Are real objects more intuitive than plane UI elements in VR?

I´m analysing various VR apps and I found Tvori, and I love how it handles the different actions that can be done, because instead of using interface elements such as icons or buttons, it uses real objects, such as cameras, brushes, light bulbs, spotlights, and I’m pretty much convinced that how the actions are represented makes their use more intuitive, since the gestures that are made to use them are natural, and also, the behavior that they have can be intuited by the operation of these objects in the real world, which makes it more intuitive. For example, if I want to insert an ambient light, i would choose a lightbulb and I can turn it on and off, or I can choose a pencil to draw from the tip, and erase with the bottom part.

As I say, I am practically convinced that using real objects is more intuitive, but I do not find research about this aspect of the user experience and I would be happy to confirm whether or not I am right.

I wanted to ask if someone knew any source that could deal with this topic in order to go deeper. Maybe the source does not prevent from VR but from other paradigms. Also, if you have any opinion about this topic it will be well received.

Thank you so much in advance!

Plane transfer at YUL

I will be traveling to an international destination in June from Orlando FL. I have a stop in YUL with 3-hour layover. Would that be long enough? I have never gone through Canada before and don’t know what to expect. I’ll be flying on air canada both flights. This is my first time traveling overseas and I’m a little nervous.

What are the ramifications of creating a homebrew world without an Astral Plane?

I’m currently working on a homebrew world for a campaign of mine, which is currently on hold indefinitely, so there’s no time pressure.

Overall design intent:

  1. I don’t want my world to be a clone of the general world and lore of D&D (including the Forgotten Realms & the planar cosmology), with the only difference being the Material Plane.
  2. I’m not entirely content with the planar cosmology and pantheons in the Forgotten Realms and other existing settings (Eberron, etc).

Since I personally don’t like the Astral Plane in particular, I’m thinking about outright removing it from my world.

However, the DMG states on page 43 on “The Planes”:

At minimum, most D&D campaigns require these elements:

  • […]
  • A way of getting from one plane to another
  • A way for spells and monsters that use the Astral Plane and the Ethereal Plane to function

Obviously, I don’t have to adhere to these guidelines. However, I’m aware that a number of spells, creatures, magical items and other things in 5e directly refer to the Astral Plane. Miniman’s answer to the question What are all the ways a player can get to the Astral Plane? lists quite a few of these.

Naturally, spells (like Astral Projection), creatures (including playable races like Gith) or magical objects that refer to the Astral Plane simply don’t exist (in unmodified form) in this campaign. I’d homebrew something for what happens when you put e.g. two Bags of Holding into each other.

I also know that the Astral Plane can be used as a means of travelling between different worlds, using the color pools located on it. I’m thinking about implementing a Yggdrasil-style World Tree in my world, which would assume this job.

Are there any other ramifications as a result of not having an Astral Plane in a 5e campaign setting?

An injection from curve to projective plane is subscheme inclusion

Let $ X$ be a connected scheme, $ X\rightarrow \mathrm{Spec}\,\mathbb{C}$ be a morphism of finite type and relative dimension 1. Assume that there is a $ \mathbb{C}$ -morphism $ f:X\rightarrow \mathbb{P}^2$ which is injective on the underlying topological spaces.

By Chevalley’s theorem we know that $ f(X)$ is a finite disjoint union of locally closed subsets of $ \mathbb{P}^2$ . Is it true that $ f(X)$ is a locally closed subset of $ \mathbb{P}^2$ ?

I think one way to show this would be to show that $ f$ is a topological embedding. Then if it is also true that $ \overline{f(X)}\backslash f(X)$ is finite, it is game over (because for a connected one-dimensional scheme of finite type over $ \mathrm{Spec}\,\mathbb{C}$ the topology on the set of closed points is cofinite).

Quotient space of harmonic functions on punctured plane

Let $ a_1,\ldots,a_n$ be $ n$ distinct points in $ \mathbb{C}$ and let $ \Omega := \mathbb{C} \setminus \{a_1,\ldots,a_n\}$ . Define $ H(\Omega)$ to be the space of harmonic functions on $ \Omega$ and $ R(\Omega)$ the subspace of $ H(\Omega)$ consisting of real parts of holomorphic functions on $ \Omega$ . I want to show that the equivalence classes of $ $ \log\vert z – a_1 \vert,\ldots, \log \vert z – a_n \vert$ $ form a basis for the quotient space $ H(\Omega)/R(\Omega)$ . I know how to show linear independence. I have seen rather lengthy arguments that the above functions span the space, but I am wondering if there is a way to show that the dimension of $ H(\Omega)/R(\Omega)$ must be $ n$ without actually computing a basis. That way I can conclude the above functions form a basis based on their linear independence.

Orthogonal projection of line onto plane

I have already read the topic Orthogonal Projection of vector onto plane, but I have a different task. I need to make a notebook in Mathematica where the users would be able to manually add parameters of a line and plane equation, given in forms x=x1+ta1, y=y1+ta2, z=z1+ta3, where (a1,a2,a3) are the coordinates of a vector the line is parallel to and ax+bx+cz+d=0 for a plane, and I need both to return the equation of a projection and graphic representation (plotting the solution).

How could I modify the code in previous topic to correspond to what I am looking for?

Thank you in advance for your help.

Checking small Items on a plane?

Is there any lower limit to the size of a checked item on an airplane? I am traveling internationally and I would like to bring a few small bottles of sauce as a gift.

I have them packed in a box that is just large enough to hold three ketchup-sized bottles with plenty of bubble wrap. But looking at it, I am wondering if it will screw anything up to check a box that small.

I keep most of the clothes I need at my destination and everything else fits nicely in my carry-on. I am just having to check the sauce because of the liquid restrictions.

algorithm to compute the convex hull of a set of m possibly intersecting convex polygons in the plane

I am trying to find an algorithm to compute the convex hull of a set of m possibly intersecting convex polygons in the plane, with a total of n vertices. Let h denote the number of vertices on the boundary of the desired convex hull. The algorithm should run in O(mh+n) time

Curvature of plane curves

My text defines the curvature of a plane curve as $ <\ddot{x},N>$ where $ N$ is the normal to the normalized tangent of $ x$ and $ x$ is the curve. I thought the $ \ddot{x}$ also was perpendicular to $ x$ , making this projection kind of odd. Can someone see where I go wrong? Isnt projectuon of parallel lines a wierd thing?