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...
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.
We don't have much sound optimization CAD programs, so we worked with light as replacement for sound, and looked at the reflections with raytracers. For the big, expensive concert halls and opera houses.
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.
This is quite similar to education research on Teachable Agents , which is an embodiment of the idea that to know something you must be able to teach it to someone else. In Teachable Agents you teach the computer rules (e.g. how ecosystems work), and then it gets a quiz where it compares the output to the right answer. When its wrong, you as the teacher must figure out whether the rules you taught it were correct and/or if it needs more rules.
Teachable Agents works for things where there's a right or wrong answer, because the computer is doing the test proctoring. But in your method the human is doing that, and I think it works quite well for things of a more qualitative nature like the arts, with the human playing the role of the critic or curator.
- generate a couple examples
- see something wrong
- add a rule
(For example, in the NFL, the teams in each division play each other twice, and then get the rest of their games by rotating through teams from the rest of the league)
Many times people have specifically researched why a certain method is better than status quo in practice, on real world data with real world operating constraints.
A good example is the paper “Let’s Put the Garbage-Can Regressions and Garbage-Can Probits Where They Belong” - explain an extremely common and hugely severe problem with “garbage can” regression models.
Try writing a simple calculator app with ML and you won't even have marked up enough training data by the time I have written it algorithmically. When it's finished, the ML one won't be as reliable.
I've been involved in a few projects where ML was a candidate approach. Mostly the answer was just to write down what we already know about the problem domain instead.
 e.g. https://www.youtube.com/watch?v=65n9h3tFpVg
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.
edit: pasted the first yt result here: https://www.youtube.com/watch?v=MHTizZ_XcUM
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.
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.
If the physics engine can't efficiently solve the inverse problem here, it is probably only well-suited for simulating a final solution for validation, not iterating over the rather large space of possible shot trajectories times possible backboard angles at the point of impact.
Isn't solving the physics problem a straightforward ODE integration?
And that process needs to be done for all possible incoming ball trajectories that would hit that point of the backboard in order to figure out what backboard angle will maximize the number of shots that go in.
Is it though? Isn't the final shape just a paraboloid, like a parabolic antenna with the hoop in the focal point?
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.
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.
I've also never seen someone cut wood on their Tormach CNC. Seems to work well!
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.
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.
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?).
To err is human. To own it on YouTube, divine.
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.
Perhaps it could be done with the parabolic antenna solution with a frame of reference change, to account for the acceleration due to gravity?
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.
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?
Dart Board: https://www.youtube.com/watch?v=MHTizZ_XcUM
Rigged Carnival Games: 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
In the video he mentioned doing a least squares fit to get the final surface, so that sounds about right.
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).
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.
Monte Carlo Algorithm: Always fast, probably correct.
Las Vegas Algorithm: Probably fast, always correct.
Atlantic City Algorithm: Probably fast, probably correct.
It's the type of place where James Bond likes to play in the movies and books.
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?
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.
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.
Also a paraboloid would work only for rays that are parallel to one another.
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
And your intuition on the launch angle is just flat wrong. In fact, I believe it's one of the primary predictive factors in a shots success with a normal backboard!