What is the difference between pixel pitch and pixel density?

It’s just a reciprocal relationship. Where pixel density measures, say, the number of pixels per inch, pixel pitch measures the number of inches per pixel (or the center-to-center spacing between pixels).

Pixel pitch expressed as a linear measurement, and if the pixels are non-square you may see two values specified. Pixel density, on the other hand, may be expressed as a linear measurement (pixels per inch or millimeter or what have you) or as an area measurement (pixels per square inch or pixels per square millimeter) — your equation assumes an area measure of pixel density and square pixels, and converts to a linear value.

I should probably add that pixel pitch is usually used to state device specifications (screens or sensors) — you wouldn’t often see it used to describe, say, the resolution settings you used to print an image.

usability – What information density is reasonable?

The most general answer of course is, “it depends.” Who are the people using the product? What are they trying to achieve? Are they using it on a desktop or mobile phone? Are they using a mouse, touch screen, or keyboard to navigate (or other assistive technologies)? Is there flexibility for them to increase or reduce the density to what suits them?

Here is an interesting article I found on UX Collective “How white space killed an enterprise app (and why data density matters)” written by Christie Lenneville and Patrick Deuley.

Everything that article says is a good point and says it better than I could say, so I recommend checking it out.

You also need to ensure accessibility for those with vision, mobility, and/or cognitive considerations. Make sure everything is keyboard accessible. Make sure tables are marked up semantically and read correctly by a screen-reader. Make sure color contrast is compliant. Make sure text and content reflows so nothing overlaps or gets cut off when users zoom in or resize their screen. Read up on WCAG 2.2 for specifications on making sure content is readable and accessible no matter how dense or sparse.

And do thorough user interviews/observations and usability testing. If this is a redesign, have the users perform tasks on the previous/current version and time it. Then have them perform the same task in the redesign/prototype and time it. Did it save time? Did it prevent costly errors? Did it improve retention or conversions?

I think the best framework is around the UX research, though I know that doesn’t provide the kind of specific answer you were looking for. The most reasonable density is the one that allows people to do complete their task(s) most efficiently and without error, frustration, or the need for home-made workarounds.

Minimum image size to be displayed well(without pixelization) on full screen of 10 inches Android device which has xxxhdpi density screen type?

What must be the minimum size of an image in pixels to be displayed well(without pixelization) on full screen portrait mode of 10 inches Android device which has xxxhdpi density screen type?

K&F Concept ND2-ND32 Neutral Density Filter for Canon EF 100mm

For that particular filter at Amazon, it appears K&F Concept probably just provided the exact same “52 mm” descriptive text, regardless of which filter diameter is chosen.

The confusion here isn’t a filter or lens thing; it’s merely an example of technical issues, misunderstanding at the supplier end, or laziness in providing the correct descriptive text, with regards to e-commerce.

If you order the 67mm filter, it will fit your lens. If you order a 67mm filter but are delivered 52mm, then you were sent the wrong one through no fault of your own, and you should return it to Amazon and complain about the seller’s product page.

topological groups – CH and the density topology on $mathbb{R}$

In the article AN EXAMPLE INVOLVING BAIRE SPACES (https://www.ams.org/journals/proc/1975-048-01/S0002-9939-1975-0362249-1/S0002-9939-1975-0362249-1.pdf) of H. E. White Jr. it is shown that, assuming CH, there exists a Baire space $Y$ such that $Ytimes Y$ is not Baire.

For the construction of this space, is used the density topology on $mathbb{R}$ (for details of this topology you can see https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-62/issue-1/The-density-topology/pjm/1102867878.full).

Denote by $mathcal{T}$ the density topology on $mathbb{R}$ and by $mathcal{E}$ the Euclidean topology on $mathbb{R}$.

The construction of the space $Y$ begins with an enumeration $(F_{alpha})_{alpha<omega_{1}}$ of all $mathcal{E}$-Borel sets of measure zero (Lebesgue measure on $mathbb{R}$). Then, by transfinite recursion on $omega_{1}$ is construct a sequence $(Y_{alpha})_{alpha<omega_{1}}$ of countable rational vector subspaces of $mathbb{R}$ and finally our space is $Y=bigcup_{alpha<omega_{1}}Y_{alpha}$.

My question is the following :

In the article it is mentioned that $Y$ is not extremally disconnected, does anyone have any idea how to prove that fact?

Remember that a topological space $X$ is extremally disconnected if the closure of every open subset of $X$ is open.

Thanks a lot.

Trying to figure out the asymptotic density

Let $a>0$.

I have the following function $f: mathbb{N} to mathbb{R} $ defined in the following way:

begin{equation}label{km relation}
f(m) = m +lfloor a m – tfrac{a }{2} +tfrac12 rfloor.

Now, define the counting function of a set $A$ of integers by
A(x) = sum_{substack{a in A \ 1 le a le x}} 1.

Now let the set of interest be $A=f(mathbb{N})$.

What is $lim_{n to infty} tfrac{A(n)}{n}$?

I think that it should be $frac{1}{a+1}$, but since $a$ can be irrational, I can’t seem to quite prove it- I get stuck.

plotting – Rotation density plot with fixed Frame

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