How to plot the surface defined by x^3+4y^2=10z; use (-3,3) as the range for x & y

Plot the surface defined by x^3+4y^2=10z; use (-3,3) as the range for x & y

Converting a 2d surface into a 3d volume

I have a 2d surface shown in the image below using ListPlot3D[]:

It is generated with one line of code:

``ListPlot3D[RandomVariate[UniformDistribution[], {10,10}]]     ``

Currently, it’s a ‘white noise’ surface, meaning the surface is more or less random between zero and one. I’d like to give this thickness (so I can ultimately 3d print it).

I’d like the remaining 5 sides to be flat, so that I’d end up with a "cube" with one surface jagged.

Is there an easy way to do this? Essentially just fill in everything below the surface?

Thanks!

Does Hold Person cast on a Spider Climbing NPC affect their ability stay on a vertical surface?

An NPC spell caster that is using spider climb at the top of a 30′ pillar where it meets the ceiling is magically held by hold person. I have two related questions:

1. When Hold Person goes into effect, does the NPC fall, or does the Spider Climb magic (which is still in effect) keep his hands and feet bound to the pillar and leaving him suspended 30′ off the floor?

2. Assuming he does not fall immediately, if the party shoots him with an arrow or other ranged attack, since Dex checks auto-fail when Paralyzed, would that knock him off (and thus fall for 3d6 damage).

Does the spell erupting earth disrupt the surface it’s cast on?

The spell Erupting Earth says:

A fountain of churned earth and stone erupts in a 20-foot cube centered on that point.

Does this mean about 20 cubic feet of material from the ground is churned up and disrupted? Or is the fountain comprised of newly created or summoned material?

RAW the spell only deals damage to creatures and makes the terrain difficult. My player is wanting to use the spell to damage stone and dislodge a deposit of ore, arguing the ‘erupting‘ wording means it should deal damage to the terrain as well.

If it churns up material from the ground I can see this working, however, if the material is created by the spell, then that would explain why it doesn’t explicitly damage objects/terrain.

What is the correct or intended interpretation?

Can Mordenkainen’s Faithful Hound be made mobile by casting it on a mobile surface?

The description of the Mordenkainen’s faithful hound spell says, in part:

You conjure a phantom watchdog in an unoccupied space that you can see within range, where it remains for the duration, until you dismiss it as an action, or until you move more than 100 feet away from it.

If I were to cast Mordenkainen’s faithful hound to conjure the hound on a wagon, or on Tenser’s floating disk, would the hound then be able to follow me around and remain active for it’s 8 hour duration?

calculate the flux of a vector field through a surface

How to calculate the flux of a vector field through a surface in mathematica? I’ve this field:

``F = (x, x^2 * y, y^2 * z)  ``

and this surface:

``S = { (x,y,z) ∈ R^3 | 2 * Sqrt[x^2+y^2] <= z <= 1 + x^2 + y^2} ``

So, I’m trying:

``region = ImplicitRegion[2 * Sqrt[x^2+y^2] <= z <= 1 + x^2 + y^2, {x, y, z}];  Integrate[#, {x,y,z} ∈ region]& /@ ({x, x^2 * y, y^2 * z} . {x, y, z}) ``

I expect Pi/30 as a result, but it comes out "Infinity"…

Does hashing client-side increase attack surface (assuming TLS and serverside salt+hash)? [duplicate]

This question asks whether one should hash on the client or the server. I want to know if there is any reason, aside from having to maybe handle one extra hashing library (if it’s not already in your security stack), why you wouldn’t want to hash both on the client and on the server. Extra code complexity is fine, you are just invoking one extra pure-functional method.

Workflow: User submits username/password. Assert the usual password strength check. Submit HTTPS `username=username` and `password2=cryptohash(password)`. Backend generates `salt := make_nonce()` and stores `username=username, salt=salt, key=cryptohash(password2 + salt)`.

I ask because I still see lots of websites which set a maximum number of characters to some obnoxiously small number, like 16, 14, 10, or even 8 (I’m fine if you want to cap at 64). Also many limit the types of characters you can input. Ostensibly, this is to protect against buffer overflows, escapes, injection attacks, etc, as well as avoid under-defined internationalization behavior. But why not just take that field and run `SomeHash.ComputeHash(Encoding.Unicode.GetBytes(value))`, ideally a key-derivation function? That’ll take any trash you could put into that field and yield nice random bytes.

This question and this question are kinda similar, but mostly addresses whether you’d want to do only client-side hashing from a security point of view. I’m assuming the security would be at-least-as-good-as regular password form submission.

Can ‘mold earth’ create climbable steps in a stone surface?

The cantrip Mold earth allows

"shapes, colors, or both to appear on the dirt or stone, spelling out words, creating images, or shaping patterns"

Could those shapes be a series of ledges and/or indentations to make a ladder for climbing out of a pit or up a stone wall? The degree to which those letters/patterns have depth isn’t specified.

The steps would disappear after 1 hr., and only two ‘areas’ of such steps could exist, but within those limits ascent could be via a series of castings of this spell:

1. Cast and climb as high as possible on that first section.
2. Cast again above the first area and climb as high a possible on it.
3. Repeat.

Presumably, one would ascend at at rate of 5′ per round this way: the excavation use of mold earth specifies a 5′ cube. There is no specification of the area that can be affected by a shaping use of this spell, but 5′ x 5′ seems reasonable and consistent with that 5′ cube.

The higher level spell stone shape allows more sophisticated, and durable manipulation of stone: as a weapon or coffer, and possibly with 2 hinges and a latch. Would using mold earth to create steps steal the thunder from stone shape? I would argue that the 1 hr. duration and limits on 2 ‘areas’ (however big those might be), and the implied limit that mold earth can only work–literally–superficially (as the "shaping patterns" suggests), could be sufficient to keep this use of the cantrip from being overpowered.

However, another objection might be that the spell as written specifies creating shapes, patterns, colors, and letters suggests manipulations of the stone that are visually detectable–I could see those at more in line with creating a sign is viewable, or readable like braille, but not climbable. That is a harder argument to rebut.

Stone Shape, body surface area, and imprisonment [closed]

While examining various uses for stone shape and trying to double check the math on them all (such as cages, jamming doors, making poles, etc) it occurred to me that a use potentially far better than ‘encasing them in a box of rock’ would be instead to do a skin tight encasing of the individual (making it, practically speaking, impossible to move). Granted, for high (18-20) strength characters and creatures I suspect it’d be a full round action to simply break out of it, but I’m curious how the math exactly checks out, and what the exact numbers are. Surface area of a person (or a ‘medium’ creature) would need to be determined, and for small or large creatures there’d be other determinations one would have to make.

Still, it seems to me that it would be using significantly less stone than encasing someone in a box or cage.

It wouldn’t be my go to use, but I can imagine that against say some sort of goblin spell caster, or an evil elf wizard it could have some practical use.

Batching multiple nearest surface queries: Is it faster? Are there better algorithms?

I’m working on an algorithm that computes lots of "nearest point on a triangulated surface" queries in 3d as a way to resample data sets, and I’m wondering if there is any information out there on speeding up these queries. My gut tells me that partitioning the set of query points in a voxel grid or something, and doing them in batches could be a speedup, but I can’t quite see how I could efficiently use that. Also I’m not sure if the time cost of partitioning would balance the search speedup. Is running N independent queries really the best way?

I found that there are papers and research for the all-knn algorithm, but that’s for searching within a single set. And then, those speedups take advantage of the previously computed neighbors or structure within the single set, so I can’t use them. It feels close though.

Any help is appreciated.