Christopher Durham f578181351 Fix glm::is_normalized epsilon ... The existing comparison bound of $\epsilon^2$ is improperly scaled for testing an epsilon of the squared vector magnitude. Let $\epsilon$ be our specified epsilon and $\delta$ be the permissible delta of the squared magnitude. Thus, for a nearly-normalized vector, we have $$\begin{align} \sqrt{1 + \delta} &= 1 + \epsilon \\ \delta &= (1 + \epsilon)^2 - 1 \\ \delta &= \epsilon^2 + 2\epsilon \text{ .}\end{align}$$ Since we only care about small epsilon, we can assume that $\epsilon^2$ is small and just use $\delta = 2\epsilon$. And in fact, [this is the bound used by GLM][GLM#isNormalized] (MIT license) ... except they're using `length` and not `length2` for some reason. [GLM#isNormalized]: b06b775c1c/glm/gtx/vector_query.inl (L102) If we stick an epsilon of `1.0e-6` into the current implementation, this gives us a computed delta of `1.0e-12`: smaller than the `f32` machine epsilon, and thus no different than direct float comparison without epsilon. This also gives an effetive epsilon of `5.0e-13`; *much* less than the intended `1.0e-6` of intended permitted slack! By doing a bit more algebra, we can find the effective epsilon is $\sqrt{\texttt{epsilon}^2 + 1} - 1$. This patch makes the effective epsilon $\sqrt{2\times\texttt{epsilon} + 1} - 1$ which still isn't *perfect*, but it's effectively linear in the domain we care about, only really making a practical difference above an epsilon of 10%. TL;DR: the existing `is_normalized` considers a vector normalized if the squared magnitude is within `epsilon*epsilon` of `1`. This is wrong and it should be testing if it's within `2*epsilon`. This PR fixes it. For absence of doubt, a comparison epsilon of $\texttt{epsilon}^2$ is correct when comparing squared magnitude against zero, such as when testing if a displacement vector is nearly zero.		2024-01-13 00:02:26 -05:00
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src	Fix glm::is_normalized epsilon	2024-01-13 00:02:26 -05:00
tests	Run cargo fmt.	2020-04-05 18:49:48 +02:00
Cargo.toml	Remove CUDA support relying on abandoned toolchain	2024-01-11 23:09:17 -08:00
LICENSE	Fix and clarify license in crate metadata and add missing license files	2023-10-24 18:33:53 +02:00