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Avoiding Trigonometry (2013)

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Re: Avoiding Trigonometry (2013)

#51

Post by BenoitP »

aap_ wrote: post #48

He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions this would be easier: just calculate the quotient between z and d and take the square root (which means adding 1 and renormalising). the square root is necessary if one is dealing with vectors, which live in a kind of square-y space. finding the rotation between two spinors is even simpler: it's just the qu…

> He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions ...

Fair point, but I think you misspelled Projective Geometric Algebra

Re: Avoiding Trigonometry (2013)

#52

Post by fn-mote »

srean wrote: post #32
zzless wrote: post #31

Earlier quoted context omitted.

With all due respect, no, it isn't. His drivel against set theory shows that he didn't even read the basic axiomatic set theory texts. In one of his papers, he is ranting against the axiom of infinity saying that 'there exists an infinite set' is not a precise mathematical statement. However, the axiom of infinity does not say any such thing! It precisely states the existence of some object than can be thought of as…

"Sound" means free of contradiction with respect to the axioms assumed. If you can derive a contradiction using his methods of computation I would study that with interest. By "sound" I do not mean provably sound. I mean I have not seen a proof of unsoundness yet.

To clarify:

“Sound” != proof of soundness in the same way that the Riemann Hypothesis being true is not the same as RH being proven.

Re: Avoiding Trigonometry (2013)

#53

Post by srean »

fn-mote wrote: post #52
srean wrote: post #32

Earlier quoted context omitted.

"Sound" means free of contradiction with respect to the axioms assumed. If you can derive a contradiction using his methods of computation I would study that with interest. By "sound" I do not mean provably sound. I mean I have not seen a proof of unsoundness yet.

To clarify: “Sound” != proof of soundness in the same way that the Riemann Hypothesis being true is not the same as RH being proven.

Not a bad analogy. Damn good.

Re: Avoiding Trigonometry (2013)

#54

Post by aap_ »

BenoitP wrote: post #51
aap_ wrote: post #48

He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions this would be easier: just calculate the quotient between z and d and take the square root (which means adding 1 and renormalising). the square root is necessary if one is dealing with vectors, which live in a kind of square-y space. finding the rotation between two spinors is even simpler: it's just the qu…

> He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions ... Fair point, but I think you misspelled Projective Geometric Algebra

If you only care about rotations in 3d, quaternions do everything you need :) with all the added benefits of having a division algebra to play with (after all the cross product is a division-algebraic operation). PGA is absolutely great, but quite a bit more complex mathematically, and its spinors are not as obvious as quaternionic ones. in addition GA is commonly taught in a very vector-brained way, but i find spinors much easier to deal with.

Re: Avoiding Trigonometry (2013)

#55

Post by ajkjk »

Razengan wrote: post #40
chriswarbo wrote: post #3

Norman Wildberger takes this to the extreme with Rational Trigonometry https://en.wikipedia.org/wiki/Divine_Proportions:_Rational_T... It eschews angles entirely, sticking to ratios. It avoids square roots by sticking to "quadrances" (squared distance; i.e. pythagoras/euclidean-distance without taking square roots). I highly recommend Wildberger's extensive Youtube channels too https://www.youtube.com/@njwildberger a…

Stuff like this is what really interests me in trying to imagine how differently aliens might use things that we consider to be immutable fundamentals.

personal theory: I think there's going to turn out to be a parallel development of math that is basically strictly finitist and never contends with the concept of an infinite set, much less the axiom of choice or any of its ilk. Which would require the foundation being something other than set theory. You basically do away with referring to the real numbers or the set of all natural numbers or anything like that, and skip all the parts of math that require them. I suspect that for any real-world purpose you basically don't lose anything. (This is a stance that I keep finding reinforced as a learn more math, but I don't really feel like I can defend it... it's a hunch I guess.)

Re: Avoiding Trigonometry (2013)

#56

Post by ajkjk »

aap_ wrote: post #48

He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions this would be easier: just calculate the quotient between z and d and take the square root (which means adding 1 and renormalising). the square root is necessary if one is dealing with vectors, which live in a kind of square-y space. finding the rotation between two spinors is even simpler: it's just the qu…

the dot/cross product are the same operation but expanded into coordinates. Maybe the quaternion (/geometric algebra) version is more compact but it's not like it's a different set of computations. Whereas their removal of the trig functions actually does skip a bunch of unnecessary steps.

Re: Avoiding Trigonometry (2013)

#58

Post by waffletower »

et1337 wrote: post #26
20k wrote: post #14

>poorly designed third party APIs I think this is missing the reason why these APIs are designed like this: because they're convenient and intuitive Its rare that this kind of performance matters, or that the minor imprecisions of this kind of code matter at all. While its certainly true that we can write a better composite function, it also means that.. we have to write a completely new function for it Breaking thin…

Based on my experience writing many games that work great barring the occasional random physics engine explosion, I suspect that trigonometry is responsible for a significant proportion of glitches. I think over the years I subconsciously learned to avoid trig because of the issues mentioned, but I do still fall back to angles, especially for things like camera rotation. I am curious how far the OP goes with this cru…

You can definitely handle camera rotation via vector operations on rotation matrices.

Re: Avoiding Trigonometry (2013)

#59

Post by kstrauser »

srean wrote: post #32
zzless wrote: post #31

Earlier quoted context omitted.

With all due respect, no, it isn't. His drivel against set theory shows that he didn't even read the basic axiomatic set theory texts. In one of his papers, he is ranting against the axiom of infinity saying that 'there exists an infinite set' is not a precise mathematical statement. However, the axiom of infinity does not say any such thing! It precisely states the existence of some object than can be thought of as…

"Sound" means free of contradiction with respect to the axioms assumed. If you can derive a contradiction using his methods of computation I would study that with interest. By "sound" I do not mean provably sound. I mean I have not seen a proof of unsoundness yet.

> "Sound" means free of contradiction with respect to the axioms assumed.

Gödel wept.

Re: Avoiding Trigonometry (2013)

#60

Post by yobert »

moi2388 wrote: post #36
virgil_disgr4ce wrote: post #20

OK I have a genuine question outside the topic of TFA. Do people really prefer "orientate" over "orient"? This pattern baffles me. You don't get out of the subway and "orientate" yourself, you "orient" yourself. I mean I'm perfectly aware that language is a descriptive cultural process etc etc but man this bugs the crap out of me for some reason

I absolutely get out of the subway and orientate myself. If I orient myself I have not taken the subway but the orient express, I’m afraid..

When I get out of the subway, I always occident myself.
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