you can sometimes trade time for tool cost), but these days finding an equivalent to a maker space or hacker space shouldn't be too difficult. * ClickSpring's clock series is one of my favorite video series ever. Wandel is a little unconventional that he builds many of his own tools, but I find he's quite practical and insightful in doing things.
- jzwinck 6y agoThe style of presentation, the manner of speaking, seems to be inspired by This Old Tony [0]. This is no bad thing. I wonder if Tony picked it up from somewhere else. [0] https://www.youtube.com/user/featony/videos https://www.youtube.com/user/featony/videos
- baruch 6y agoHe needs to do some more monte-carlo simulations on the jokes to get to the level of ToT. But it was a very nice presentation of the topic and a neat result.
- jasoncartwright 6y agoA non-US perspective: it's quite weird hearing someone younger than about 50-60yo use inches as a measurement. Especially for something scientific.
- gorgoiler 6y agoDo you mean the reference to four-by-two timber. It’s not really measurement when it’s a standard size like that. More like a well known discrete unit like a pint of beer or a 54” pizza.
- jasoncartwright 6y agoNo. When he measures the ball to move the hoop
- gorgoiler 6y agoOh right. With a precision caliper no less. Another video posted here the other day used the word thou (as in thousandth of an inch) which is a word I haven’t heard in a long time!
- s0rce 6y agoIts frustrating. I'm a Canadian born and raised engineer/scientist working at a US-based medical device startup and I'm constantly converting between thou and microns and mm. Often stuff will be "in spec" for both, ex. 0.002" = 50um (assuming some tolerances for the part. Hopefully, we don't destroy any satellites by mixing the units up.
- chombier 6y agonice work! you could probably speed the computation quite a lot by using a small deformation basis (e.g. using modal analysis) and optimize in this smaller space instead.
- riyaktm 6y agocool
- hawos 6y agoCan anyone tell me what tablet and app he is using for the drawing?
- candeira 6y agoI wonder if Greg Egan reads HN or whether he learnt about this in some other way, but this was his analysis of the same problem from five hours ago: https://twitter.com/gregeganSF/status/1251390966356795392 https://twitter.com/gregeganSF/status/1251390966356795392
- bitxbit 6y agoThis is so awesome! I love the way you went about solving this problem.
- paul_f 6y agoDo the inverse of this and open a stand at a fair :-)
- someguyorother 6y agoHe wouldn't have to, he could just use the original one where the ball hits the rim every time :-)
- gorgoiler 6y agoAbsolutely brilliant. The plot twist requiring the additional metal bracket at the end was fantastic. To err is human. To own it on YouTube, divine.
- londons_explore 6y agoI think the results would have been much better if he'd taken into account the rotational inertia of the ball... It turns out that affects the bounce angle quite significantly...
- nitrogen 6y agoI really enjoyed the length and depth of this video. Though I wonder if a good hybrid strategy for YT popularity is to have a viral-edited video on a main channel, and more depth linked on a second channel.
- Wistar 6y agoThis is very cool. As I watched the video, I began to think about a stupidly over-the-top version of the backstop that uses many real-time-deformable panels similar to the adaptive-optic mirrors used in advanced astronomical telescopes but informed to guide the ball by a machine vision view of the inbound ball in flight.
- mikorym 6y agoSo I am guessing that the reason why this doesn't look like a sattelite dish is because 1) the focal point is not in the centre and 2) the ball doesn't rebound in straight lines. Oh shoot, he does actually explain this exactly. He also mentions 3) speed of the ball. And then, 4) for lines that hit at the same point but with different trajectories and speeds, he takes the "average basketball shot". The only other thing I am wondering about is what would happen if the ball were flat.
- lovetocode 6y agoI’m not really impressed. This only applies to shots directly taken from the free throw line . Make a basketball hoop that moves based on ball flight Now that would be impressive. I have seen someone on YouTube do that with a dart board.