Ask HN: Anyone Have Expertise in Trigonometry?

https://news.ycombinator.com/item?id=32905156

17 20 4 years ago

news.ycombinator.com

howdy hn

im looking to collaborate with someone who is passionate about trigonometry, computational geometry, or just math in general! im trying to figure out if the white dot in the animation linked below can be computed in constant time, and if not what is the best that can be done? all the code i write these days is open-source, and i believe cracking this nut will go a long way for many!! any takers??

loop anatomy animation:

https://youtube.com/shorts/M83QFzrcnlc?feature=share

waynesonfire• 4 years ago

you forgot to mention the pay rate?

clumsycomputer9• 4 years ago

haha fair question... i'm hoping to find someone who will donate their time as i am doing myself. its important that improvements to the current solution i have remain in the open and free to use. otherwise said help may be counterproductive and even destructive

reallymental• 4 years ago

Considering that only one of those circles' radius is variable, and the other two circles intersect with the yellow loop, you can determine the equation of the yellow loop, which will give you the position of the white point, at any time, in constant time.

clumsycomputer9• 4 years ago

your reply certainly gives me hope that its possible, though i fear i've stared at this diagram for too long and am having difficulty viewing it with a fresh perspective.

some additional context.

im constructing the loop (yellow) with the black dots, which im computing in constant time. the dynamic circle (blue) is being constructed from the two static circles (pink, orange). the white dot is currently being computed by sweeping the already computed loop points from the center of the small circle (pink).

are there any laws or key points that may help me along? are there any similar problems that are well documented that you are aware of?

thanks

lupire• 4 years ago

Can you explain the formula or model for the white dot?

gus_massa3• 4 years ago

Did you make the animation or you found it somewhere in the internet?

Do you have a formula for each of these things?

What do you mean by "constant time"? From your description it seams all the points have a closed formula, there are no iterative steps that may be long? Do you want a simpler direct formula?

pubby• 4 years ago

If you can't figure it out, memoize the results in a table and interpolate.

clumsycomputer9• 4 years ago

i have an implementation that does something along those lines, which suffices for graphics but doesn't work well for audio applications. think 48 000 samples per second.

the computation i've outlined in the animation is also just a small but very important piece of a much more complex computation

this white dot is my bottle neck

thomassmith652• 4 years ago

I'd start by running the table through a curve-fitting program to see if it finds a simple formula like the OP is seeking. I've used this paid app https://www.curveexpert.net/products/curveexpert-professiona... but there are also free curve-fitting web apps out there.

clumsycomputer9• 4 years ago

awesome thanks for the recommendation

my only worry about curve fitting is that the recommended function won't generalize to other loop configurations

Ask HN: Anyone Have Expertise in Trigonometry?

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