Isometric tiles on wrong positions if the mouse points at a negative world coordinate

I am using this approach:

http://clintbellanger.net/articles/isometric_math/

Basically, you can calculate the iso coordinates based on the screen coordinates. What I am doing is, getting the actual world position the mouse is pointing at using get_mouse_global_position() and convert this position to isometric values.

Then I translate those coordinates back to world space coordinates to actually display the sprite.

Problem is, that when the world coordinates come from a negative position, the tiles get offset by almost an entire tile amount. Here is the relevant code.

The get_coord() function returns the actual world position of the tile used to display the Sprite

func get_coord(pos : Vector2):     var t = Vector2()     var e = screen_to_iso(pos)     t = iso_to_screen(e)     print(pos)     print(e)     print(t)     return t     pass var buildings  func screen_to_iso(pos :Vector2):     var flipx = 0     var flipy = 0     var t = Vector2()     var x_size = size/2     var y_size = size/4     t.x = int((pos.x/x_size) + (pos.y/y_size))/2     t.y = int((pos.y/y_size) - (pos.x/x_size))/2     return t     pass  func iso_to_screen(pos : Vector2):     var t = Vector2()     var x_size = size/2     var y_size = size/4     t = Vector2((pos.x-pos.y)*x_size, (pos.x+pos.y)*y_size)     return t     pass 

I can’t seem to figure out a way

Does this character concept involving never taking a long rest and converting spell slots to sorcery points (aka coffeelock) violate RAW?

Does the following, very cheesy character concept, violate any RAW? Please cite rules or official rulings in your answer. (Apart from RAW, I expect my DM to disallow or limit the concept, in the interest of balance. That is not part of my question.)

Elf. Multiclass: Sorcerer 2+ / Warlock 1+ / Bard 1

  • Never takes a long rest. Ever. See question, Must 5e elves take a long rest? Specifically, whether adventuring or not, she makes sure that every 8 hour block includes more than 2 hours of combat or strenuous activity, to ensure that no interpretation of long rest rules would allow a long rest to be automatically triggered.
  • Converts warlock spell slots into sorcery points. See @JeremyECrawford’s tweet.
  • Converts sorcery points into sorcery spell slots (or into spellcasting spell slots, once also multiclassing Bard) via Flexible Casting
  • Spell slots created from sorcery points disappear upon long rest, as per Flexible Casting and a tweet from @JeremyECrawford; therefore these created spell slots will not disappear until used, e.g. for a character taking no long rests
  • Spell slots created from sorcery points are in addition to, and not restoration of the sorcerer’s spell slots which refresh on a long rest. This is not 100% clear from RAW or clarifications. But:
    (a) Flexible Casting uses the phrase, “additional Spell Slots”;
    (b) the rule stating that created spell slots disappear on long rests is superfluous if created spell slots can only replace expended spell slots — to have meaning it must be possible to create spell slots which are not replacements;
    (c) flexible casting does not use the word “recover”, which is the word used for wizards’ Arcane Recovery
  • Restores warlock spell slots on a short rest, and repeats the cycle above, converting warlock spell slots to sorcery points to sorcerer (or spellcasting) spell slots
  • During periods of downtime, takes as many short rests per day as permissible, to build up a stockpile of created sorcerer spell slots
  • Stockpiling requires using bonus actions out of combat, discussed elsewhere
  • Stockpiling requires having short rests on downtime days, discussed in a comment below
  • While adventuring, during combat, uses created spell slots to cast spells, and/or uses flexible casting to convert those spell slots back into sorcery points
  • While adventuring, after combat, will use created spell slots with Bard spells to restore hits points, since restoring hit points via long rest is unavailable, and via hit dice is mostly unavailable

I’m pretty sure this is not RAI, but does it violate RAW in some way?

Can a Monk use multiple Ki points to get more unarmed strikes from Flurry of Blows in a single turn?

In a recent session of 5e, our monk (4th lvl, way of Drunken Master) was using unarmed strikes, and the DM claimed that she could use any number of available Ki points to increase the amount of unarmed strikes granted by Flurry of Blows by an equal amount(spend 1 point to make 2 strikes, spend 2 points to make 3 strikes, etc.). I argued that since the Furry of Blows text says you can make two unarmed strikes as a bonus action, only one Ki point could be spent on this specific feature per turn. By RAW, how many strikes can be made in a single turn using this particular feature?

