graphics – Colour region by some property based on stochastic geometry

I have some circles placed at random within a region (here, the region is a circle-circle intersection).

pts1 = RandomPoint(
   ImplicitRegion(
    EuclideanDistance({x, y}, 0) < 1 && 
     EuclideanDistance({x, y}, {2.5, 0}) < 2, {x, y}), 3);
pts2 = RandomPoint(
   ImplicitRegion(
    EuclideanDistance({x, y}, 0) < 2 && 
     EuclideanDistance({x, y}, {2.5, 0}) < 1, {x, y}), 3);
Graphics(Prepend(
  Join(Circle(#, 1) & /@ pts1, Disk(#, 0.01) & /@ pts1, 
   Disk(#, 0.01) & /@ pts2), {Circle({0, 0}, 1), Circle({2.5, 0}, 1), 
   Circle({0, 0}, 2), Circle({2.5, 0}, 2), Opacity(0.4)}), 
 ImageSize -> Full)

Each circle covers some portion of another circle-circle intersection, as in this picture:

enter image description here

The regions in the right “lens” (circle-circle intersection) which are covered by 3 circles are in deep blue, by 2 circles in light blue and by 1 in yellow. The remaining region is left white.
This is done with Paintbrush.

Can I get Mathematica to colour the continuum of points automatically, like this, with $n$ colours if there are $n$ points in pts1?

It appears easy to do this with a Plot of function, and then ColorFunction, but with some property of a set of points in Graphics?

graphics – Using EuclideanDistance consecutively

triangle

To get the distance between point c and d, I tried using the following

EuclideanDistance[c, d] /. %["Points"]

Then I want to find the length of another line from the same scene, but I cannot use the above code twice.

EuclideanDistance[c, d] /. %["Points"]
EuclideanDistance[d, p] /. %["Points"]

What should I use then?

graphics – Drawing two altitudes of a triangle

I am trying to construct a triangle with 2 altitudes. It worked for ‘All’ vertices.

a = {5, 0};
b = {0, 0};
c = {3, 6};
tri = {a, b, c};
alt = TriangleConstruct[tri, {"Altitude", All}];
Graphics[{Style[Triangle[tri], Opacity[0.2]], alt}]

But when I tried to specify two vertices,

alt = TriangleConstruct[tri, {"Altitude", {a, b}}]

The following message came out:

TriangleConstruct is not a Graphics primitive or directive.

How do I specify two vertices to draw the altitudes?

graphics – Mathematica 12.1 Crashes when making large partitions of an image

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How to make a function plot dynamic in a combined graphics?

Here is the code:

Dynamic@Show[{Graphics[{LightGray, Rectangle[{0, -1}, {Pi, 1}]}], 
   Plot[Sin[a x], {x, 0, Pi}]}]
Slider[Dynamic[a]]

The Slider controls the value of a in Plot[] to produce a dynamic plot of Sin[].
I would like to make the Plot[] dynamic only, but it didn’t work if i only wrapped plot[] with dynamic[], so i added dynamic to the whole show[]. So how to dynamically update plot[] solely?

graphics card – High CPU & MEMORY usage during online video play

I have multiple questions related to high CPU and memory usage during play of live video in internet.

Problems:

CPU at 100% and RAM at 90% during playing online video like Amazon Prime, ZEE5, Netflix. Except ZEE5, others are still watchable as there is no lag, but ZEE5 causes videos to freeze.

Computer System:
4 year old. Gigabyte GA-N3050M main board with onboard Celeron Dual core CPU @1.6 GHZ. 4GB DDR3 RAM @1600MHz. A-DATA Ultimate SU650 3D NAND 120GB SSD. Sony 21 inch TV as monitor. Monitor connection is VGA. Motherboard supports a maximum resolution of 1920×1200@60 Hz in VGA mode and a maximum resolution of 3840×2160@30 Hz in HDMI mode. I use VGA. It has one 1 x PCI Express x4 slot, running at x1

Questions:

  1. The motherboard is capable of descent resolution then why the CPU starts to struggle at playing online video?

  2. If I connect the monitor to HDMI port will that lower the burden on CPU and RAM ?

  3. Will it be possible to install a graphics card on this board and if yes, will that make the video playing smoother and lower the CPU and RAM usage?

What are the cartoony graphics on landing pages called

Many landing pages have some sort of cartoony wacky caricatures depicting humans. What are they called?.

I mean characters like the ones here, here, here, here

Thanks.

graphics card – OBS Studio + NVidia GeForce: is it possible to record in higher resolution than the display permits?

The relevant part of my set up:

  • A monitor with max. resolution 1920×1200
  • Nvidia GeForce 2070 Super
  • OpenSuse Leap 15.2
  • OBS-studio installed and working

I’ve either read or heard somewhere, that with Nvidia graphic card it is possible, with some tweaks, to record the screen with higher resolution than the maximum resolution of the physical monitor. Does anyone know, is it possible at all, and if it is, how to do it on OpenSuse?

graphics – How to generate a star onto a render texture with spherical warping

How would one proceduraly generate a star in a compute shader that looks like one of thes two at any size needed. Also any way transfer this into a spherical map, would be appreciated.
Goal is to create a spherical skybox of stars, (stars a pre generated, and not just decoration).

So far got accurate positioning of the stars on the spherical skybox but lack the equations to get it looking like I want.

Preferably the one on the right.

enter image description here enter image description here

This below is what I currently have, ~~5 to 15ms processing time, little over 30k stars

enter image description here

Using Unity2019.3.1f1, needs to be compute shader compatible. (if not I will convert it somehow)
Render Texture output.