Lagrange interpolation of 2000 equidistant points on $\frac{1}{1+x^2}$ crashes mathematica/does not evaluate

My Code:

Points := Table[-5 + 10 j/2048, {j, 1, 2047}] Data := Table[1/(1 + x^2), {x, Points}] Data2 := Transpose[{Points, Data}] p[x_] = InterpolatingPolynomial[Data2, x] 

I am not sure why this crashes Mathematica. It seems it cannot handle this. I have a HW assignment that requires for me to find the interpolating polynomial of $ \frac{1}{1+x^2}$ at the points $ -5+10j/2048$ for $ j$ between 1 and 2047. The code above is my best attempt at doing so. I could not figure out how to make a table of the form $ \{\{x_1,y_1\}…\}$ so I just combined the two sets by transposition. Mathematica handles The first three lines properly. However, when trying to evaluate

p[x_] = InterpolatingPolynomial[Data2, x]

after about 2-3 minutes crashes. I am not sure what the issue is. Is this impossible for mathematica? I tried the command parallelize but that di not help. The goal of the problem is to find the error of this interpolatoin, and compare it to the error of interpolation using chebyshev points (which I will try doing after I can do this)

Can players choose specific points in space, down to the inch, to cast a spell so as to avoid hitting a prone character?

Say there is a character that is prone, such as if they were unconscious, and they are surrounded on all 8 square grids (assuming that a grid is being used) by other creatures. Can a player cast a spell that has a sphere effect such as fireball or shatter such that only the 8 creatures surrounding the one that is prone be hit?

Would this potentially have any adverse effects with potentially breaking or having any unintended consequences for any other spells/effects down the line if this were allowed?

Obviously when it comes to casting some spells, the caster has the option to "choose a point in space", but when playing with the understanding of a grid system that works in chunks of a given dimension does is it feasible to have spells cast in such a way so that a body lying prone won’t be affected by a spell cast just overhead?

Can shadow sorcerer cast darkness using sorcerer points and metamagic at the same time?

I hope that the title is clear, but let me go a bit in detail.

Let’s say that I want to use the shadow sorcerer feature "eyes of the dark" to cast darkness using two sorcerer points. More, I would like to cast it as a bonus action, with quick spell metamagic option.

Is this possible? The final results is that the sorcerer cast darkness as bonus action, using 4 sorcerer points and no spell slot.

Thanks for any reply. (:

Can a Simulacrum of a sorcerer regain its sorcery points?

The description of Simulacrum states:

The simulacrum lacks the ability to learn or become more powerful, so it never increases its level or other abilities, nor can it regain expended spell slots.

If someone cast Simulacrum on a sorcerer, would the Simulacrum be able to regain its sorcery points by taking a long rest? (Can simulacra even take rests?) In particular, I ask because the sorcerer has the Font of Magic class feature at level 2 that allows them to convert their sorcery points into spell slots or vice versa.

(This question can also be extended to other limited-use class features like a fighter’s Action Surge, a druid’s Wild Shape, etc., but I don’t know if the answer would be different since sorcery points can specifically be used to create spell slots.)

Do you get skill points retroactively for increased Int?

In D&D 3.5 you don’t get skill points retroactively, only from the next level onwards after you increase your intelligence enough to gain an increased bonus, leading to extra skill points per level.

However when playing today a friend of mine mentioned that Pathfinder is different, and that skill points are applied retroactively when your intelligence bonus increases. But I can’t find anything in the rule book that mentions which it is either way.

Can someone please clarify for me which it is and point out where it is stated?

What is the points of knacks like animal-lore or dodge at level 1?

In the Warrior Adventure Game, animal lore (at level 1) gives +1 per intelligence chip on intelligence or ponder for animal-related checks.

First, ponder is an intelligence skill, so why is it mentioned separately? Second, what’s the point when I can get a +1 per chip anyway?

Likewise, dodge gives +1 per spirit chip on jump for dodge checks. Again, I can do the same without that knack.

Is there any value in having such knacks at level 1, or is it just a starting point for getting higher bonuses at later levels?